FIN545/FIN534 Class Web Page, Summer '21

Jacksonville University

Instructor: Maggie Foley

The Syllabus

Term Project


Weekly SCHEDULE, LINKS, FILES and Questions



Coverage, HW, Supplements

-        Required




Live session URL:




6/26 on zoom: Join Zoom Meeting

Weekly Q&A Saturday 7-8 pm URL:




Morning 8:30 12:00 - DCOB #159 or take it online

-          chapters 2, 3: class video url (

-          set up game and start trading stocks like a pro.

-          Term project assignment. Term project due by 6/26/2021

-          Case Study of chapters 2 and 3, due by 6/5/2021

(help video: posted

-          First Discussion Board Assignments due by 6/5/2021, posted on blackboard under discussion





Morning 8:30-12:00 - DCOB #159 or take it online


-          chapters 1, 4, 5: class video url


-          Homework of chapter 4 (see attached, and solution attached FYI, updated), due by 7/11/2021

-          Case Study of Chapter 5, due by 7/11/2021

(help video part i: --- Posted

(help video part ii: --- Posted



Afternoon 1:15 4:30 - DCOB #159 or take it online (updated)


-          chapters 6: class video url


-          Case study assignment of chapter 6, due by 7/11/2021

(help video: --- Posted


-          Second Discussion Board Assignment, due by 7/11/2021, posted on blackboard under discussion



Mid Term Exam (from 6/11 6/20 on blackboard, short answer questions and multiple choice question, T/F)

midterm review





Morning 8:30-12:00 - DCOB #159 or take it online (updated)


-          Chapters 7: class video url (

-          Chapters 9: class video url (



-          Case study assignment of chapter 7, due by 7/11/2021

(help video: Posted

-          Case study assignment of chapter 9, due by 6/30/2021

(help video: - Posted





Afternoon1:15 4:30 - DCOB #159 or take it online (updated)


-          Chapters 10: class video url (

-          Chapters 11: class video url (



-          Case study assignment of chapter 10, due by 7/11/2021

(help video: Posted

-          Case study assignment of chapter 11, due by 6/30/2021

chapter 11 (help video:

-          Homework of Chapter 14, (see attached, and solution attached FYI), due by 6/30/2021

-          Third Discussion Board Assignment, due by 7/11/2021, posted on blackboard under discussion




Final Exam (take home exam, non-cumulative, chapters 7, 9, 10, 11, from 6/27 7/4) (study guide )

Notes about live sessions:

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

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

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


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:  (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



Topics in Chapter 2:

        Introduction of Financial Statement

        Firms 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


Income Statement Template


Cash flow template



************ 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 companys 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.


FCF calculator


In class exercise

1. Firm AAA has EBIT (operating income) of $3 million, depreciation of $1 million. Firm AAAs 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)




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)




Income Statement




Total cost of goods sold


Gross profit (EBITDA)




Operating expenses


Operating income (EBIT)


Interest expenses


Taxable income (EBT)


Taxes on income


Net income




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)



Cash Flow Statement Template

Cash at the beginning of the year


Cash from operation

net income


plus depreciation


-/+ AR


-/+ Inventory


+/- AP


net change in cash from operation


Cash from investment

-/+ (NFA+depreciation)


net change in cash from investment


Cash from financing

+/- long term debt


+/- common stock


- dividend


net change in cash from investment


Total net change of cash


Cash at the end of the year



Solution excel file




Chapter 3 Analysis of Financial Statements



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 for ratio analysis (


Financial ratio analysis  (VIDEO)


Ratio formulas



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



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 AAAs 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: -- posted



How much does Amazon worth? --- FYI only: Inc. (AMZN)



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




FCFFt or Terminal value (TVt)


Present value at 16.17%






(4,286)  (1 + 0.00%)



  (1 + 0.00%)



  (1 + 0.00%)



  (1 + 0.00%)



  (1 + 0.00%)


Terminal value (TV5)

  (1 + 0.00%) (16.17%  0.00%)

Intrinsic value of's capital

Less: Debt (fair value)


Intrinsic value of's common stock

Intrinsic value of's common stock (per share)


Current share price



Weighted Average Cost of Capital (WACC) Inc., cost of capital




Required rate of return2


Equity (fair value)




Debt (fair value)




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 Inc., PRAT model



Dec 31, 2017

Dec 31, 2016

Dec 31, 2015

Dec 31, 2014

Dec 31, 2013

Selected Financial Data (USD $ in millions)

Interest expense






Net income (loss)






Effective income tax rate (EITR)1






Interest expense, after tax2






Interest expense (after tax) and dividends












Current portion of long-term debt






Current portion of capital lease obligation






Current portion of finance lease obligations






Long-term debt, excluding current portion






Long-term capital lease obligations, excluding current portion






Long-term finance lease obligations, excluding current portion






Total stockholders' equity






Total capital







Retention rate (RR)4





Return on invested capital (ROIC)5











Growth rate of FCFF (g)6


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 Inc., H-model

















5 and thereafter



1 is implied by PRAT model
5 is implied by single-stage model
2g3 and g4 are calculated using linear interpoltion between g1 and g5


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



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.




