FIN 509 Class Web Page, Fall 2 semester' 24

 

The Syllabus     Grade Calculator    Overall Grade Calculator  Risk Tolerance Test (FYI)

  

Weekly SCHEDULE, LINKS, FILES and Questions

Week

Coverage, HW, Supplements

-       Required

Equations and Assignments

 

·      Weekly Thursday class url on blackboard collaborate: On Blackboard under “Join Course Room”

Or from here  

https://us.bbcollab.com/guest/a070558d332041888dd5772fefccc290

 

 

·       Weekly Q&A Session on Blackboard URL (on Saturday from 7 – 8 PM): 

 https://us.bbcollab.com/guest/7ee6be25e06546949517ebf89ef980b5

 

 

 

 

 

Class Schedule:

 

 

 

Topic and Activities,

class video web links

Assignments and Key Due Dates

Week 1

10/8 at 6 pm #263 (or online)

Time value of money, chapter 5

Class video link

Discussion Board #1 on market watch game,   due by  Tuesday, week 5 (11/3)   

Week 2

10/15 at 6 pm #263 (or online)

 

Discounted Cash Flow Valuation, chapter 6

 

Class video link

 

 

Quiz 1, due by Monday (10/21)  11:59 pm,  

 

Homework of chapters 5, 6

due by  Thursady, week 5 (11/3)

Week 3

10/22 at 6 pm #263 (or online)

 

Interest Rates and Bond Valuation, chapter 7

 

Class video link

 

 

Quiz 2, due by  Monday (10/28)  11:59 pm

 

Homework of chapter 7

due by  Thursady, week 4 (10/29)

Week 4

10/29 at 6 pm #263 (or online)

 

Stock valuation, chapter 8

 

Class video link

 

 

 

Quiz 3, due by  Monday  11/4) 11:59 pm

 

Homework of chapter 8  due with final

 

Week 5

11/5 at 6 pm #263 (or online)

 

 

Capital Budgeting, WACC, chapters 9 &14

 

Class video link

 

Discussion Board # 2: Fed Monetary Policy,  due with final

 

 

 

Quiz 4 (only chapter 9), due by  Monday  (11/11) 11:59 pm.

 

 

Homework of chapter 9 due with Final

 

Week 6

11/12 at 6 pm #263 (or online)

 

Chapter 13, risk and return

 

Class video link

Discussion Board #3: The Impact of the Presidential Election on the Stock Market,  due with final

 

 

Quiz 5, due by  Monday  (11/18) 11:59 pm

 

Homework of chapter 13  due with Final

 

Week 7

 

Part I

11/19 Review and Final

Video

·       Final on   at 1 AM, on blackboard final folder, due by Sunday (11/24)11:59 pm

·      Final prep video (on youtube)

Week 7

 

Part II

Chapter 2, chapter 3, not required

 

Class video link

 

 

 

 

Week 0

Market Watch Game 

  Use the information and directions below to join the game.

1.      URL for your game: 
 https://www.marketwatch.com/game/fin509-24fall

 

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!

 

·       How To Win The MarketWatch Stock Market Game (youtube) based on https://www.finviz.com

 

 

·        A shorting strategy based on finviz.com (FYI)  

 https://www.jufinance.com/game/short_selling.html 

 

 

Pre-class assignment:

Set up marketwatch.com account and have fun

Week1,2

image002.jpg

 

 

 

 

Chapter 5 Time value of money – Part 1

 

 Chapter 5 In Class Exercise   (Solution Word File)

 

Chapter 5 ppt 

 

The time value of money - German Nande (youtube)

 

Concept of FV, PV, Rate, Nper

Calculation of FV, PV, Rate, Nper

Concept of interest rate, compounding rate, discount rate

 

image001.jpg

 

 

Present value – Future value – Demonstration Game

 

 

 

In class exercise (conceptual)

 

 

 

 

Chapter 6 Time Value of Money – Part 2

 

Chapter 6 PPT

 

Chapter 6 In Class Exercise               (Chapter 6 In Class Exercise Solution Word File)

 

Concept of PMT, NPV

Calculation of FV, PV, Rate, Nper, PMT, NPV, NFV

Concept of EAR, APR

Calculation of EAR, APR

 

 

First Discussion Board  Assignment (post your writing on blackboard under discussion folder):

 Market Watch Game

Let's start trading in the stock market! Please join a game and report back on your experience.

