Each live session will start as scheduled. Students are encouraged to attend the class on campus in DCOB #159. If students cannot come, they could watch the video for what they miss.

Extra credit opportunity

Interested in earning extra credits? Please calculate the average returns, standard deviation, stock correlations, and betas for the three stocks in your term project. The CAPM part is not required. The excel template is available at https://www.jufinance.com/risk-return/.

Just turn it in before final.

And then I will add 20 points to your midterm exam grade (or final grade).

A help video is available at https://www.jufinance.com/video/fin534_excel_template_spring_2021.mp4

Term Project due by 7/11/2021

Term Project General Requirements --- due by 7/11/2021

· Word document of about 10 pages (including cover page and appendix), Times New Roman font size 12 for the main body

· Sample firms’ financial statements should be attached as an appendix to the report

· Tables or graphs for ratio analysis should be inserted in appropriate sections

· Instructions

1. Preparation: Read Chapters 2 and 3 and the corresponding PPTs for Chapters 2 and 3 and the corresponding sections in the textbook.

2. Pick the firms: Select a common theme (industry) for your project and choose three companies in that industry. Describe briefly the industry and company profiles, and analyze the firms’ competitive positions in that industry.

3. Collect data: Download the financial statements (balance sheet and income statement) of those companies for the last three years from the same source to ensure data consistency (e.g. Zacks Investment Research). Describe the data briefly in your report.

4. Perform ratio analysis: Calculate the various financial ratios discussed in Chapter 3, including liquidity ratios, asset management ratios, debt management ratios, profitability ratios, and market value ratios; also use the DuPont equation to calculate ROEs. Present the results in an organized way in your report. (All ratios in Table 3-1 on p. 119 should be included in your report; other ratios mentioned in the textbook are optional.)

5. Analyze the results: Conduct trend analysis (time-series) and comparative analysis (cross-section) for the various ratios to interpret the results and identify potential problems for sample firms. (Common size analysis and percentage change analysis are not required.)

6. Recommend changes: Propose possible changes to address the identified problems to achieve competitive advantages.

7. Term project sample study FYI only

Final Exam Study Guide – FYI - Help Video

Short answer questions 1-10 (total 70 points)

1. Calculate stock returns based on dividend growth model, assuming dividend will grow at the constant rate.

2. Given D0, dividend growth rate from year 1-3, and the constant dividend growth rate after year 3, required rate of return , calculate P0

3. Given D0, dividend growth rate from year 1-3, and the constant dividend growth rate after year 3, required rate of return , calculate P0

4. Calculate stock price based on dividend growth model, assuming dividend will grow at the constant rate. The required rate of return is not given. Need to calculate based on CAPM.

5. Given capital structure. Calculate before tax cost of debt, cost of equity, and WACC

6. Give cash flows of two projects, and calculate NPV, IRR, crossover rate, and make investment decisions for given cost of capital

7. Given cash flows, cost of capital = financing costs, reinvestment rate, calculate MIRR, discount payback, PI

8. Calculate initial investment outlay, given cost of equipment, initial requirement for capital, R&D costs, depreciation, and selling price of the equipment by the end of the project.

9. Calculate the equipment salvage value given original cost, how much has been depreciated, the selling price, and the tax rate.

10. Given sales, cost of goods sold, depreciation expenses, and tax rate. Calculate operation cash flows.

Conceptual Questions (total of 50 points)

1. What is WACC? What are the components of WACC? Which one is higher? Which is lower?

2. What is preferred stock?

3. What is NPV? What is IRR? What is the rule used to make decision on project acceptance.

4. Why is there a multi-irr problem?

5. What is capital structure? What is the optimal capital structure?

6. What calculating operating cash flows, which item should be included? Which should not?

7. Terminal year cash flow: What should be included and what should not?

8. Flotation costs comparison between selling equity and selling debt

9. What does dividend growth rate mean?

5/15 Morning

Marketwatch Stock Trading Game (Pass code: havefun)

Use the information and directions below to join the game.

1. URL for your game:
https://www.marketwatch.com/game/fin534-21summer (game will start on 5/15/2021)

2. Password for this private game: havefun.

3. Click on the 'Join Now' button to get started.

4. If you are an existing MarketWatch member, login. If you are a new user, follow the link for a Free account - it's easy!

5. Follow the instructions and start trading!

Chapter 2 Financial Statements

Ppt

Topics in Chapter 2:

· Introduction of Financial Statement

· Firm’s Intrinsic Value

· Balance Sheet

· Income Statement

· Cash Flow Statement

· Free Cash Flow

Using a Balance Sheet to Analyze a Company (VIDEO)

What is an Income Statement? (Video)

How Do You Read a Cash Flow Statement? | (VIDEO)

Balance Sheet Template

http://www.jufinance.com/10k/bs

Income Statement Template

http://www.jufinance.com/10k/is

Cash flow template

http://www.jufinance.com/10k/cf

************ What is Free Cash Flow **************

What is free cash flow (video)

What is free cash flow (FCF)? Why is it important?

• FCF is the amount of cash available from operations for distribution to all investors (including stockholders and debtholders) after making the necessary investments to support operations.

• A company’s value depends on the amount of FCF it can generate.

What are the five uses of FCF?

1. Pay interest on debt.

2. Pay back principal on debt.

3. Pay dividends.

4. Buy back stock.

5. Buy nonoperating assets (e.g., marketable securities, investments in other companies, etc.)

What are operating current assets?

• Operating current assets are the CA needed to support operations.

• Op CA include: cash, inventory, receivables.

• Op CA exclude: short-term investments, because these are not a part of operations.

What are operating current liabilities?

• Operating current liabilities are the CL resulting as a normal part of operations.

• Op CL include: accounts payable and accruals.

• Op CL exclude: notes payable, because this is a source of financing, not a part of operations.

Capital expenditure = increases in NFA + depreciation

Or, capital expenditure = increases in GFA

Note: All companies, foreign and domestic, are required to file registration statements, periodic reports, and other forms electronically through EDGAR. https://www.sec.gov/edgar/searchedgar/companysearch.html

FCF calculator

https://www.jufinance.com/fcf

In class exercise

1. Firm AAA has EBIT (operating income) of $3 million, depreciation of $1 million. Firm AAA’s expenditures on fixed assets = $1 million. Its net operating working capital = $0.6 million. Calculate for free cash flow. Imagine that the tax rate =40%.

a. $1.2

b. $1.3

c. $1.4

d. $1.5

FCF = EBIT(1 – T) + Deprec. – (Capex + NOWC)

answer:

EBIT $3

Tax rate 40%

Depreciation $1

Capex + NOWC $1.60

So, FCF = $1.2

2. The following information should be used for the following problems:

2014 2015

Sales $ 740 $ 785

COGS 430 460

Interest 33 35

Dividends 16 17

Depreciation 250 210

Cash 70 75

Accounts receivables 563 502

Current liabilities 390 405

Inventory 662 640

Long term debt 340 410

Net fixed assets 1,680 1,413

Common stock 700 235

Tax rate 35% 35%

• What is the net income for 2015? ($52)

Answer: https://www.jufinance.com/10k/is/

Income Statement

Amount

Sales

$785

Total cost of goods sold

$460

Gross profit (EBITDA)

$325

Depreciation

$210

Operating expenses

Operating income (EBIT)

$115

Interest expenses

$35

Taxable income (EBT)

$80

Taxes on income

$28

Net income

$52

• What is the cash flow from investment for 2015? ($57)

• What is the cash flow from operating for 2015? ($360)

• What is the cash flow from financing for 2015? ($-412)

Answer: https://www.jufinance.com/10k/cf/

Cash Flow Statement Template
Cash at the beginning of the year	70
*Cash from operation*
net income	52
plus depreciation	210
-/+ AR	61
-/+ Inventory	22
+/- AP	15
net change in cash from operation	360

*Cash from investment*
-/+ (NFA+depreciation)	57
net change in cash from investment	57

*Cash from financing*
+/- long term debt	70
+/- common stock	-465
- dividend	-17
net change in cash from investment	-412

Total net change of cash	5
Cash at the end of the year	75

Solution – excel file

Chapter 3 Analysis of Financial Statements

Ppt

Topics in Chapter 3:

1. Ratio analysis

2. DuPont equation

3. Benchmarking for ratio analysis

4. Limitations of ratio analysis

5. Qualitative factors

Ratio Analysis template

https://www.jufinance.com/ratio

Finviz.com/screener for ratio analysis (https://finviz.com/screener.ashx

Financial ratio analysis (VIDEO)

Ratio formulas

****** DuPont Identity *************

video

ROE = (net income / sales) * (sales / assets) * (assets / shareholders' equity)

This equation for ROE breaks it into three widely used and studied components:

ROE = (net profit margin) * (asset turnover) * (equity multiplie)

In class exercise

Firm AAA’s total asset = $720,000. This company has no debt, so its debt/equity ratio = 0%. Now the CEO wants to raise the debt/assets ratio to 40%. How much must the firm borrow to achieve this goal?

a. $273,600

b. $288,000

c. $302,400

d. $327,100

answer: Total assets $720,000

Target debt ratio 40%

Debt to achieve target ratio = Amount borrowed = Target % × Assets = $288,000

Week 1 case study – chapters 2 and 3 (due by 6/5/2021)

Help video url: https://www.jufinance.com/video/fin534_case1_2021_spring.mp4 -- posted

How much does Amazon worth?” --- FYI only: Amazon.com Inc. (AMZN) https://www.stock-analysis-on.net/NASDAQ/Company/Amazoncom-Inc/DCF/Present-Value-of-FCFF

Present Value of Free Cash Flow to the Firm (FCFF)

In discounted cash flow (DCF) valuation techniques the value of the stock is estimated based upon present value of some measure of cash flow. Free cash flow to the firm (FCFF) is generally described as cash flows after direct costs and before any payments to capital suppliers.

Intrinsic Stock Value (Valuation Summary)

Amazon.com Inc., free cash flow to the firm (FCFF) forecast

Year	Value	FCFF_t or Terminal value (TV_t)	Calculation	Present value at 16.17%
0¹	FCFF₀	(4,286)
1	FCFF₁	–	= (4,286) × (1 + 0.00%)	–
2	FCFF₂	–	= – × (1 + 0.00%)	–
3	FCFF₃	–	= – × (1 + 0.00%)	–
4	FCFF₄	–	= – × (1 + 0.00%)	–
5	FCFF₅	–	= – × (1 + 0.00%)	–
5	Terminal value (TV₅)	–	= – × (1 + 0.00%) ÷ (16.17% – 0.00%)	–
Intrinsic value of Amazon.com's capital				–
Less: Debt (fair value)				45,696
Intrinsic value of Amazon.com's common stock				–

Intrinsic value of Amazon.com's common stock (per share)				$–
Current share price				$1,642.81

Weighted Average Cost of Capital (WACC)

Amazon.com Inc., cost of capital

	Value¹	Weight	Required rate of return²	Calculation
Equity (fair value)	803,283	0.95	16.97%
Debt (fair value)	45,696	0.05	2.10%	= 2.99% × (1 – 29.84%)

¹ USD $ in millions

Equity (fair value) = No. shares of common stock outstanding × Current share price
= 488,968,628 × $1,642.81 = $803,282,551,764.68

Debt (fair value). See Details »

² Required rate of return on equity is estimated by using CAPM. See Details »

Required rate of return on debt. See Details »

Required rate of return on debt is after tax.