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






Chapter 4 Time Value of Money (review)




        Future Value and Compounding

        Present Value and Discounting

        Rates of Return/Interest Rates

        Number of periods




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: --- TVM calculator --- net future value calculator




FV = PV *(1+r)^n

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

N = ln(FV/PV) / ln(1+r)

Rate = (FV/PV)1/n -1


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: Bryans 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



Topics in Chapter 5:

        Key features of bonds

        Bond valuation

        Measuring yield

        Assessing risk


Market data website:

1.   FINRA (FINRA bond market data)

2.      WSJ

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

3.      Bond Online


Simplified Balance Sheet of WalMart


In Millions of USD 

As of 2020-01-31

Total Assets


Total Current Liabilities


Long Term Debt


Total Liabilities


Total Equity


Total Liabilities & Shareholders' Equity





FINRA Bond market information




Coupon Rate



Maturity Date






Next Call Date


Last Trade Price


Last Trade Yield


Last Trade Date


US Treasury Yield



Trade History

Credit and Rating Elements

Moody's Rating

Aa2 (5/9//2018)

Standard & Poor's Rating

AA (02/10/2000)


Investment Grade





Mortgage Insurer


Additional Description

Senior Unsecured Note

Classification Elements

Bond Type

US Corporate Debentures

Debt Type

Senior Unsecured Note

Industry Group


Industry Sub Group


Sub-Product Asset


Sub-Product Asset Type

Corporate Bond


Use of Proceeds

Security Code

Special Characteristics

Medium Term Note


Issue Elements

*dollar amount in thousands

Offering Date


Dated Date


First Coupon Date


Original Offering*


Amount Outstanding*



Issue Description

Project Name

Payment Frequency


Day Count



Book Entry


Depository Trust Company

Security Level


Collateral Pledge

Capital Purpose

Bond Elements

*dollar amount in thousands

Original Maturity Size*


Amount Outstanding Size*


Yield at Offering


Price at Offering


Coupon Type


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 firms 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: posted

part 2 (help video: 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.



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 moneyinstead of spending moneywith 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 dropall of which reinforces peoples 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.


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( settlementmaturityrateyldredemptionfrequency[basis] )


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

The syntax of the function is:

YIELD( settlementmaturityrateprredemptionfrequency[basis] )


Where the arguments are as follows:





The security's price per $100 face value.




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



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



The security's annual coupon rate.



The annual yield of the security.



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



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












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


Day Count Basis

0 (or omitted)

US (NASD) 30/360








European 30/360

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



Function Description

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

The syntax of the function is:


ACCRINT( issuefirst_interestsettlementrate[par]frequency[basis][calc_method] )


Where the arguments are as follows:



The issue date of the security.



The security's first interest date.



The security's settlement date.



The security's annual coupon rate.



The security's par value.

If omitted, [par] takes the default value of 1,000.



The number of coupon payments per year (must be equal to 1, 2 or 4).



An optional argument, that specifies the day count basis to be used in the calculation.



Chapter 6 Risk and Return



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


1.      Realized return

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

HPR calculator (


2.      Expected return of this stock and its standard deviation

Expected return and risk (standard deviation) calculator (



A portfolio of two stocks, like WMT and Amazon

Portfolio Calculator ( see equations below



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,
  • pi = the probability of state i,
  • R1i = the return on stock 1 in state i,
  • E[R1] = the expected return on stock 1,
  • R2i = 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.

  sp falls very slowly after about 40 stocks are included.  The lower limit for sp is about 20% = sM (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 securitys stand-alone risk that cannot be eliminated by diversification.

  Firm-specific, or diversifiable, risk is that part of a securitys 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 bills beta? S&P500 indexs beta? WMTs beta? Amazons 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:


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

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 portfolios return. (15.04%)


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 portfolios 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 portfolios 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 portfolios Beta first) (2.1)


         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 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:


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?  


                                Conditions                          Prob.                                     Return

                                Strong                                   30%                                            32.0%

                                Normal                                 40%                                            10.0%

                                Weak                                    30%                                          -16.0%

ANSWER: Use the calcualtor at:


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%



                                         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)







Chapter 7 Valuation of Stocks and Corporations




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 firms intrinsic value?

        Are future dividends predictable?

        Refer to the following table for WMTs dividend history

    Refer to the following table for Wal-mart (WMTs dividend history)





Record Dates

Payable Dates



March 20, 2020

April 6, 2020


Regular Cash

May 8, 2020

June 1, 2020


Regular Cash

Aug. 14, 2020

Sept. 8, 2020


Regular Cash

Dec. 11, 2020

Jan. 4, 2021


Regular Cash

Record Dates

Payable Dates



March 15, 2019

April 1, 2019


Regular Cash

May 10, 2019

June 3, 2019


Regular Cash

Aug. 9, 2019

Sept. 3, 2019


Regular Cash

Dec. 6, 2019

Jan. 2, 2020


Regular Cash


Record Dates

Payable Dates



March 9, 2018

April 2, 2018


Regular Cash