Directions

1.      URL for your game: 
https://www.marketwatch.com/game/fin509-24summer

2.      Password for this private game: havefun.

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

4.      Register for a new account with your email address or sign in if you already have an account.


Discussion Board Prompts

1.      Why did you choose the stock? How much money did you think you would make? Please explain.

2.      Did you make money or lose money off of your chosen stock? Which factors contributed to that? 

3.      What did you learn from this experience and how will it affect your choices in real life when choosing stocks?

Instructions

·        Responses should be 100 to 250 words in length and should answer all three prompts

·        Optional: reply to one of your peers with meaningful, thought-provoking responses

·        Due by 7/11/2024  at 11:59 p.m. ET

 

 

 

HOMEWORK of Chapters 5 and 6 (due by 11/3 ) 

 

1. The Thailand Co. is considering the purchase of some new equipment. The quote consists of a quarterly payment of $4,740 for 10 years at 6.5 percent interest. What is the purchase price of the equipment? ($138,617.88)

 

2. The condominium at the beach that you want to buy costs $249,500. You plan to make a cash down payment of 20 percent and finance the balance over 10 years at 6.75 percent. What will be the amount of your monthly mortgage payment? ($2,291.89)

3. Today, you are purchasing a 15-year, 8 percent annuity at a cost of $70,000. The annuity will pay annual payments. What is the amount of each payment? ($8,178.07)

 

4. Shannon wants to have $10,000 in an investment account three years from now. The account will pay 0.4 percent interest per month. If Shannon saves money every month, starting one month from now, how much will she have to save each month? ($258.81)

5. Trevor's Tires is offering a set of 4 premium tires on sale for $450. The credit terms are 24 months at $20 per month. What is the interest rate on this offer? (6.27%)

6. Top Quality Investments will pay you $2,000 a year for 25 years in exchange for $19,000 today. What interest rate are you earning on this annuity? (9.42%)

7. You have just won the lottery! You can receive $10,000 a year for 8 years or $57,000 as a lump sum payment today. What is the interest rate on the annuity? (8.22%)

8. Around Town Movers recently purchased a new truck costing $97,000. The firm financed this purchase at 8.25 percent interest with monthly payments of $2,379.45. How many years will it take the firm to pay off this debt? (4.0 years)


9.  Expansion, Inc. acquired an additional business unit for $310,000. The seller agreed to accept annual payments of $67,000 at an interest rate of 6.5 percent. How many years will it take Expansion, Inc. to pay for this purchase? (5.68 years)

10. 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)

11. You just received a credit offer in an email. The company is offering you $6,000 at 12.8 percent interest. The monthly payment is only $110. If you accept this offer, how long will it take you to pay off the loan? (82.17 months)

12. 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)

13. Bridget plans to save $150 a month, starting today, for ten years. Jordan plans to save $175 a month for ten years, starting one month from today. Both Bridget and Jordan expect to earn an average return of 8 percent on their savings. At the end of the ten years, Jordan will have approximately _____ more than Bridget. ($4,391)

(Hint: Bridget’s is an annuity due, so abs(fv(8%/12, 10*12, 150, 0, 1)) --- type =1; Jordan’s is an ordinary annuity, so abs(fv(8%/12, 10*12, 175, 0) --- type =0, or omitted. There is a mistake in the help video for this question. Sorry for the mistake.)