Estimated (average) effective income tax rate
= (20.20% + 36.61% + 60.59% + 0.00% + 31.80%) ÷ 5 = 29.84%

WACC = 16.17%

FCFF Growth Rate (g)

FCFF growth rate (g) implied by PRAT model

Amazon.com Inc., PRAT model

	Average	Dec 31, 2017	Dec 31, 2016	Dec 31, 2015	Dec 31, 2014	Dec 31, 2013
*Selected Financial Data (USD $ in millions)*
Interest expense		848	484	459	210	141
Net income (loss)		3,033	2,371	596	(241)	274

Effective income tax rate (EITR)¹		20.20%	36.61%	60.59%	0.00%	31.80%

Interest expense, after tax²		677	307	181	210	96
Interest expense (after tax) and dividends		677	307	181	210	96

EBIT(1 – EITR)³		3,710	2,678	777	(31)	370

Current portion of long-term debt		100	1,056	238	1,520	753
Current portion of capital lease obligation		5,839	3,997	3,027	2,013	955
Current portion of finance lease obligations		282	144	99	67	28
Long-term debt, excluding current portion		24,743	7,694	8,235	8,265	3,191
Long-term capital lease obligations, excluding current portion		8,438	5,080	4,212	3,026	1,435
Long-term finance lease obligations, excluding current portion		4,745	2,439	1,736	1,198	555
Total stockholders' equity		27,709	19,285	13,384	10,741	9,746
Total capital		71,856	39,695	30,931	26,830	16,663
*Ratios*
Retention rate (RR)⁴		0.82	0.89	0.77	–	0.74
Return on invested capital (ROIC)⁵		5.16%	6.75%	2.51%	-0.12%	2.22%
*Averages*
RR	0.80
ROIC	3.31%

Growth rate of FCFF (g)⁶	0.00%

¹ See Details »

2017 Calculations

² Interest expense, after tax = Interest expense × (1 – EITR)
= 848 × (1 – 20.20%) = 677

³ EBIT(1 – EITR) = Net income (loss) + Interest expense, after tax
= 3,033 + 677 = 3,710

⁴ RR = [EBIT(1 – EITR) – Interest expense (after tax) and dividends] ÷ EBIT(1 – EITR)
= [3,710 – 677] ÷ 3,710 = 0.82

⁵ ROIC = 100 × EBIT(1 – EITR) ÷ Total capital
= 100 × 3,710 ÷ 71,856 = 5.16%

⁶ g = RR × ROIC
= 0.80 × 3.31% = 0.00%

FCFF growth rate (g) forecast

Amazon.com Inc., H-model

Year	Value	g_t
1	g₁	0.00%
2	g₂	0.00%
3	g₃	0.00%
4	g₄	0.00%
5 and thereafter	g₅	0.00%

where:
g₁ is implied by PRAT model
g₅ is implied by single-stage model
g₂, g₃ and g₄ are calculated using linear interpoltion between g₁ and g₅

Calculations

g₂ = g₁ + (g₅ – g₁) × (2 – 1) ÷ (5 – 1)
= 0.00% + (0.00% – 0.00%) × (2 – 1) ÷ (5 – 1) = 0.00%

g₃ = g₁ + (g₅ – g₁) × (3 – 1) ÷ (5 – 1)
= 0.00% + (0.00% – 0.00%) × (3 – 1) ÷ (5 – 1) = 0.00%

g₄ = g₁ + (g₅ – g₁) × (4 – 1) ÷ (5 – 1)
= 0.00% + (0.00% – 0.00%) × (4 – 1) ÷ (5 – 1) = 0.00%

6/5 -1

Chapter 1 An Overview of Financial Management

Ppt

Chapter overview:

This chapter provides a basic idea of what financial management/managerial finance/corporate finance is all about, including an overview of the financial environment (financial markets, institutions, and securities/instruments) in which corporations operate.

Note:

Flow of funds describes the financial assets flowing from various sectors through financial intermediaries for the purpose of buying physical or financial assets.

*** Household, non-financial business, and our government

Financial institutions facilitate exchanges of funds and financial products.

*** Building blocks of a financial system. Passing and transforming funds and risks during transactions.

*** Buy and sell, receive and deliver, and create and underwrite financial products.

*** The transferring of funds and risk is thus created. Capital utilization for individual and for the whole economy is thus enhanced.

Negative interest rate

How do negative interest rates work? | CNBC Explains

ppt

Topics:

· Future Value and Compounding

· Present Value and Discounting

· Rates of Return/Interest Rates

· Number of periods

· Amortization

Amortization Table example:

Develop an amortization schedule in Excel for a five-year car loan of $30,000 with APR of 3% (use the home mortgage loan as an example)

Hint: In excel, find amortization template.

Calculator:

https://www.jufinance.com/tvm/ --- TVM calculator

https://www.jufinance.com/nfv/ --- net future value calculator

Equations:

FV = PV *(1+r)^n

PV = FV / ((1+r)^n)

N = ln(FV/PV) / ln(1+r)

Rate = (FV/PV)^1/n -1

Annuity:

N = ln(FV/C*r+1)/(ln(1+r))

N = ln(1/(1-(PV/C)*r)))/ (ln(1+r))

Excel Formulas

To get FV, use FV function.

=abs(fv(rate, nper, pmt, pv))

To get PV, use PV function

= abs(pv(rate, nper, pmt, fv))

To get r, use rate function

= rate(nper, pmt, pv, -fv)

To get number of years, use nper function

= nper(rate, pmt, pv, -fv)

To get annuity payment, use PMT function

= abs(pmt(rate, nper, pv, -fv))

In Class Exercise:

1. You want to retire early so you know you must start saving money. Thus, you have decided to save $4,500 a year, starting at age 25. You plan to retire as soon as you can accumulate $500,000. If you can earn an average of 11 percent on your savings, how old will you be when you retire? (49.74 years)

Answer: nper(11%, 4500, 0, -500000)+25

2. Fred was persuaded to open a credit card account and now owes $5,150 on this card. Fred is not charging any additional purchases because he wants to get this debt paid in full. The card has an APR of 15.1 percent. How much longer will it take Fred to pay off this balance if he makes monthly payments of $70 rather than $85? (93.04 months)

Answer: nper(15.1%/12, 70, -5150, 0) - nper(15.1%/12, 85, -5150, 0)

3. At the end of this month, Bryan will start saving $80 a month for retirement through his company's retirement plan. His employer will contribute an additional $.25 for every $1.00 that Bryan saves. If he is employed by this firm for 25 more years and earns an average of 11 percent on his retirement savings, how much will Bryan have in his retirement account 25 years from now? ($157,613.33)

Answer: Bryan’s monthly contribution: 80+80*0.25 = 100

Fv(11%/12, 25*12, 100, 0))

4. Sky Investments offers an annuity due with semi-annual payments for 10 years at 7 percent interest. The annuity costs $90,000 today. What is the amount of each annuity payment? ($6,118.35)

Answer: pmt(7%/2, 10*2, 90000, 0,1)

5. Mr. Jones just won a lottery prize that will pay him $5,000 a year for thirty years. If Mr. Jones can earn 5.5 percent on his money, what are his winnings worth to him today? ($72,668.73)

Answer: pv(5.5%, 30, 5000, 0)

Chapter 5 Bond, Bond Valuation and Interest Rates

Ppt

Topics in Chapter 5:

· Key features of bonds

· Bond valuation

· Measuring yield

· Assessing risk

Market data website:

1. FINRA

http://finra-markets.morningstar.com/BondCenter/Default.jsp (FINRA bond market data)

2. WSJ

Market watch on Wall Street Journal has daily yield curve and bond yield information.

http://www.marketwatch.com/tools/pftools/

https://www.youtube.com/watch?v=yph8TRldW6k

3. Bond Online

http://www.bondsonline.com/Todays_Market/

Simplified Balance Sheet of WalMart

In Millions of USD	As of 2020-01-31
Total Assets	236,495,000
Total Current Liabilities	16,203,000
Long Term Debt	64,192,000
Total Liabilities	154,943,000
Total Equity	81,552,000
Total Liabilities & Shareholders' Equity	236,495,000

https://www.wsj.com/market-data/quotes/WMT/financials/annual/balance-sheet

FINRA – Bond market information

http://finra-markets.morningstar.com/BondCenter/Default.jsp

WAL-MART STORES INC

http://finra-markets.morningstar.com/BondCenter/BondDetail.jsp?ticker=C104227&symbol=WMT.GP

Coupon Rate

7.550

Maturity Date

02/15/2030

Symbol

WMT.GP

CUSIP

931142BF9

Next Call Date

—

Callable

—

Last Trade Price

$146.28

Last Trade Yield

1.776%

Last Trade Date

06/04/2021

US Treasury Yield

—

Trade History

Credit and Rating Elements

Moody's® Rating	Aa2 (5/9//2018)
Standard & Poor's Rating	AA (02/10/2000)
TRACE Grade	Investment Grade
Default	—
Bankruptcy	N
Insurance	—
Mortgage Insurer	—
Pre-Refunded/Escrowed	—
Additional Description	Senior Unsecured Note

Classification Elements

Bond Type	US Corporate Debentures
Debt Type	Senior Unsecured Note
Industry Group	Industrial
Industry Sub Group	Retail
Sub-Product Asset	CORP
Sub-Product Asset Type	Corporate Bond
State	—
Use of Proceeds	—
Security Code	—

Special Characteristics

Medium Term Note

Issue Elements

*dollar amount in thousands
Offering Date	02/09/2000
Dated Date	02/15/2000
First Coupon Date	08/15/2000
Original Offering*	$1,000,000.00
Amount Outstanding*	$1,000,000.00
Series	—
Issue Description	—
Project Name	—
Payment Frequency	Semi-Annual
Day Count	30/360
Form	Book Entry
Depository/Registration	Depository Trust Company
Security Level	Senior
Collateral Pledge	—
Capital Purpose	—

Bond Elements

*dollar amount in thousands
Original Maturity Size*	1,000,000.00
Amount Outstanding Size*	1,000,000.00
Yield at Offering	7.56%
Price at Offering	$99.84
Coupon Type	Fixed
Escrow Type

· The attached Wal-mart Bond prospects says: “We are offering $500,000,000 of our 1.000% notes due 2017 (symbol WMT4117476), $1,000,000,000 of our 3.300% notes due 2024 (symbol WMT4117477) and $1,000,000,000 of our 4.300% notes due 2044 (symbol WMT4117478). Which of the two outstanding WMT bonds are more attractive one to you? Why? Wal-mart Bond prospects

Risk of Bonds

Class discussion: Is bond market risky?

Bond risk (video)

Bond risk – credit risk (video)

Bond risk – interest rate risk (video)

Bond risk – how to reduce your risk (video)

In Class Exercise:

1. AAA firm’s bonds’ market value is $1,120, with 15 years maturity and coupon of $85. What is YTM? (7.17%, rate(15, 85, -1120, 1000))

2. Sadik Inc.'s bonds currently sell for $1,180 and have a par value of $1,000. They pay a $105 annual coupon and have a 15-year maturity, but they can be called in 5 years at $1,100. What is their yield to call (YTC)? (7.74%, rate(5, 105, -1180, 1100))

3. Assume that you are considering the purchase of a 20-year, noncallable bond with an annual coupon rate of 9.5%. The bond has a face value of $1,000, and it makes semiannual interest payments. If you require an 8.4% nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond? ($1,105.69, abs(pv(8.4%/2, 20*2, 9.5%*1000/2, 1000)) )

4. McCue Inc.'s bonds currently sell for $1,250. They pay a $90 annual coupon, have a 25-year maturity, and a $1,000 par value, but they can be called in 5 years at $1,050. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. What is the difference between this bond's YTM and its YTC? (Subtract the YTC from the YTM; it is possible to get a negative answer.) (2.62%, YTM = rate(25, 90, -1250, 1000), YTC = rate(5, 90, -1250, 1050))

5. A 25-year, $1,000 par value bond has an 8.5% annual payment coupon. The bond currently sells for $925. If the yield to maturity remains at its current rate, what will the price be 5 years from now? ($930.11, rate(25, 85, -925, 1000), abs(pv( rate(25, 85, -925, 1000), 20, 85, 1000))

Assignments (due with the mid-term exam)

1. Chapter 5 case study

part 1 (help video: https://www.jufinance.com/video/fin534_case2_2021_spring_part_1.mp4) – posted

part 2 (help video: https://www.jufinance.com/video/fin534_case2_2021_spring_part_2.mp4) – posted

2. Develop an amortization schedule in Excel for a five-year car loan of $30,000 with APR of 3%

(hint: use amortization loan template in excel)

3. Chapter 4 End of Chapter Problems (not questions): 1, 2, 3, 4, 16, 17, 19, 27 (chapter 4 homework solution all inclusive fyi only)

Chapter 4 Homework assignments – Spring 2021

Page 186:

4-1: If you deposit $10,000 in a bank account that pays 10% interest annually. How much will be in your account after 5 years?