 

 

14. What is the future value of weekly payments of $25 for six years at 10 percent? ($10,673.90)


15. 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)

 

16. 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)


17. Mr. Jones just won a lottery prize that will pay him $5,000 a year for thirty years. He will receive the first payment today. If Mr. Jones can earn 5.5 percent on his money, what are his winnings worth to him today? ($76,665.51)

 

18. You want to save $75 a month for the next 15 years and hope to earn an average rate of return of 14 percent. How much more will you have at the end of the 15 years if you invest your money at the beginning of each month rather than the end of each month? ($530.06)

 

19. What is the effective annual rate of 10.5 percent compounded semi-annually? (10.78%) 

20. What is the effective annual rate of 9 percent compounded quarterly? (9.31%)

21. Fancy Interiors offers credit to customers at a rate of 1.65 percent per month. What is the effective annual rate of this credit offer? (21.70%)

 

22. What is the effective annual rate of 12.75 percent compounded daily? (13.60 percent)

 

23. Your grandparents loaned you money at 0.5 percent interest per month. The APR on this loan is _____ percent and the EAR is _____ percent. (6.00; 6.17)

24. Three years ago, you took out a loan for $9,000. Over those three years, you paid equal monthly payments totaling $11,826. What was the APR on your loan? (18.69%)

 

 

FYI only: help for homework

Part 1(Qs 1-2)         Part 2(Qs 4-8)          Part 3(Qs 9-12)

Part 4(Qs 13-16)     Part 5(Qs 17-20)      Part 6(Qs 21-24)

(Q13: Bridget’s is an annuity due, so abs(fv(8%/12, 10*12, 150, 0, 1)) --- type =1; Jordan’s is an ordinary annuity, so abs(fv(8%/12, 10*12, 175, 0) --- type =0, or omitted. There is a mistake in the help video for this question. Sorry for the mistake.)

 

Quiz 1- Help Videos   - Practice Quiz

Part I           Part II        Part III

 

Calculators


NPV calculator
 

 

NFV calculator

 

Time Value of Money Calculator 

 

© 2002 - 2019 by Mark A. Lane, Ph.D.

 

 

Math Formula

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))

Or

N = ln(1/(1-(PV/C)*r)))/ (ln(1+r))

 

image001.jpg

 

 

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                                          

 = abs(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      

APR = nominal(effective rate,  npery)

 

To get NPV, use NPV function

NPV = npv(rate, cf1, cf2,…) + cf0

 

 

Week3

Chapter 7 Bond Pricing

 

Ppt

 

Part I - Yield Curve     Quiz      Self-Produced Video

 

image161.jpg

https://www.ustreasuryyieldcurve.com/

 

US Treasuries Yield Curve - October 22, 2024

·        Inverted Yield Curve: The curve starts high at the short end, with a peak around 1-month maturity, and then declines, hitting a low point at around 3 years. This is indicative of an inverted yield curve, which often signals an impending economic recession.

·        Steepening Beyond 10 Years: After the 10-year mark, the curve starts to rise again, indicating investors expect higher returns for longer maturities, possibly due to anticipated future inflation or uncertainty.

  • Fed Funds Target Range: The checked Fed Funds Target Range highlights that short-term interest rates are influenced by the Federal Reserve's policy, which is likely elevated in this case to combat inflation.

 

 

image162.jpg

 

Or at https://www.gurufocus.com/yield_curve.php

 

Current Treasury Yield Curve vs. prior years’

  • Flatter Yield Curve: This graph compares the yield curve for current, October 2023, and October 2022. All three curves are relatively flat, indicating limited difference in yields across maturities. This can signal economic stagnation or low growth expectations.
  • Declining Trend: Yields from 2022 to 2023 and now show a decline, reflecting that interest rates have decreased over time, largely due to The Federal Reserve’s policies.

Summary:

  ·  Inflation:

  • A flattening or inverted yield curve can indicate lower inflation expectations. If the yield curve is flat or inverted, it suggests that investors expect slower economic growth, which may dampen inflation in the future.
  • Long-term rates are low, reflecting that investors do not foresee a significant rise in inflation over time. The Federal Reserve’s efforts to control inflation through higher short-term rates appear to be having the desired effect.

·  Stock Market:

  • An inverted yield curve is often a predictor of economic recessions, which tend to negatively affect the stock market. Historically, such curves are followed by a period of reduced corporate profits and economic contraction, leading to lower stock prices.
  • The flattening curve signals caution among investors. The expectation of slower growth could lead to a more volatile or downward-trending stock market as investors become more risk-averse, favoring safer, interest-bearing assets like bonds over equities.

·  Economic Growth:

  • The inverted or flattening yield curve typically signals slowing economic growth or an impending recession. In this scenario, investors are betting that the Federal Reserve’s actions (e.g., raising short-term rates) to combat inflation will lead to reduced economic activity in the near term.
  • The low long-term yields reflect an outlook of subdued growth over the long term, meaning the economy could be entering a period of stagnation or slow recovery, rather than robust expansion.

 

 

Part II – Bond Definition

 

 

How Bonds Work (video)

 

 

For discussion:  https://jufinance.com/risk_tolerance.html

 

Bond Type         

 Characteristics                                  

 Suitability                                 

 Risk                                   

Short-Term Bonds  

Quick maturity, Low risk, Lower returns         

Conservative, Need liquidity               

Reinvestment Risk                      

Long-Term Bonds   

Higher returns, High risk                       

Long-term, High risk tolerance              

Default Risk; Market interest rate risk

 Corporate Bonds   

Higher yields, Higher risk, Company influence   

Seeking returns, Accepting higher risk     

Default Risk; Market interest rate risk (assuming long maturity)

 Treasury Securities

Low risk, Steady income, Different maturities   

Conservative, Stable income requirement    

Market interest rate risk (assuming long maturity) 

 Municipal Bonds   

Tax advantages, Credit risk                     

Tax-efficient income, Higher tax bracket   

Default Risk; Market interest rate risk (assuming long maturity)

 

 

·       Among the aforementioned bonds, do you have a preference? If so, what factors influence your choice?

 

 

 image141.jpg

Outlook for Investing in Bonds in 2024 (FYI only)

After starting the year recommending that investors focus on the middle of the yield curve, we began to advise investors to lengthen their duration in our midyear bond market update. According to our forecasts, we continue to think investors will be best served in longer-duration bonds and locking in the currently high interest rates. https://www.morningstar.com/markets/where-invest-bonds-2024

 

  

Where can you find bond information?

·       All types of bonds: https://www.finra.org/finra-data/fixed-income

·       Treasury Bond Auction and Market information

http://www.treasurydirect.gov/

 

Are bonds Risky?                   Self-produced video               Quiz 

 

Bond risk credit risk (video)

Bond risk interest rate risk (video)

 

 

 

Bond Type

Risk

Return

Potential Investors

Website for Info

Government Bonds

Low (for developed countries)

Low

Conservative, risk-averse investors

https://www.treasurydirect.gov

Corporate Bonds

Moderate to High

Moderate to High

Investors seeking higher returns

https://www.finra.org

Convertible Bonds

Moderate to High

Moderate with potential for high (if stock rises)

Investors willing to take risk for potential stock upside

https://www.investopedia.com

Zero-coupon Bonds

Moderate

Moderate

Investors seeking tax advantages or fixed returns

https://www.investor.gov

Floating-rate Bonds

Moderate

Variable (depends on rates)

Investors seeking protection against interest rate changes

https://www.investopedia.com

Callable Bonds

Moderate to High

Moderate (with potential for early redemption)

Investors betting on lower interest rates

https://www.finra.org

Puttable Bonds

Low to Moderate

Low

Conservative investors seeking flexibility

https://www.investopedia.com

Inflation-linked Bonds (TIPs)

Low

Moderate (inflation-adjusted)

Investors seeking protection against inflation

https://www.treasurydirect.gov

Foreign Bonds

Moderate (depends on issuer)

Moderate

Investors seeking international exposure

https://www.investopedia.com

Savings Bonds

Very Low

Low

Individual, conservative investors

https://www.treasurydirect.gov

 

 

 

 

   

 

 

image143.jpg       

The above graph shows the cash flow of a five year 5% coupon bond. The bond has a duration of 4.49 years.