4-2: What is the present value of a security that will pay $5000 in 20 years if securities of equal risk pay 7% annually.

4-3: Your parents will retire in 18 years. They currently have $250,000 and they think they will need $1 million at retirement. What annual interest rate must they earn to reach their goal, assuming they do not save any additional funds?

4-4: If you deposit money today in an account that pays 6.5% annual interest, how long will it take to double your money?

4-16: Find the amount to which $500 will grow under each of the following conditions.

a. 12% compounded annually for 5 years.

b. 12% compounded semiannually for 5 years.

c. 12% compounded quarterly for 5 years.

d. 12% compounded monthly for 5 years.

4-17: Find the present value of $500 due in the future under each of the following conditions.

a. 12% nominal rate, semiannual compounding, discounted back 5 years

b. 12% nominal rate, quarterly compounding, discounted back 5 years

c. 12% nominal rate, monthly compounding, discounted back 5 years

4-19: Universal bank pays 7% interest, compounded annually, on time deposits. Regional bank pays 6% interest, compounded quarterly.

a. Based on effective interest rates, in which bank would you prefer to deposit your money?

b. Could your choice of banks be influenced by the fact that you might want o withdraw your funds during the year as opposed to at the end of the year? In answering this question, assume that funds must be left on deposit during an entire compounding period in order for you to receive any interest.

4-27: What is the present value of a perpetuity of $100 per year if the appropriate discount rate is 7%? If interest rates in general were to double and the appropriate discount rate rose to 14%, what would happen to the present value of the perpetuity?

Updated Feb 26, 2021

What Are Negative Interest Rates? (FYI)

Negative interest rates occur when borrowers are credited interest rather than paying interest to lenders. While this is a very unusual scenario, it is most likely to occur during a deep economic recession when monetary efforts and market forces have already pushed interest rates to their nominal zero bound.

Typically, a central bank will charge commercial banks on their reserves as a form of non-traditional expansionary monetary policy, rather than crediting them interest. This extraordinary monetary policy tool is used to strongly encourage lending, spending, and investment rather than hoarding cash, which will lose value to negative deposit rates. Note that individual depositors will not be charged negative interest rates on their bank accounts.

KEY TAKEAWAYS

• Negative interest rates occur when borrowers are credited interest rather than paying interest to lenders.

• With negative interest rates, central banks charge commercial banks on reserves in an effort to incentivize them to spend rather than hoard cash positions.

• With negative interest rates, commercial banks are charged interest to keep cash with a nation's central bank, rather than receiving interest. Theoretically, this dynamic should trickle down to consumers and businesses, but commercial banks have been reluctant to pass negative rates onto their customers.

Understanding a Negative Interest Rate

While real interest rates can be effectively negative if inflation exceeds the nominal interest rate, the nominal interest rate is, theoretically, bounded by zero. Negative interest rates are often the result of a desperate and critical effort to boost economic growth through financial means.

The zero-bound refers to the lowest level that interest rates can fall to; some forms of logic would dictate that zero would be that lowest level. However, there are instances where negative rates have been implemented during normal times. Switzerland is one such example; as of mid-2020, its target interest rate was -0.75%.1 Japan adopted a similar policy, with a mid-2020 target rate of -0.1%.2

Negative interest rates may occur during deflationary periods. During these times, people and businesses hold too much money—instead of spending money—with the expectation that a dollar will be worth more tomorrow than today (i.e., the opposite of inflation). This can result in a sharp decline in demand, and send prices even lower.

Often, a loose monetary policy is used to deal with this type of situation. However, when there are strong signs of deflation factoring into the equation, simply cutting the central bank's interest rate to zero may not be sufficient enough to stimulate growth in both credit and lending.

In a negative interest rate environment, an entire economic zone can be impacted because the nominal interest rate dips below zero. Banks and financial firms have to pay to store their funds at the central bank, rather than earn interest income.

Consequences of Negative Rates

A negative interest rate environment occurs when the nominal interest rate drops below zero percent for a specific economic zone. This effectively means that banks and other financial firms have to pay to keep their excess reserves stored at the central bank, rather than receiving positive interest income.

A negative interest rate policy (NIRP) is an unusual monetary policy tool. Nominal target interest rates are set with a negative value, which is below the theoretical lower bound of zero percent.

During deflationary periods, people and businesses tend to hoard money, instead of spending money and investing. The result is a collapse in aggregate demand, which leads to prices falling even further, a slowdown or halt in real production and output, and an increase in unemployment.

A loose or expansionary monetary policy is usually employed to deal with such economic stagnation. However, if deflationary forces are strong enough, simply cutting the central bank's interest rate to zero may not be sufficient to stimulate borrowing and lending.

Example of a Negative Interest Rate

In recent years, central banks in Europe, Scandinavia, and Japan have implemented a negative interest rate policy (NIRP) on excess bank reserves in the financial system. This unorthodox monetary policy tool is designed to spur economic growth through spending and investment; depositors would be incentivized to spend cash rather than store it at the bank and incur a guaranteed loss.

It's still not clear if this policy has been effective in achieving this goal in those countries, and in the way it was intended. It's also unclear whether or not negative rates have successfully spread beyond excess cash reserves in the banking system to other parts of the economy.

Frequently Asked Questions

How can interest rates turn negative?

Interest rates tell you how valuable money is today compared to the same amount of money in the future. Positive interest rates imply that there is a time value of money, where money today is worth more than money tomorrow. Forces like inflation, economic growth, and investment spending all contribute to this outlook. A negative interest rate, by contrast, implies that your money will be worth more in the future, not less.

What do negative interest rates mean for people?

Most instances of negative interest rates only apply to bank reserves held by central banks; however, we can ponder the consequences of more widespread negative rates. First, savers would have to pay interest instead of receiving it. By the same token, borrowers would be paid to do so instead of paying their lender. Therefore, it would incentivize many to borrow more and larger sums of money and to forgo saving in favor of consumption or investment. If they did save, they would save their cash in a safe or under the mattress, rather than pay interest to a bank for depositing it. Note that interest rates in the real world are set by the supply and demand for loans (despite central banks setting a target). As a result, the demand for money in-use would grow and quickly restore a positive interest rate.

Where do negative interest rates exist?

Some central banks have set a negative interest rate policy (NIRP) in order to stimulate economic growth in the financial sector, or else to protect the value of a local currency against exchange-rate increases due to large inflows of foreign investment. Countries including Japan, Switzerland, Sweden, and even the ECB (eurozone) have adopted NIRPs at various points over the past two decades.

Why would a central bank adopt a NIRP to stimulate the economy?

Monetary policymakers are often afraid of falling into a deflationary spiral. In harsh economic times, such as deep economic recessions or depressions, people and businesses tend to hold on to their cash while they wait for the economy to improve. This behavior, however, can weaken the economy further as a lack of spending causes further job losses, lowers profits, and prices to drop—all of which reinforces people’s fears, giving them even more incentive to hoard. As spending slows even more, prices drop again, creating another incentive for people to wait as prices fall further. And so on. When central banks have already lowered interest rates to zero, the NIRP is a way to incentivize corporate borrowing and investment and discourage hoarding of cash.

https://www.investopedia.com/terms/n/negative-interest-rate.asp

Bond Pricing Formula (FYI)

Bond Pricing Excel Formula

To calculate bond price in EXCEL (annual coupon bond):

Price=abs(pv(yield to maturity, years left to maturity, coupon rate*1000, 1000)

To calculate yield to maturity (annual coupon bond)::

Yield to maturity = rate(years left to maturity, coupon rate *1000, -price, 1000)

To calculate bond price (semi-annual coupon bond):

Price=abs(pv(yield to maturity/2, years left to maturity*2, coupon rate*1000/2, 1000)

To calculate yield to maturity (semi-annual coupon bond):

Yield to maturity = rate(years left to maturity*2, coupon rate *1000/2, -price, 1000)*2

Function Description

The Excel Price function calculates the price, per $100 face value of a security that pays periodic interest.

The syntax of the function is:

PRICE( settlement, maturity, rate, yld, redemption, frequency, [basis] )

The Excel YIELD function calculates the Yield of a security that pays periodic interest.

The syntax of the function is:

YIELD( settlement, maturity, rate, pr, redemption, frequency, [basis] )

Where the arguments are as follows:

The security's price per $100 face value.

settlement

The settlement date of the security (i.e. the date that the coupon is purchased).

maturity

The maturity date of the security (i.e. the date that the coupon expires).

Rate

The security's annual coupon rate.

Yld

The annual yield of the security.

redemption

The security's redemption value per $100 face value.

frequency

The number of coupon payments per year. This must be one of the following:

1	-	Annually
2	-	Semi-Annually
4	-	Quarterly

[basis]

An optional integer argument which specifies the financial day count basis that is used by the security. Possible values are:

Basis	Day Count Basis
0 (or omitted)	US (NASD) 30/360
1	actual/actual
2	actual/360
3	actual/365
4	European 30/360

The financial day count basis rules are explained in detail on the Wikipedia Day Count Convention page

https://www.excelfunctions.net/excel-price-function.html

https://www.excelfunctions.net/excel-yield-function.html

Function Description

The Excel Accrint function returns the accrued interest for a security that pays periodic interest.

The syntax of the function is:

ACCRINT( issue, first_interest, settlement, rate, [par], frequency, [basis], [calc_method] )

Where the arguments are as follows:

issue	-	The issue date of the security.
first_interest	-	The security's first interest date.
settlement	-	The security's settlement date.
rate	-	The security's annual coupon rate.
[par]	-	The security's par value. If omitted, [par] takes the default value of 1,000.
frequency	-	The number of coupon payments per year (must be equal to 1, 2 or 4).
[basis]	-	An optional argument, that specifies the day count basis to be used in the calculation.

Chapter 6 Risk and Return

ppt

Topics in Chapter 6:

· Basic return and risk concepts

· Stand-alone risk

· Risk in a Portfolio Context

· Risk and return: CAPM/SML

· Market equilibrium and market efficiency

Please use the following Excel file to learn how to estimate how risky those securities are.

WMT, Tesla, Apple, and S&P500 stock prices April 2016 ~ May 2021

(solution. Updated for S&P on 6/4/2021)

Summary of Excel functions:

Mean --- average function

Risk (standard deviation) --- stdev function

Correlation between two stocks --- correl function

Covariance between two stocks --- covar function

Beta (risk) --- slope function

A Single Stock, like WMT

Example:

1. Realized return

Holding period return (HPR) = (Selling price – Purchasing price + dividend)/ Purchasing price

HPR calculator (www.jufinance.com/hpr)

2. Expected return of this stock and its standard deviation

Expected return and risk (standard deviation) calculator (www.jufinance.com/return)

A portfolio of two stocks, like WMT and Amazon

Portfolio Calculator (www.jufinance.com/portfolio) – see equations below

Equation:

W1 and W2 are the percentage of each stock in the portfolio.

σ₁₂ = the correlation coefficient between the returns on stocks 1 and 2,
Cov₁₂ = the covariance between the returns on stocks 1 and 2,
σ₁ = the standard deviation on stock 1, and
σ₂ = the standard deviation on stock 2.

σ₁₂ = the covariance between the returns on stocks 1 and 2,
N = the number of states,
p_i = the probability of state i,
R_1i = the return on stock 1 in state i,
E[R₁] = the expected return on stock 1,
R_2i = the return on stock 2 in state i, and
E[R₂] = the expected return on stock 2.

A portfolio of three stocks, like WMT, Amazon, and APPLE

Three stocks is the sum of three pairs of two-stock-portfolio. So same as above but repeat it three times.

A diversified portfolio with 25 stocks and more

As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio.

s_p falls very slowly after about 40 stocks are included. The lower limit for s_p is about 20% = s_M (M: market portfolio).

By forming well-diversified portfolios, investors can eliminate about half the risk of owning a single stock.

Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification.

Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification.