 

What is Duration?

  • Duration is a measure of how long it takes, in years, for the price of a bond to be repaid by its internal cash flows (coupon payments and the principal).
  • It’s also used to assess how sensitive a bond is to changes in interest rates. A higher duration means the bond's price will drop more when interest rates rise.

 

In the image:

  • Each year there’s a cash flow of $50, and in the final year (Year 5), there's a final payment of $1050 (including $50 interest and $1000 principal).
  • Duration tells you how much time, on average, it takes to get those cash flows.

 

If the bond has a duration of 4.49 years, this means that the average time to receive the bond's payments (weighted by their value) is about 4.49 years. This also means that for every 1% increase in interest rates, the bond's price would drop by approximately 4.49%.

 

In Excel: to get duration, use duration function, such as “=DURATION(DATE(2024, 10, 17), DATE(2029, 10, 17), 5%, 5%, 2, 1)=4.49

Or visit https://www.jufinance.com/bond_chatgpt/ to get both duration and convexity (FYI only).

 

 

Relationship between bond prices and interest rates (Khan academy)

 

 

 

 Market data website:

FINRA:      https://www.finra.org/finra-data/fixed-income/corp-and-agency   (FINRA bond market data, 10/22/2024)

 image163.jpgimage164.jpg

 

For example:

image165.jpg

 

 

 

 

 

 

  Bond Calculation    Bond Calculator

 

Investing Basics: Bonds(video)

 

 

2.      1. Understand what is coupon, coupon rate, yield, yield to maturity, market price, par value, maturity, annual bond, semi-annual bond, current yield.

 

3.      2. Understand how to price bond

Bond price = abs(pv(yield, maturity, coupon, 1000))  ------- annual coupon

Bond price = abs(pv(yield/2, maturity*2, coupon/2, 1000)) ------- semi-annual coupon

 

Also change the yield and observe the price changes. Summarize the price change pattern and draw a graph to demonstrate your findings.

 

Again, when yield to maturity of this semi_annual coupon bond is 4%, how should this WMT bond sell for?

 

3.      Understand how to calculate bond returns

Yield to maturity = rate(maturity, coupon,  -market price, 1000) ---- annual coupon

Yield to maturity = rate(maturity*2, coupon/2,  -market price, 1000)*2 ----- semi-annual coupon

 

Bond Calculator (www.jufinance.com/bond)

 

For example, when the annual coupon bond is selling for $1,100, what is its return to investors?

 

For example, when the semi-annual coupon bond is selling for $1,100, what is its return to investors?

 

4.      Current yield: For the above bond, calculate current yield. Note: current yield = coupon/bond price

5.      Zero coupon bond: coupon=0 and treat it as semi-annual coupon bond.

Example: A ten year zero coupon bond is selling for $400. How much is its yield to maturity?

A ten year zero coupon bond’s yield to maturity is 10%. How much is its price?

 

6)   coupon: use pmt function in excel. 

·       =abs(pmt(yield to maturity, years left to maturity, -price, 10000) for annual coupon

·       =abs(pmt(yield to maturity/2, years left to maturity*2, -price, 10000)*2 for semi-annual coupon

 

 

7.      Understand what is bond rating and how to read those ratings.

a.       Who are Moody, S&P and Fitch?

b.      What is WMT’s rating?

c.       Is the rating for WMT the highest?

d.      Who earned the highest rating?

 

       8. FYI only

o   A quick quiz on the conceptual comprehension of the bond chapter (FYI only, not required):

www.jufinance.com/bond.html

 

o   An exercise on bond concepts with expiations (FYI only)

https://www.jufinance.com/game/bond/index.html

 

 

Supplement: Municipal Bond

image051.jpg

https://emma.msrb.org/

 

·       Corporate Bond Data is available at FINRA.ORG:  https://www.finra.org/finra-data/fixed-income/corp-and-agency

·       Muni Bond Data is available at EMMA https://emma.msrb.org/

·       Treasury Securities Data is available at Treasury Direct: https://www.treasurydirect.gov/

 

 

 

 

For class discussion:

·       Shall you invest in municipal bonds?

·       Are municipal bonds better than investment grade bonds?

 

 

 

Homework ( due by week 5, 11/3)

 

1.  Firm AAA’s bonds price = $850.  Coupon rate is 5% and par is $1,000. The bond has six years to maturity. Calculate for current yield? (5.88%)

2. For a zero coupon bond, use the following information to calculate its yield to maturity. (14.35%)  Years left to maturity = 10 years. Price = $250. 

3.  For a zero coupon bond, use the following information to calculate its price. ($456.39) Years left to maturity = 10 years. Yield = 8%.

4.  Imagine that an annual coupon bond’s coupon rate = 5%, 15 years left. Draw price-yield profile. (hint: Change interest rate, calculate new price and draw the graph). 

5. IBM 5 year 2% annual coupon bond is selling for $950. How much this IBM bond’s YTM?  3.09%

6.  IBM 10 year 4% semi-annual coupon bond is selling for $950. How much is this IBM bond’s YTM?  4.63%

7. IBM 10 year 5% annual coupon bond offers 8% of return. How much is the price of this bond?   798.7

8. IBM 5 year 5% semi-annual coupon bond offers 8% of return. How much is the price of this bond?  $878.34

9.  IBM 20 year zero coupon bond offers 8% return. How much is the price of this bond? 208.29

10.   Collingwood Homes has a bond issue outstanding that pays an 8.5 percent coupon and matures in 18.5 years. The bonds have a par value of $1,000 and a market price of $964.20. Interest is paid semiannually. What is the yield to maturity? (8.90%)

11.  Grand Adventure Properties offers a 9.5 percent coupon bond with annual payments. The yield to maturity is 11.2 percent and the maturity date is 11 years from today. What is the market price of this bond if the face value is $1,000?

($895.43)

12.  The zero coupon bonds of D&L Movers have a market price of $319.24, a face value of $1,000, and a yield to maturity of 9.17 percent. How many years is it until these bonds mature? (12.73 years)

13.  A zero coupon bond with a face value of $1,000 is issued with an initial price of $212.56. The bond matures in 25 years. What is yield to maturity?  (6.29%)

14.   The bonds issued by Stainless Tubs bear a 6 percent coupon, payable semiannually. The bonds mature in 11 years and have a $1,000 face value. Currently, the bonds sell for $989. What is the yield to maturity? (6.14%)

 

Videos --- homework help (due by week 5, 11/3)

Part I        Q1-Q2       Q3-Q4     Q5-Q8      Q9-Q14

 

 

Quiz 2- Help Video   Practice Quiz

 

 

 

 

 

 

 

 

Bond Calculator

www.jufinance.com/bond

 

 

 

Bond Pricing Formula (FYI)

 

image033.jpg

 

 

 

image035.jpg

 

 

image036.jpg

 

 

image037.jpg

 

image038.jpg

 

 

 

 

Bond Pricing Excel Formula

 

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 coupon (semi-annual coupon bond)

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

Coupon rate = coupon / 1000

 

 

 

Week 4

Chapter 8 Stock Valuation

 

ppt

 

Part I Dividend payout and Stock Valuation

 

 

For class discussion:

·         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

 

 

 

 

Wal-Mart Dividend History

 

https://www.macrotrends.net/stocks/charts/WMT/walmart/dividend-yield-history

image166.jpg

 

WMT Dividend History

https://www.nasdaq.com/market-activity/stocks/wmt/dividend-history

Walmart Inc. Common Stock (WMT) Dividend History

 

·        Ex-Dividend Date08/16/2024

·        Dividend Yield1.01%

·        Annual Dividend$0.83

·        P/E Ratio13.72

 