CAPM model (CAPM calculator)

1. What is Beta? Where to find Beta?

2. Why can we use beta as measure for risk?

3. What is three month Treasurye bill’s beta? S&P500 index’s beta? WMT’s beta? Amazon’s beta? Why are they different?

4. Use CAPM to calculate the expected return of the above stocks

5. Find those stocks in SML

6. What is market efficiency? Do you agree with the hypothesis that market is efficient? Do you have any evidence to disapprove it? What Is the Efficient Market Hypothesis? (youtube)

Assignment of chapter 6: Chapter 6 Case study (due with mid term exam)

(help video: https://www.jufinance.com/video/fin534_case3_2021_spring.mp4)

No other problem solving assignments for chapter 6

How do you compute the Beta of a company

First, we need to have two samples of the same size: The returns for a company, and the returns of the market for the same period of time. Note: You need to provide the returns and NOT the actual stock values in order for the calculations to be correct.

Then, a linear regression is conducted and the estimated slope of the regression model using the returns of the company as the dependent variable and the returns of the market as the independent variable will be the beta we are looking for.

Alternative formulas to compute the beta https://mathcracker.com/beta-calculator

The actual definition of beta is :

This formula is less clear for many people because the covariance is a less understood measure and some people do not know how to compute it.

Ultimately, the calculation of the beta as a slope coefficient of the regression between company and market returns has a stronger intuitive appeal.

Beta Calculator Excel

Calculation beta in Excel is easy. You need to go to a provider of historical prices, such as Yahoo finance. Then you clean all you need to clean and leave only adjusted prices.

Your market data could be the S&P 500 or any other market proxy. Then, by subtracting and dividing by the base value, you will get the returns, for both your company and the market.

Then, you will run a regression with the company returns as the dependent variable, and the market returns as the independent variable.

Finally, you will examine your regression output, and select the estimated slope coefficient. That will be the beta you are looking for.

Beta calculator and the CAPM

Why is it useful to compute the beta of a firm? Because it gives a measure of how risky the firm's stock is with respect to the market, and it tells us how much should be our expected return based ion that level of risk, via de CAPM model.

RISK and Return General Template (standard deviation, correlation, beta)

In Class Exercise

1. An investor currently holds the following portfolio: He invested 30% of the fund in Apple with Beta equal 1.1. He also invested 40% in GE with Beta equal 1.6. The rest of his fund goes to Ford, with Beta equal 2.2. Use the above information to answer the following questions.

1) The beta for the portfolio is? (1.63)

2) The three month Treasury bill rate (this is risk free rate) is 2%. S&P500 index return is 10% (this is market return). Now calculate the portfolio’s return. (15.04%)

Answer:

1) Portfolio beta = 0.3*1.1 + 0.4*1.6 + (1-0.3-0.4)*2.2 = 1.63

2) Portfolio return = 2% + 1.63*(10%-2%) = 15.04%

2. Your current portfolio’s BETA is about 1.2. Your total investment is worth around $200,000. You uncle just gave you $100,000 to invest for him. With this $100,000 extra funds in hand, you plan to invest the whole $100,000 in additional stocks to increase your whole portfolio’s BETA to 1.5 (Your portfolio now worth $200,000 plus $100,000). What is the average BETA of the new stocks to achieve your goal? (hint: write down the equation of the portfolio’s Beta first) (2.1)

Answer:

· Weight of the original fund = 200000/(200000+100000) = 2/3

· Weight of new fund = 1-2/3 = 1/3

· So protfolio beta = 1.5 = (2/3)*1.2 + (1/3)* X è X=2.1

3. What is the coefficient of variation on the company's stock?

Probability Stock's

State of of State

the Economy Return

Boom 0.45 25%

Normal 0.50 15%

Recession 0.05 5%

ANSWER: Use the calcualtor at: https://www.jufinance.com/return/

Or,

Probability of Return Deviation Squared State Prob.

This state This state from Mean Deviation × Sq. Dev.

0.45 25.00% 6.00% 0.36% 0.1620%

0.50 15.00% -4.00% 0.16% 0.0800%

0.05 5.00% -14.00% 1.96% 0.0980%

Expected return = 19.00% 0.34% 0.3400% = Expected variance

σ = 5.83%

Coefficient of variation = σ/Expected return = 0.3069

4. What's the standard deviation?

Economic

Conditions Prob. Return

Strong 30% 32.0%

Normal 40% 10.0%

Weak 30% -16.0%

ANSWER: Use the calcualtor at: https://www.jufinance.com/return/

Or,

Economic Return Dev. from Squared Sqd. dev.

Conditions Prob. This state Mean Dev. × Prob

Strong 30% 32.0% 23.20% 5.38% 1.61%

Normal 40% 10.0% 1.20% 0.01% 0.01%

Weak 30% -16.0% -24.80% 6.15% 1.85%

100% 8.8% Variance 3.47%

σ = Sqrt of variance 18.62% 18.62% by Excel

5. returns are shown below. What's the standard deviation of the firm's returns? (Hint: This is a sample, not a complete population. USE the sample standard deviation formula)

Year Return

2008 21.00%

2007 -12.50%

2006 25.00%

ANSWER: IN EXCEL, STDEV SYNTAX.

Or,

Deviation Squared

Year Return from Mean Deviation

2008 21.00% 9.83% 0.97%

2007 -12.50% -23.67% 5.60%

2006 25.00% 13.83% 1.91%

Expected return 11.17% 8.48% Sum sqd deviations

4.24% Sum/(N − 1)

SQRT = σ = 20.59% 20.59% with Excel

Mid Term Exam (on blackboard, 6/11 – 6/20)

Review: https://www.jufinance.com/video/fin534_week4_2021_spring.mp4

Chapter 7 Valuation of Stocks and Corporations

ppt

Topics in Chapter 7:

· Features of common stock

· Valuing common stock

o Dividend growth model

o Market multiples

· Preferred stock

Part I: Dividends

For class discussion:

· What is dividend growth model? Why can we use dividend to estimate a firm’s intrinsic value?

· Are future dividends predictable?

· Refer to the following table for WMT’s dividend history

http://stock.walmart.com/investors/stock-information/dividend-history/default.aspx

· Refer to the following table for Wal-mart (WMT’s dividend history)

http://stock.walmart.com/investors/stock-information/dividend-history/default.aspx

Record Dates	Payable Dates	Amount	Type
March 20, 2020	April 6, 2020	$0.54	Regular Cash
May 8, 2020	June 1, 2020	$0.54	Regular Cash
Aug. 14, 2020	Sept. 8, 2020	$0.54	Regular Cash
Dec. 11, 2020	Jan. 4, 2021	$0.54	Regular Cash
Record Dates	Payable Dates	Amount	Type
March 15, 2019	April 1, 2019	$0.53	Regular Cash
May 10, 2019	June 3, 2019	$0.53	Regular Cash
Aug. 9, 2019	Sept. 3, 2019	$0.53	Regular Cash
Dec. 6, 2019	Jan. 2, 2020	$0.53	Regular Cash

Record Dates	Payable Dates	Amount	Type
March 9, 2018	April 2, 2018	$0.52	Regular Cash
May 11, 2018	June 4, 2018	$0.52	Regular Cash
Aug. 10, 2018	Sept. 4, 2018	$0.52	Regular Cash
Dec. 7, 2018	Jan. 2, 2019	$0.52	Regular Cash
Record Dates	Payable Dates	Amount	Type
March 10, 2017	April 3, 2017	$0.51	Regular Cash
May 12, 2017	June 5, 2017	$0.51	Regular Cash
Aug. 11, 2017	Sept. 5, 2017	$0.51	Regular Cash
Dec. 8, 2017	Jan. 2, 2018	$0.51	Regular Cash

Record Dates	Payable Dates	Amount	Type
March 11, 2016	April 4, 2016	$0.50	Regular Cash
May 13, 2016	June 6, 2016	$0.50	Regular Cash
Aug. 12, 2016	Sep. 6, 2016	$0.50	Regular Cash
Dec. 9, 2016	Jan. 3, 2017	$0.50	Regular Cash
Record Dates	Payable Dates	Amount	Type
March 13, 2015	April 6, 2015	$0.490	Regular Cash
May 8, 2015	June 1, 2015	$0.490	Regular Cash
Aug. 7, 2015	Sep. 8, 2015	$0.490	Regular Cash
Dec. 4, 2015	Jan. 4, 2016	$0.490	Regular Cash

Stock Splits

Wal-Mart Stores, Inc. was incorporated on Oct. 31, 1969. On Oct. 1, 1970, Walmart offered 300,000 shares of its common stock to the public at a price of $16.50 per share. Since that time, we have had 11 two-for-one (2:1) stock splits. On a purchase of 100 shares at $16.50 per share on our first offering, the number of shares has grown as follows:

2:1 Stock Splits	Shares	Cost per Share	Market Price on Split Date	Record Date	Distributed
On the Offering	100	$16.50
May 1971	200	$8.25	$47.00	5/19/71	6/11/71
March 1972	400	$4.125	$47.50	3/22/72	4/5/72
August 1975	800	$2.0625	$23.00	8/19/75	8/22/75
Nov. 1980	1,600	$1.03125	$50.00	11/25/80	12/16/80
June 1982	3,200	$0.515625	$49.875	6/21/82	7/9/82
June 1983	6,400	$0.257813	$81.625	6/20/83	7/8/83
Sept. 1985	12,800	$0.128906	$49.75	9/3/85	10/4/85
June 1987	25,600	$0.064453	$66.625	6/19/87	7/10/87
June 1990	51,200	$0.032227	$62.50	6/15/90	7/6/90
Feb. 1993	102,400	$0.016113	$63.625	2/2/93	2/25/93
March 1999	204,800	$0.008057	$89.75	3/19/99	4/19/99

Can you estimate the expected dividend in 2022? And in 2023? And on and on…

Can you write down the math equation now?

WMT stock price = ?

Can you calculate now? It is hard right because we assume dividend payment goes to infinity. How can we simplify the calculation?

We can assume that dividend grows at certain rate.

Discount rate is r (based on Beta and CAPM that we have learned in chapter 6)

From finance.yahoo.com

What does each item indicate?

From finviz.com https://finviz.com/quote.ashx?t=WMT

Part II: Constant Dividend Growth-Dividend growth model

Calculate stock prices

1) Given next dividends and price expected to be sold for

Po=

Po= +

Po= + +

Po= + ++

……

Refer to http://www.calculatinginvestor.com/2011/05/18/gordon-growth-model/

· Now let’s apply this Dividend growth model in problem solving.

Constant dividend growth model calculator (www.jufinance.com/stock)

Equations

· Po= D1/(r-g) or Po= Do*(1+g)/(r-g)

· r = D1/Po+g = Do*(1+g)/Po+g; So r = total return = dividend yield + capital gain yield

· g= r-D₁/Po = r- Do*(1+g)/Po

· Capital Gain yield = g = (P₁-Po)/Po; P₁: Stock price one year later (P₁=D₂/(r-g))

· Dividend Yield = r – g = D₁ / Po = Do*(1+g) / Po

· D₁=Do*(1+g); D₂= D₁*(1+g); D₃=D₂*(1+g)…

Exercise:

1. Consider the valuation of a common stock that paid $1.00 dividend at the end of the last year and is expected to pay a cash dividend in the future. Dividends are expected to grow at 10% and the investors required rate of return is 17%. How much is the price? How much is the dividend yield? Capital gain yield?

2. The current market price of stock is $90 and the stock pays dividend of $3 with a growth rate of 5%. What is the return of this stock? How much is the dividend yield? Capital gain yield?

Part III: Non-Constant Dividend Growth

Calculate stock prices

1) Given next dividends and price expected to be sold for

Po=

Po= +

Po= + +

Po= + ++

……

Non-constant dividend growth model calculator (https://www.jufinance.com/dcf/)

Equations

P_n = D_n+1/(r-g) = D_n*(1+g)/(r-g), since year n, dividends start to grow at a constant rate.

Where D_n+1= next dividend in year n+1;

Do = just paid dividend in year n;

r=stock return; g= dividend growth rate;

Pn= current market price in year n;

Po = npv(r, D₁, D₂, …, D_n+P_n)

Or,

Po = D₁/(1+r) + D₂/(1+r)² + … + (D_n+P_n)/(1+r)ⁿ

In class exercise for non-constant dividend growth model

1. You expect AAA Corporation to generate the following free cash flows over the next five years:

Year	1	2	3	4	5
FCF ($ millions)	75	84	96	111	120

Since year 6, you estimate that AAA's free cash flows will grow at 6% per year. WACC of AAA = 15%

· Calculate the enterprise value for DM Corporation.

· Assume that AAA has $500 million debt and 14 million shares outstanding, calculate its stock price.

Answer:

FCF grows at 6% ==> could use dividend constant growth model to get the value at year 5

Value in year five = FCF in year 6 /(WACC - g)

FCF in year 6 = FCF in year 5 *(1+g%), g=6%

FCF in year 6 = 120 *(1+6%)

value in year five = 120*(1+6%)/(15%-6%) = 1433.13

value in year 0 (current value) =1017.66 = npv(15%, 75, 84, 96, 111, 120+1433.13)

Note: Po = D1/(r-g) ==> Firm value = FCF1/(WACC-g) = FCFo *(1+g)/(WACC-g)

Assume that AAA has $500 million debt and 14 million shares outstanding, calculate its stock price.

equity value = 1017.66 - 500 = 517.66 millions

stock price = 517.66 / 14

2. AAA pays no dividend currently. However, you expect it pay an annual dividend of $0.56/share 2 years from now with a growth rate of 4% per year thereafter. Its equity cost = 12%, then its stock price=?

Answer:

Do=0

D1=0

D2=0.56

g=4% after year 2 è P2 = D3/(r-g), D3=D2*(1+4%) è P2 = 0.56*(1+4%)/(12%-4%) = 7.28

r=12%

Po=? Po = NPV(12%, D1, D2+P2), D2 = 0.56, P2=7.28. SO Po = NPV(12%, 0,0.56+7.28) = 6.25

(Note: for non-constant growth model, calculate price when dividends start to grow at the constant rate. Then use NPV function using dividends in previous years, last dividend plus price. Or use calculator at https://www.jufinance.com/dcf/ )

3. Required return =12%. Do = $1.00, and the dividend will grow by 30% per year for the next 4 years. After t = 4, the dividend is expected to grow at a constant rate of 6.34% per year forever. What is the stock price ($40)?

Answer:

Do=1

D1 = 1*(1+30%) = 1.3

D2= 1.3*(1+30%) = 1.69

D3 = 1.69*(1+30%) = 2.197

D4 = 2.197*(1+30%) = 2.8561

D5 = 2.8561*(1+6.34%), g=6.34%

P4 = D5/(r-g) = 2.8561*(1+6.34%) /(12% - 6.34%)

Po = NPV(12%, 1.3, 1.69, 2.197, 2.8661+2.8561*(1+6.34%)) /(12% - 6.34%)) = 40

Or use calculator at https://www.jufinance.com/dcf/

Assignment (due by 7/11):

Case Study - Chapter 7 Case study

(help video: https://www.jufinance.com/video/fin534_case_4_2021_spring.mp4) - posted

Chapter 9 The Cost of Capital

ppt

Topics in Chapter 9:

· Cost of capital components

o Debt

o Preferred stock

o Common equity

· WACC

· Factors that affect WACC

For class discussion:

What is WACC?

· WACC sets the lowest bar, or rate of return, a company needs to get over here.

Why is it important?

· It tells the minimum rate of return to target for the investment.

· If the rate of return of the investment < WACC, then the company is losing value

· If the rate of return of the investment > WACC, then it is creating value above its cost of capital.

How to apply WACC to figure out firm value?

What is DCF?

One option (if beta is given)

Another option (if dividend is given):

WACC Formula

WACC calculator (with preferred stock, annual coupon bond)

(www.jufinance.com/wacc)

WACC calculator (with preferred stock, semi-annual coupon bond)

(www.jufinance.com/wacc_1)

Discount rate to figure out the value of projects is called WACC (weighted average cost of capital)

WACC = weight of debt * cost of debt + weight of equity *( cost of equity)

Wd= total debt / Total capital = total borrowed / total capital

We= total equity/ Total capital

Cost of debt = rate(nper, coupon, -(price – flotation costs), 1000)*(1-tax rate)

Cost of Equity = D1/(Po – Flotation Cost) + g

D1: Next period dividend; Po: Current stock price; g: dividend growth rate

Note: flotation costs = flotation percentage * price

Or if beta is given, use CAPM model (refer to chapter 6)

Cost of equity = risk free rate + beta *(market return – risk free rate)

Cost of equity = risk free rate + beta * market risk premium

In Class Exercise

1. Firm AAA sold a noncallable bond now has 20 years to maturity. 9.25% annual coupon rate, paid semiannually, sells at a price = $1,075, par = $1,000. Tax rate = 40%, 0% flotation fee, calculate after tax cost of debt (5.08%)

Answer:

· before tax cost of debt = rate(20*2, 9.25%*1000/2, -(1075-0%*1075), 1000)*2

· after tax cost of debt = rate(20*2, 9.25%*1000/2, -(1075-0%*1075), 1000)*2*(1-40%) = 5.08%

2. Firm AAA’s equity condition is as follows. D₁ = $1.25; P₀ = $27.50; g = 5.00%; and Flotation = 6.00% of price. Calculate cost of equity (9.84%)

Answer:

· Cost of equity = 1.25/(27.5-6%*27.5)+5% = 9.84%

3. Firm AAA raised 10m from the capital market. In it, 3m is from the debt market and the rest from the equity market. Calculate WACC.

Answer:

WACC= (3/10)*5.08% + (7/10)*9.84%

Template is available at https://www.jufinance.com/wacc_1/

~~Assignment (due with final):~~

~~Case study 5 - Chapter 9 Case study~~ ~~(due with final)~~

~~(help video: https://www.jufinance.com/video/fin534_case_5_2021_spring.mp4) - posted~~

Details about how to derive the model mathematically (FYI)

The Gordon growth model is a simple discounted cash flow (DCF) model which can be used to value a stock, mutual fund, or even the entire stock market. The model is named after Myron Gordon who first published the model in 1959.

The Gordon model assumes that a financial security pays a periodic dividend (D) which grows at a constant rate (g). These growing dividend payments are assumed to continue forever. The future dividend payments are discounted at the required rate of return (r) to find the price (P) for the stock or fund.

Under these simple assumptions, the price of the security is given by this equation:

In this equation, I’ve used the “0” subscript on the price (P) and the “1” subscript on the dividend (D) to indicate that the price is calculated at time zero and the dividend is the expected dividend at the end of period one. However, the equation is commonly written with these subscripts omitted.

Obviously, the assumptions built into this model are overly simplistic for many real-world valuation problems. Many companies pay no dividends, and, for those that do, we may expect changing payout ratios or growth rates as the business matures.

Despite these limitations, I believe spending some time experimenting with the Gordon model can help develop intuition about the relationship between valuation and return.

Deriving the Gordon Growth Model Equation

The Gordon growth model calculates the present value of the security by summing an infinite series of discounted dividend payments which follows the pattern shown here:

Multiplying both sides of the previous equation by (1+g)/(1+r) gives:

We can then subtract the second equation from the first equation to get:

Rearranging and simplifying:

Finally, we can simplify further to get the Gordon growth model equation

dividend growth model:

Refer to http://www.calculatinginvestor.com/2011/05/18/gordon-growth-model/

· Now let’s apply this Dividend growth model in problem solving.

P/E Ratio Summary by industry (FYI) --- Thanks to Dr Damodaran

Data Used: Multiple data services

Date of Analysis: Data used is as of January 2021

Download as an excel file instead: http://www.stern.nyu.edu/~adamodar/pc/datasets/pedata.xls

For global datasets: http://www.stern.nyu.edu/~adamodar/New_Home_Page/data.html

*Industry Name*	*Number of firms*	Current PE	Expected growth - next 5 years	PEG Ratio
Advertising	61	20.95	83.44%	0.19
Aerospace/Defense	72	291.56	5.78%	3.55
Air Transport	17	8.14	-14.27%	NA
Apparel	51	22.38	13.60%	1.63
Auto & Truck	19	164.37	18.80%	8.87
Auto Parts	52	27.43	12.42%	2.92
Bank (Money Center)	7	8.46	5.27%	2.83
Banks (Regional)	598	13.5	5.74%	2.32
Beverage (Alcoholic)	23	45.64	17.53%	2.06
Beverage (Soft)	41	201.34	10.24%	2.93
Broadcasting	29	15.1	12.93%	0.96
Brokerage & Investment Banking	39	21.14	8.88%	1.81
Building Materials	42	28.19	15.28%	1.43
Business & Consumer Services	169	38.25	12.28%	3.28
Cable TV	13	68.46	29.41%	1.04
Chemical (Basic)	48	13.8	9.70%	1.79
Chemical (Diversified)	5	13.89	5.55%	2.35
Chemical (Specialty)	97	36.06	9.18%	3.4
Coal & Related Energy	29	2.85	-20.90%	NA
Computer Services	116	45.38	9.98%	1.86
Computers/Peripherals	52	40.61	12.30%	2.97
Construction Supplies	46	84.99	11.21%	2.27
Diversified	29	26.18	9.58%	1.86
Drugs (Biotechnology)	547	31	18.96%	1.14
Drugs (Pharmaceutical)	287	122.82	11.28%	2.09
Education	38	26.92	14.76%	1.75
Electrical Equipment	122	51.61	1.85%	15.93
Electronics (Consumer & Office)	22	57.06	20.95%	0.66
Electronics (General)	157	81.09	15.15%	2.72
Engineering/Construction	61	27.42	11.33%	2.38
Entertainment	118	908.12	17.03%	3.18
Environmental & Waste Services	86	538.13	11.58%	3.72
Farming/Agriculture	32	26.45	17.84%	1.38
Financial Svcs. (Non-bank & Insurance)	235	24.3	13.59%	1.08
Food Processing	101	268.11	13.87%	1.54
Food Wholesalers	18	320.61	11.97%	0.71
Furn/Home Furnishings	40	29.97	15.23%	1.25
Green & Renewable Energy	25	56	12.25%	5.25
Healthcare Products	265	330.73	16.92%	2.81
Healthcare Support Services	129	101.84	16.32%	1.03
Heathcare Information and Technology	139	189.47	21.56%	1.82
Homebuilding	30	19.46	16.91%	0.67
Hospitals/Healthcare Facilities	32	72.23	13.75%	1.33
Hotel/Gaming	66	51.99	-15.51%	NA
Household Products	140	592.23	9.46%	2.98
Information Services	77	102.24	11.15%	4.86
Insurance (General)	21	65.34	33.98%	0.63
Insurance (Life)	26	18.97	7.81%	1
Insurance (Prop/Cas.)	55	44.23	8.58%	1.55
Investments & Asset Management	348	480.92	10.73%	1.64
Machinery	125	59.51	12.27%	2.63
Metals & Mining	86	30.21	72.06%	0.51
Office Equipment & Services	22	16.09	8.16%	3.09
Oil/Gas (Integrated)	3	33.88	7.20%	7.29
Oil/Gas (Production and Exploration)	278	25.15	-25.81%	NA
Oil/Gas Distribution	57	10.84	6.69%	2.28
Oilfield Svcs/Equip.	135	40.3	7.98%	0.34
Packaging & Container	26	25.24	11.40%	2.37
Paper/Forest Products	15	20.06	7.00%	1.96
Power	55	21.48	7.02%	2.96
Precious Metals	93	19.65	12.85%	1.52
Publishing & Newspapers	29	48	9.21%	4.51
R.E.I.T.	238	49.79	2.10%	17.69
Real Estate (Development)	25	31.02	14.50%	1.1
Real Estate (General/Diversified)	11	40.16	-3.24%	NA
Real Estate (Operations & Services)	61	1199.26	21.97%	1.01
Recreation	69	39.3	22.98%	3.22
Reinsurance	2	9.56	30.10%	0.51
Restaurant/Dining	79	70.43	12.54%	3.93
Retail (Automotive)	30	30.46	13.29%	1.27
Retail (Building Supply)	15	152.69	18.72%	1.23
Retail (Distributors)	85	41.38	9.94%	2.59
Retail (General)	17	23.23	2.14%	10.77
Retail (Grocery and Food)	14	40.6	12.26%	0.78
Retail (Online)	75	133.68	20.17%	3.51
Retail (Special Lines)	85	30.51	9.91%	4.19
Rubber& Tires	3	39.19	7.45%	1.76
Semiconductor	70	1291.42	13.63%	2.3
Semiconductor Equip	40	108.68	24.68%	1.14
Shipbuilding & Marine	11	23.47	11.30%	2.19
Shoe	11	31.53	15.84%	4.45
Software (Entertainment)	101	100.59	19.72%	1.67
Software (Internet)	36	92.26	23.68%	1.36
Software (System & Application)	388	193.65	22.61%	1.73
Steel	32	76.29	1.93%	8.99
Telecom (Wireless)	16	29.65	10.30%	4.67
Telecom. Equipment	96	69.36	14.07%	1.57
Telecom. Services	58	158.41	6.90%	2.17
Tobacco	15	28.53	9.83%	2.48
Transportation	21	27.84	11.20%	2.77
Transportation (Railroads)	6	25.54	9.37%	2.87
Trucking	35	30.51	4.76%	5.53
Utility (General)	16	20.24	4.95%	3.21
Utility (Water)	17	54.77	8.56%	4.83
Total Market	7582	109.79	11.64%	2.35
Total Market (without financials)	6253	103.33	12.17%	2.5

Walmart Inc (NYSE:WMT) WACC %:3.36% As of Today (6/25/2021)

As of today, Walmart Inc's weighted average cost of capital is 3.36%. Walmart Inc's ROIC % is 8.81% (calculated using TTM income statement data). Walmart Inc generates higher returns on investment than it costs the company to raise the capital needed for that investment. It is earning excess returns. A firm that expects to continue generating positive excess returns on new investments in the future will see its value increase as growth increases.

https://www.gurufocus.com/term/wacc/WMT/WACC/Walmart%2BInc

Amazon.com Inc (NAS:AMZN) WACC %:8.06% As of Today (6/25/2021)

As of today, Amazon.com Inc's weighted average cost of capital is 8.06%. Amazon.com Inc's ROIC % is 13.47% (calculated using TTM income statement data). Amazon.com Inc generates higher returns on investment than it costs the company to raise the capital needed for that investment. It is earning excess returns. A firm that expects to continue generating positive excess returns on new investments in the future will see its value increase as growth increases.

https://www.gurufocus.com/term/wacc/AMZN/WACC-Percentage/Amazon.com%20Inc

Ticker	Company	Market Cap (M)	WACC %
AMZN	Amazon.com Inc	$1,555,758.24	8.07
HKSE:09988	Alibaba Group	$631,785.07	6.45
HKSE:03690	Meituan	$252,602.83	7.63
PDD	Pinduoduo Inc	$197,512.71	7.63
HKSE:09618	JD.com Inc	$137,594.60	6.32
CPNG	Coupang Inc	$83,132.87	0
MELI	MercadoLibre Inc	$77,305.56	10.45
CVNA	Carvana Co	$49,385.49	17.6
EBAY	eBay Inc	$37,968.87	7.71
CHWY	Chewy Inc	$35,322.56	7.64

Tesla (NAS:TSLA) WACC %:13.42% (6/25/2021)

As of today, Tesla’s weighted average cost of capital is 13.42%. Apple Inc's ROIC % is 5.67% (calculated using TTM income statement data).

https://www.gurufocus.com/term/wacc/TSLA/WACC/Tesla%2Binc

Competitive Comparison Data
Ticker	Company	Market Cap (M)	WACC %
TSLA	Tesla Inc	$665,879.17	14.35
TSE:7203	Toyota Motor Corp	$208,955.81	2.33
XTER:VOW3	Volkswagen AG	$128,507.15	2.73
XTER:DAI	Daimler AG	$90,436.93	2.62
GM	General Motors Co	$85,388.49	4.73
XTER:NSU	Audi AG	$84,294.28	5.62
LTS:0FG8	Audi AG	$82,752.31	5.62
HKSE:01211	BYD Co Ltd	$76,495.24	6.81
NIO	NIO Inc	$70,930.41	7.61
XTER:BMW	Bayerische Motoren Werke AG	$59,930.08	3.36

Apple Inc (NAS:AAPL) WACC %:8.89% As of Today (6/25/2021)

As of today, Apple Inc's weighted average cost of capital is 9.04%. Apple Inc's ROIC % is 29.77% (calculated using TTM income statement data). Apple Inc generates higher returns on investment than it costs the company to raise the capital needed for that investment. It is earning excess returns. A firm that expects to continue generating positive excess returns on new investments in the future will see its value increase as growth increases.

https://www.gurufocus.com/term/wacc/AAPL/WACC/Apple%2Binc

*Industry Name*	*Number of Firms*	*Cost of Equity*	*E/(D+E)*	*Cost of Debt*	*Tax Rate*	*D/(D+E)*	*Cost of Capital*
Advertising	40	8.27%	57.51%	6.91%	6.38%	42.49%	6.99%
Aerospace/Defense	87	7.91%	84.42%	3.91%	11.59%	15.58%	7.14%
Air Transport	17	7.54%	58.48%	3.91%	24.57%	41.52%	5.64%
Apparel	51	7.58%	74.52%	3.91%	10.35%	25.48%	6.40%
Auto & Truck	18	8.49%	40.31%	3.61%	8.15%	59.69%	5.06%
Auto Parts	62	7.68%	77.94%	3.91%	7.71%	22.06%	6.64%
Bank (Money Center)	11	5.65%	38.87%	3.61%	27.31%	61.13%	3.87%
Banks (Regional)	612	4.96%	63.02%	3.61%	25.57%	36.98%	4.14%
Beverage (Alcoholic)	28	9.15%	79.27%	3.91%	10.12%	20.73%	7.87%
Beverage (Soft)	35	5.99%	81.26%	3.91%	6.41%	18.74%	5.42%
Broadcasting	27	8.10%	47.13%	3.91%	17.18%	52.87%	5.39%
Brokerage & Investment Banking	42	8.70%	31.26%	3.91%	14.56%	68.74%	4.76%
Building Materials	39	8.04%	82.33%	3.91%	23.34%	17.67%	7.15%
Business & Consumer Services	169	8.35%	78.47%	3.91%	11.09%	21.53%	7.19%
Cable TV	14	7.09%	65.34%	3.61%	22.23%	34.66%	5.58%
Chemical (Basic)	38	8.49%	70.78%	3.91%	9.76%	29.22%	6.88%
Chemical (Diversified)	7	12.74%	78.63%	4.66%	11.66%	21.37%	10.78%
Chemical (Specialty)	99	8.07%	77.52%	3.91%	9.64%	22.48%	6.93%
Coal & Related Energy	30	8.75%	68.77%	8.16%	4.94%	31.23%	7.96%
Computer Services	111	8.00%	76.43%	3.91%	9.40%	23.57%	6.82%
Computers/Peripherals	58	7.54%	84.62%	3.91%	5.03%	15.38%	6.84%
Construction Supplies	49	8.10%	75.49%	3.91%	17.36%	24.51%	6.85%
Diversified	24	8.48%	75.48%	3.61%	12.09%	24.52%	7.07%
Drugs (Biotechnology)	459	9.72%	86.33%	8.16%	1.36%	13.67%	9.24%
Drugs (Pharmaceutical)	185	8.55%	87.24%	6.91%	2.11%	12.76%	8.13%
Education	34	8.27%	72.03%	3.91%	8.24%	27.97%	6.79%
Electrical Equipment	118	7.92%	86.32%	4.66%	5.06%	13.68%	7.32%
Electronics (Consumer & Office)	24	7.96%	93.51%	4.66%	5.98%	6.49%	7.67%
Electronics (General)	167	7.17%	86.98%	3.91%	8.34%	13.02%	6.63%
Engineering/Construction	49	8.86%	77.09%	3.91%	13.37%	22.91%	7.51%
Entertainment	90	8.26%	74.77%	3.91%	5.45%	25.23%	6.93%
Environmental & Waste Services	87	6.87%	74.15%	4.66%	4.45%	25.85%	6.01%
Farming/Agriculture	34	6.19%	64.29%	3.91%	7.69%	35.71%	5.04%
Financial Svcs. (Non-bank & Insurance)	264	5.49%	8.83%	3.61%	19.89%	91.17%	2.99%
Food Processing	87	5.84%	76.44%	3.91%	15.13%	23.56%	5.17%
Food Wholesalers	15	11.48%	72.75%	3.91%	11.91%	27.25%	9.16%
Furn/Home Furnishings	31	6.42%	78.21%	3.91%	12.56%	21.79%	5.67%
Green & Renewable Energy	22	8.51%	50.45%	3.91%	2.41%	49.55%	5.77%
Healthcare Products	251	7.19%	85.41%	4.66%	4.79%	14.59%	6.66%
Healthcare Support Services	115	6.97%	80.11%	3.91%	13.69%	19.89%	6.17%
Heathcare Information and Technology	112	7.38%	83.83%	3.91%	5.96%	16.17%	6.67%
Homebuilding	32	8.04%	71.61%	3.91%	23.86%	28.39%	6.60%
Hospitals/Healthcare Facilities	35	8.40%	36.16%	3.91%	10.57%	63.84%	4.93%
Hotel/Gaming	70	7.18%	71.48%	3.91%	14.01%	28.52%	5.98%
Household Products	131	7.47%	82.63%	3.91%	7.35%	17.37%	6.69%
Information Services	61	6.89%	86.42%	3.91%	15.90%	13.58%	6.36%
Insurance (General)	21	6.39%	72.20%	3.61%	14.71%	27.80%	5.38%
Insurance (Life)	25	7.53%	63.67%	3.61%	15.32%	36.33%	5.79%
Insurance (Prop/Cas.)	50	6.67%	79.10%	3.61%	18.50%	20.90%	5.85%
Investments & Asset Management	165	7.43%	70.38%	3.91%	8.30%	29.62%	6.11%
Machinery	126	8.25%	83.51%	3.91%	14.05%	16.49%	7.38%
Metals & Mining	102	8.01%	76.61%	6.91%	1.66%	23.39%	7.37%
Office Equipment & Services	24	9.39%	65.94%	3.91%	18.37%	34.06%	7.20%
Oil/Gas (Integrated)	5	9.38%	86.74%	3.11%	10.96%	13.26%	8.45%
Oil/Gas (Production and Exploration)	311	8.80%	70.47%	6.91%	2.18%	29.53%	7.76%
Oil/Gas Distribution	16	8.54%	51.70%	3.91%	4.84%	48.30%	5.85%
Oilfield Svcs/Equip.	130	8.64%	76.35%	4.66%	5.27%	23.65%	7.44%
Packaging & Container	25	6.16%	66.57%	3.61%	22.37%	33.43%	5.02%
Paper/Forest Products	21	8.50%	71.42%	3.91%	14.18%	28.58%	6.92%
Power	61	4.97%	56.70%	3.61%	20.31%	43.30%	4.01%
Precious Metals	111	7.30%	84.85%	8.16%	2.16%	15.15%	7.14%
Publishing & Newspapers	41	7.59%	69.21%	3.91%	11.92%	30.79%	6.17%
R.E.I.T.	244	5.76%	56.02%	3.61%	1.96%	43.98%	4.43%
Real Estate (Development)	20	6.22%	68.82%	3.91%	5.80%	31.18%	5.21%
Real Estate (General/Diversified)	10	6.20%	80.90%	3.91%	12.77%	19.10%	5.58%
Real Estate (Operations & Services)	60	7.60%	68.16%	3.91%	8.82%	31.84%	6.13%
Recreation	70	6.73%	77.17%	3.91%	10.16%	22.83%	5.87%
Reinsurance	3	5.06%	78.29%	3.11%	10.92%	21.71%	4.47%
Restaurant/Dining	81	6.73%	75.64%	3.91%	14.99%	24.36%	5.81%
Retail (Automotive)	25	7.55%	56.83%	3.91%	19.04%	43.17%	5.57%
Retail (Building Supply)	8	6.76%	84.85%	3.91%	15.36%	15.15%	6.19%
Retail (Distributors)	92	8.25%	68.69%	3.91%	14.20%	31.31%	6.59%
Retail (General)	18	7.74%	76.25%	3.91%	22.96%	23.75%	6.61%
Retail (Grocery and Food)	14	6.00%	54.44%	3.91%	21.04%	45.56%	4.62%
Retail (Online)	61	8.41%	89.76%	3.91%	7.57%	10.24%	7.86%
Retail (Special Lines)	106	8.05%	65.36%	3.91%	22.01%	34.64%	6.29%
Rubber& Tires	4	7.25%	56.18%	3.91%	7.91%	43.82%	5.38%
Semiconductor	72	8.37%	88.42%	3.91%	8.04%	11.58%	7.74%
Semiconductor Equip	45	7.40%	89.66%	3.91%	8.51%	10.34%	6.94%
Shipbuilding & Marine	9	9.22%	68.05%	8.16%	8.31%	31.95%	8.26%
Shoe	11	6.89%	91.20%	3.91%	16.75%	8.80%	6.54%
Software (Entertainment)	13	6.94%	93.94%	3.91%	2.21%	6.06%	6.70%
Software (Internet)	305	8.52%	96.79%	4.66%	2.50%	3.21%	8.36%
Software (System & Application)	255	7.93%	87.61%	3.91%	3.98%	12.39%	7.32%
Steel	37	11.64%	73.41%	4.66%	7.05%	26.59%	9.49%
Telecom (Wireless)	18	9.02%	45.46%	3.91%	7.95%	54.54%	5.72%
Telecom. Equipment	104	7.67%	82.83%	3.91%	8.12%	17.17%	6.86%
Telecom. Services	66	7.91%	55.70%	3.91%	8.05%	44.30%	5.72%
Tobacco	24	8.82%	85.37%	3.91%	5.25%	14.63%	7.97%
Transportation	18	7.23%	76.91%	3.91%	21.92%	23.09%	6.25%
Transportation (Railroads)	8	7.52%	81.52%	3.61%	23.82%	18.48%	6.64%
Trucking	30	8.50%	58.89%	3.91%	20.56%	41.11%	6.23%
Utility (General)	18	3.90%	59.79%	3.11%	30.89%	40.21%	3.28%
Utility (Water)	23	4.15%	72.39%	3.61%	15.09%	27.61%	3.76%
Total Market	7247	7.49%	62.89%	3.91%	10.04%	37.11%	5.81%
Total Market (no financials)	6057	7.84%	76.49%	3.91%	7.92%	23.51%	6.69%

http://people.stern.nyu.edu/adamodar/New_Home_Page/datafile/wacc.htm

https://www.forbes.com/sites/greatspeculations/2016/05/12/ranking-u-s-stocks-on-weighted-average-cost-of-capital/#3e12e7f541a6

· .

Discounted Cash Flow (DCF, FYI)

By JASON FERNANDO Reviewed by KHADIJA KHARTIT Updated Mar 13, 2021

https://www.investopedia.com/terms/d/dcf.asp (video)

What Is Discounted Cash Flow (DCF)?

Discounted cash flow (DCF) is a valuation method used to estimate the value of an investment based on its expected future cash flows. DCF analysis attempts to figure out the value of an investment today, based on projections of how much money it will generate in the future.

This applies to investment decisions of investors in companies or securities, such as acquiring a company, investing in a technology startup, or buying a stock, and for business owners and managers looking to make capital budgeting or operating expenditures decisions such as opening a new factory, purchasing or leasing new equipment.

KEY TAKEAWAYS

· Discounted cash flow (DCF) helps determine the value of an investment based on its future cash flows.

· The present value of expected future cash flows is arrived at by using a discount rate to calculate the discounted cash flow (DCF).

· If the discounted cash flow (DCF) is above the current cost of the investment, the opportunity could result in positive returns.

· Companies typically use the weighted average cost of capital for the discount rate, as it takes into consideration the rate of return expected by shareholders.

· The DCF has limitations, primarily that it relies on estimations on future cash flows, which could prove to be inaccurate.

How Discounted Cash Flow Works

The purpose of DCF analysis is to estimate the money an investor would receive from an investment, adjusted for the time value of money. The time value of money assumes that a dollar today is worth more than a dollar tomorrow because it can be invested. As such, a DCF analysis is appropriate in any situation where a person is paying money in the present with expectations of receiving more money in the future.

For example, assuming a 5% annual interest rate, $1.00 in a savings account will be worth $1.05 in a year. Similarly, if a $1 payment is delayed for a year, its present value is $.95 because it cannot be put in your savings account to earn interest.

DCF analysis finds the present value of expected future cash flows using a discount rate. Investors can use the concept of the present value of money to determine whether future cash flows of an investment or project are equal to or greater than the value of the initial investment. If the value calculated through DCF is higher than the current cost of the investment, the opportunity should be considered.

In order to conduct a DCF analysis, an investor must make estimates about future cash flows and the ending value of the investment, equipment, or other asset. The investor must also determine an appropriate discount rate for the DCF model, which will vary depending on the project or investment under consideration, such as the company or investor's risk profile and the conditions of the capital markets. If the investor cannot access the future cash flows, or the project is very complex, DCF will not have much value and alternative models should be employed.

Discounted Cash Flow Formula

The formula for DCF is:

Example of Discounted Cash Flow

When a company looks to analyze whether it should invest in a certain project or purchase new equipment, it usually uses its weighted average cost of capital (WACC) as the discount rate when evaluating the DCF. The WACC incorporates the average rate of return that shareholders in the firm are expecting for the given year.

You are looking to invest in a project, and your company's WACC is 5%, so you will use 5% as your discount rate. The initial investment is $11 million and the project will last for five years, with the following estimated cash flows per year:

Cash Flow

Year Cash Flow

1 $1 million

2 $1 million

3 $4 million

4 $4 million

5 $6 million

Therefore, the discounted cash flows for the project are:

Discounted Cash Flow

Year Cash Flow Discounted Cash Flow (nearest $)

1 $1 million $952,381

2 $1 million $907,029

3 $4 million $3,455,350

4 $4 million $3,290,810

5 $6 million $4,701,157

If we sum up all of the discounted cash flows, we get a value of $13,306,728. Subtracting the initial investment of $11 million, we get a net present value (NPV) of $2,306,728. Because this is a positive number, the cost of the investment today is worth it as the project will generate positive discounted cash flows above the initial cost. If the project had cost $14 million, the NPV would have been -$693,272, indicating that the cost of the investment would not be worth it.

Dividend discount models, such as the Gordon Growth Model (GGM), for valuing stocks are examples of using discounted cash flows.

Disadvantages of Discounted Cash Flow

The main limitation of DCF is that it requires making many assumptions. For one, an investor would have to correctly estimate the future cash flows from an investment or project. The future cash flows would rely on a variety of factors, such as market demand, the status of the economy, technology, competition, and unforeseen threats or opportunities.

Estimating future cash flows too high could result in choosing an investment that might not pay off in the future, hurting profits. Estimating cash flows too low, making an investment appear costly, could result in missed opportunities. Choosing a discount rate for the model is also an assumption and would have to be estimated correctly for the model to be worthwhile.

How do you calculate discounted cash flow (DCF)?

Calculating the DCF of an investment involves three basic steps. First, you forecast the expected cash flows from the investment. Second, you select a discount rate, typically based on the cost of financing the investment or the opportunity cost presented by alternative investments. The third and final step is to discount the forecasted cash flows back to the present day, using a financial calculator, a spreadsheet, or a manual calculation.

What is an example of a DCF calculation?

To illustrate, suppose you have a discount rate of 10% and an investment opportunity that would produce $100 per year for the following three years. Your goal is to calculate the value today—in other words, the “present value”—of this stream of cashflows. Since money in the future is worth less than money today, you reduce the present value of each of these cash flows by your 10% discount rate.

Specifically, the first year’s cash flow is worth $90.91 today, the second year’s cash flow is worth $82.64 today, and the third year’s cash flow is worth $75.13 today. Adding up these three cashflows, you conclude that the DCF of the investment is $248.68.

Chapter 10 The Basics of Capital Budgeting

ppt

Topics in Chapter 10:

· Overview and “vocabulary”

· Capital Budgeting Methods

o NPV

o IRR

o Payback

o MIRR

o Profitable index

o Discounted payback

Math equation:

MIRR = (FV_CI/PV_CO)^1/n-1

· Where MIRR is the modified internal rate of return, FV_CI is the sum of future values of all net cash flows at the end of the project, PV_CO is the initial investment, and n is the number of periods

Math equation:

Profitability Index = Present Value of Future Cash Flows ÷ Initial Investment in the Project.

Excel Syntax:

1. NPV Excel syntax

Syntax

NPV(rate,value1,value2, ...)

Rate is the rate of discount over the length of one period.

Value1, value2, ... are 1 to 29 arguments representing the payments and income.

· Value1, value2, ... must be equally spaced in time and occur at the end of each period. NPV uses the order of value1, value2, ... to interpret the order of cash flows. Be sure to enter your payment and income values in the correct sequence.

2. IRR Excel syntax

Syntax

IRR(values, guess)

Values is an array or a reference to cells that contain numbers for which you want to calculate the internal rate of return.

Guess is a number that you guess is close to the result of IRR.

3) MIRR Excel syntax

Syntax

MIRR (values, finance_rate, reinvest_rate)

· values - Array or reference to cells that contain cash flows.

· finance_rate - Required rate of return (discount rate) as percentage.

· reinvest_rate - Interest rate received on cash flows reinvested as percentage.

NPV, IRR, Payback Period, MIRR, Discounted payback calculator www.jufinance.com/capital

Template in Excel https://www.jufinance.com/npv_1/

In class exercise: (none)

Let’s use the case study as in class exercise

Assignment (due with final):

Chapter 10 Case study

(help video: https://www.jufinance.com/video/fin534_case_6_2021_spring.mp4) - Posted

Simple Rules’ for Running a Business (fyi)

www.wsj.com

From the 20-page cellphone contract to the five-pound employee handbook, even the simple things seem to be getting more complicated.

Companies have been complicating things for themselves, too—analyzing hundreds of factors when making decisions, or consulting reams of data to resolve every budget dilemma. But those requirements might be wasting time and muddling priorities.

So argues Donald Sull, a lecturer at the Sloan School of Management at the Massachusetts Institute of Technology who has also worked for McKinsey & Co. and Clayton, Dubilier & Rice LLC. In the book Simple Rules: How to Thrive in a Complex World, out this week from Houghton Mifflin Harcourt HMHC -1.36%, he and Kathleen Eisenhardt of Stanford University claim that straightforward guidelines lead to better results than complex formulas.

Mr. Sull recently spoke with At Work about what companies can do to simplify, and why five basic rules can beat a 50-item checklist. Edited excerpts:

WSJ: Where, in the business context, might “simple rules” help more than a complicated approach?

Donald Sull: Well, a common decision that people face in organizations is capital allocation. In many organizations, there will be thick procedure books or algorithms–one company I worked with had an algorithm that had almost 100 variables for every project. These are very cumbersome approaches to making decisions and can waste time. Basically, any decision about how to focus resources—either people or money or attention—can benefit from simple rules.

WSJ: Can you give an example of how that simplification works in a company?

Sull: There’s a German company called Weima GmBH that makes shredders. At one point, they were getting about 10,000 requests and could only fill about a thousand because of technical capabilities, so they had this massive problem of sorting out which of these proposals to pursue.

They had a very detailed checklist with 40 or 50 items. People had to gather data and if there were gray areas the proposal would go to management. But because the data was hard to obtain and there were so many different pieces, people didn’t always fill out the checklists completely. Then management had to discuss a lot of these proposals personally because there was incomplete data. So top management is spending a disproportionate amount of time discussing this low-level stuff.

Then Weima came up with guidelines that the frontline sales force and engineers could use to quickly decide whether a request fell in the “yes,” “no” or “maybe” category. They did it with five rules only, stuff like “Weima had to collect at least 70% of the price before the unit leaves the factory.”

After that, only the “maybes” were sent to management. This dramatically decreased the amount of time management spend evaluating these projects–that time was decreased by almost a factor of 10.

Or, take Frontier Dental Laboratories in Canada. They were working with a sales force of two covering the entire North American market. Limiting their sales guidelines to a few factors that made someone likely to be receptive to Frontier—stuff like “dentists who have their own practice” and “dentists with a website”—helped focus their efforts and increase sales 42% in a declining market.

WSJ: Weima used five factors—is that the optimal number? And how do you choose which rules to follow?

Sull: You should have four to six rules. Any more than that, you’ll spend too much time trying to follow everything perfectly. The entire reason simple rules help is because they force you to prioritize the goals that matter. They’re easy to remember, they don’t confuse or stress you, they save time.

They should be tailored to your specific goals, so you choose the rules based on what exactly you’re trying to achieve. And you should of course talk to others. Get information from different sources, and ask them for the top things that worked for them. But focus on whether what will work for you and your circumstances.

WSJ: Is there a business leader you can point to who has embraced the “simple rules” guideline?

Donald Sull: Let’s look at when Alex Behring took over America Latina Logistica SARUMO3.BR +1.59%, the Brazilian railway and logistics company. With a budget of $15 million, how do you choose among $200 million of investment requests, all of which are valid?

The textbook business-school answer to this is that you run the NPV (net present value) test on each project and rank-order them by NPV. Alex Behring knows this. He was at the top of the class at Harvard Business School.

But instead, he decided what the most important goals were. You can’t achieve everything at once. In their case, their priorities were removing bottlenecks on growing revenues and minimizing upfront expenditure. So when allocating money, they had a bias for projects that both addressed the bottleneck problem and, for example, used existing tracks and trains.

Similarly, the global-health arm of the Gates Foundation gets many, many funding requests. But since they know that their goal is to have the most impact worldwide, they focus on projects in developing countries because that’s where the money will stretch farther.

Chapter 11 Cash Flow Estimation and Risk Analysis

ppt

Topics in Chapter 11:

· Estimating cash flows

o Relevant cash flows

o Working capital treatment

o Tax Depreciation

This is the Discounted Cash Flow approach.

What is Discounted Cash Flow (DCF)? (video)

11-2: an expansion project

Detail:

Project L is the application of a radically new liquid nano-coating technology to a new type of solar water heater module, which will be manufactured under a 4-year license from a university. In this section, we show how these cash flows are estimated (we only show this for Project L here). It’s not clear how well the water heater will work, how strong demand for it will be, how long it will be before the product becomes obsolete, or whether the license can be renewed after the initial 4 years. Still, the water heater has the potential for being profitable, though it could also fail miserably. GPC is a relatively large company and this is one of many projects, so a failure would not bankrupt the firm but would hurt profits and the stock’s price.

Information given as blow:

· Units sold at year 1: 10,000; increase by 15% after year 1;

· Unit sales price at year 1: $1.50; increase by 4% after year 1;

· Variable cost per unit at year 1: $1.07; increase by 3% after year 1;

· Fixed cost at year 1: $2,120; increase by 3% after year 1;

· Net working capital requirement

· NWC_t = 15%(Sales_t+1)

· Tax rate = 40%.

· Project cost of capital (WACC) = 10%.

Analysis of an Expansion Project: Project L, Guyton Products Company (GPC)
Assumptions / Inputs: Base Case
Equipment Cost				$7,750
Salvage Value of Equipment at Year 4				$639
Opportunity Cost				0
Externalities (Cannibalization)				0
Units Sold, Year 1				10,000
Annual Change Units sold after Year 1				15%
Sales Price Per Unit, Year 1				$1.50
Annual Change Sales Price after Year 1				4%
Variable Cost per Unit (VC), Year 1				$1.07
Annual Change in VC after Year 1				3%
Nonvariable Cost (FC), Year 1				$2,120
Annual Change in FC after Year 1				3%
Project WACC				10%
Tax Rate				40%
Working Capital as % of Next Year's Sales				15%

Template (excel) solution

Questions for discussion:

How to calculate OCF (operating cash flow)?

OCF

= (Sales Revenue – COGS – SG&A – Depreciation)*(1-T) + Depreciation

= EBIT *(1-T) + Depreciation

= Net Operating Profit after Taxes + Depreciation

What is incremental cash flow?

What is sunk cost? Example? Included in the cash flow?

What is opportunity cost? Example? Included in the cash flow?

~~Assignment (due with final):~~

~~Chapter 11 Case study~~

Incremental Cash Flow

By ALICIA TUOVILA Reviewed by THOMAS BROCK Updated Sep 20, 2020

https://www.investopedia.com/terms/i/incrementalcashflow.asp (video)

What is Incremental Cash Flow?

Incremental cash flow is the additional operating cash flow that an organization receives from taking on a new project. A positive incremental cash flow means that the company's cash flow will increase with the acceptance of the project. A positive incremental cash flow is a good indication that an organization should invest in a project.

KEY TAKEAWAYS

Incremental cash flow is the potential increase or decrease in a company's cash flow related to the acceptance of a new project or investment in a new asset.

Positive incremental cash flow is a good sign that the investment is more profitable to the company than the expenses it will incur.

Incremental cash flow can be a good tool to assess whether to invest in a new project or asset, but it should not be the only resource for assessing the new venture.

Understanding Incremental Cash Flow

There are several components that must be identified when looking at incremental cash flows: the initial outlay, cash flows from taking on the project, terminal cost or value, and the scale and timing of the project. Incremental cash flow is the net cash flow from all cash inflows and outflows over a specific time and between two or more business choices.

For example, a business may project the net effects on the cash flow statement of investing in a new business line or expanding an existing business line. The project with the highest incremental cash flow may be chosen as the better investment option. Incremental cash flow projections are required for calculating a project's net present value (NPV), internal rate of return (IRR), and payback period. Projecting incremental cash flows may also be helpful in the decision of whether to invest in certain assets that will appear on the balance sheet.

Example of Incremental Cash Flow

As a simple example, assume that a business is looking to develop a new product line and has two alternatives, Line A and Line B. Over the next year, Line A is projected to have revenues of $200,000 and expenses of $50,000. Line B is expected to have revenues of $325,000 and expenses of $190,000. Line A would require an initial cash outlay of $35,000, and Line B would require an initial cash outlay of $25,000.

Even though Line B generates more revenue than Line A, its resulting incremental cash flow is $5,000 less than Line A's due to its larger expenses and initial investment. If only using incremental cash flows as the determinant for choosing a project, Line A is the better option.

Limitations of Incremental Cash Flow

The simple example above explains the idea, but in practice, incremental cash flows are extremely difficult to project. Besides the potential variables within a business that could affect incremental cash flows, many external variables are difficult or impossible to project. Market conditions, regulatory policies, and legal policies may impact incremental cash flow in unpredictable and unexpected ways. Another challenge is distinguishing between cash flows from the project and cash flows from other business operations. Without proper distinction, project selection can be made based on inaccurate or flawed data.

Discounted Cash Flow (DCF)

By JASON FERNANDO Reviewed by KHADIJA KHARTIT Updated Mar 13, 2021

https://www.investopedia.com/terms/d/dcf.asp (video)

What Is Discounted Cash Flow (DCF)?

KEY TAKEAWAYS

· Discounted cash flow (DCF) helps determine the value of an investment based on its future cash flows.

· The present value of expected future cash flows is arrived at by using a discount rate to calculate the discounted cash flow (DCF).

· If the discounted cash flow (DCF) is above the current cost of the investment, the opportunity could result in positive returns.

· Companies typically use the weighted average cost of capital for the discount rate, as it takes into consideration the rate of return expected by shareholders.

· The DCF has limitations, primarily that it relies on estimations on future cash flows, which could prove to be inaccurate.

How Discounted Cash Flow Works

Discounted Cash Flow Formula

The formula for DCF is:

Example of Discounted Cash Flow

Cash Flow

Year Cash Flow

1 $1 million

2 $1 million

3 $4 million

4 $4 million

5 $6 million

Therefore, the discounted cash flows for the project are:

Discounted Cash Flow

Year Cash Flow Discounted Cash Flow (nearest $)

1 $1 million $952,381

2 $1 million $907,029

3 $4 million $3,455,350

4 $4 million $3,290,810

5 $6 million $4,701,157

Dividend discount models, such as the Gordon Growth Model (GGM), for valuing stocks are examples of using discounted cash flows.

Disadvantages of Discounted Cash Flow

How do you calculate discounted cash flow (DCF)?

What is an example of a DCF calculation?

~~Chapter 14 Distribution to Shareholders~~ ~~(deleted)~~

~~ppt~~

~~Topics in Chapter 14:~~

· ~~Theories of investor preferences~~

· ~~Clientele effect~~

· ~~Signaling effect~~

· ~~Residual distribution model~~

· ~~Stock repurchases~~

· ~~Stock dividends and stock splits~~

Summary of Equations FYI

*** time value of money***

FV = PV *(1+r)^n

PV = FV / ((1+r)^n)

N = ln(FV/PV) / ln(1+r)

Rate = (FV/PV)^1/n -1

Annuity:

N = ln(FV/C*r+1)/(ln(1+r))

N = ln(1/(1-(PV/C)*r)))/ (ln(1+r))

EAR = (1+APR/m)^m-1

APR = (1+EAR)^(1/m)*m

Excel Formulas

To get FV, use FV function.

=abs(fv(rate, nper, pmt, pv))

To get PV, use PV function

= abs(pv(rate, nper, pmt, fv))

To get r, use rate function

= rate(nper, pmt, pv, -fv)

To get number of years, use nper function

= nper(rate, pmt, pv, -fv)

To get annuity payment, use PMT function

= pmt(rate, nper, pv, -fv)

To get Effective rate (EAR), use Effect function

= effect(nominal_rate, npery)

To get annual percentage rate (APR), use nominal function

= nominal(effective rate, npery)

*** bond pricing ***

Summary of bond pricing excel functions

To calculate bond price (annual coupon bond):

Price=abs(pv(yield to maturity, years left to maturity, coupon rate*1000, 1000)

To calculate yield to maturity (annual coupon bond)::

Yield to maturity = rate(years left to maturity, coupon rate *1000, -price, 1000)

To calculate bond price (semi-annual coupon bond):

Price=abs(pv(yield to maturity/2, years left to maturity*2, coupon rate*1000/2, 1000)

To calculate yield to maturity (semi-annual coupon bond):

Yield to maturity = rate(years left to maturity*2, coupon rate *1000/2, -price, 1000)*2

To calculate number of years left(annual coupon bond)

Number of years =nper(yield to maturity, coupon rate*1000, -price, 1000)

To calculate number of years left(semi-annual coupon bond)

Number of years =nper(yield to maturity/2, coupon rate*1000/2, -price, 1000)/2

To calculate coupon (annual coupon bond)

Coupon = pmt(yield to maturity, number of years left, -price, 1000)

Coupon rate = coupon / 1000

To calculate number of years left(semi-annual coupon bond)

Number of years = pmt(yield to maturity/2, number of years left*2, -price, 1000)

Coupon rate = coupon / 1000

(annual coupon bond)

(semi annual coupon bond)

NPV and IRR

Return, Risk

Dividend Growth Model

Po= D1/(r-g) or Po= Do*(1+g)/(r-g)

R = D1/Po+g = Do*(1+g)/Po+g

D1=Do*(1+g); D2= D1*(1+g)…

WACC

WACC = weight of debt * cost of debt + weight of equity *( cost of equity)

Wd= total debt / Total capital = total borrowed / total capital

We= total equity/ Total capital

Cost of debt = rate(nper, coupon, -(price – flotation costs), 1000)*(1-tax rate)

Cost of Equity = D1/(Po – Flotation Cost) + g

D1: Next period dividend; Po: Current stock price; g: dividend growth rate

Note: flotation costs = flotation percentage * price

Or if beta is given, use CAPM model (refer to chapter 6)

Cost of equity = risk free rate + beta *(market return – risk free rate)

Cost of equity = risk free rate + beta * market risk premium