 

Ex/EFF Date

Type

Cash

Declaration

Record Date

Declaration

12/13/2024

Cash

$0.21

2/20/2024

12/13/2024

10/6/2025

8/16/2024

Cash

$0.21

2/20/2024

8/16/2024

2/10/2025

5/9/2024

Cash

$0.21

2/20/2024

5/10/2024

7/29/2024

3/14/2024

Cash

$0.21

2/20/2024

3/15/2024

4/8/2024

12/7/2023

Cash

$0.57

2/21/2023

12/8/2023

9/23/2024

8/10/2023

Cash

$0.57

2/17/2023

8/11/2023

2/2/2024

5/4/2023

Cash

$0.57

2/21/2023

5/5/2023

7/17/2023

3/16/2023

Cash

$0.57

2/21/2023

3/17/2023

4/10/2023

12/8/2022

Cash

$0.56

2/17/2022

12/9/2022

9/30/2023

8/11/2022

Cash

$0.56

2/17/2022

8/12/2022

2/4/2023

5/5/2022

Cash

$0.56

2/17/2022

5/6/2022

7/23/2022

3/17/2022

Cash

$0.56

2/17/2022

3/18/2022

4/16/2022

12/9/2021

Cash

$0.55

2/18/2021

12/10/2021

10/1/2022

8/12/2021

Cash

$0.55

2/18/2021

8/13/2021

2/5/2022

5/6/2021

Cash

$0.55

2/18/2021

5/7/2021

7/24/2021

3/18/2021

Cash

$0.55

2/18/2021

3/19/2021

4/17/2021

12/10/2020

Cash

$0.54

2/18/2020

12/11/2020

10/4/2021

8/13/2020

Cash

$0.54

2/18/2020

8/14/2020

2/8/2021

5/7/2020

Cash

$0.54

2/18/2020

5/8/2020

7/27/2020

3/19/2020

Cash

$0.54

2/18/2020

3/20/2020

4/20/2020

12/5/2019

Cash

$0.53

2/19/2019

12/6/2019

9/21/2020

image167.jpg

 An Analysis based on Walmart's (WMT) Dividend Payout Record from 2020 to 2024:

·   Annual Payouts and Trends:

  • The data reflects a stable quarterly dividend payout, with four payments made each year. This regularity aligns with Walmart's predictable cash flow and solid financial footing, making it a reliable dividend-paying stock.
  • By aggregating the quarterly payments, we can see the annual dividend payout increased gradually, supporting a strategy of incrementally rewarding shareholders.

·  Recent Dividend Leveling:

  • The dividend payments reached a plateau in recent years, with the quarterly payout stabilizing at $0.57 in 2023 and dropping slightly to $0.21 in 2024. This change may reflect adjustments based on broader economic conditions or reinvestment strategies, as companies sometimes allocate funds differently during times of economic uncertainty or market shifts.

·  Prospects and Stability:

  • Walmart's consistent dividend payments indicate its financial stability and ability to maintain shareholder returns, even during fluctuating market conditions. The slight decrease in dividends per share in recent quarters could be a signal of Walmart's strategic adjustments, but the overall payout history is indicative of strong financial health and a shareholder-focused approach.

 

image167.jpg

https://www.nasdaq.com/market-activity/stocks/wmt/dividend-history

 

image168.jpg

image169.jpg

 

P₀ = Σ [D / (1 + r)ᵗ] from t=1 to ∞

where:

  • P₀ is the Present Value or Market Price,
  • Σ represents the summation from t = 1 to infinity,
  • Dₜ is the dividend in year t,
  • r is the discount rate (required rate of return),
  • t is each time period (year).

 

Calculating the present value of dividends, especially when assuming they extend to infinity, can be challenging. To simplify, we can assume that dividends grow at a constant rate.

 

Additionally, we can use the discount rate 'r,' which is based on the Beta and Capital Asset Pricing Model (CAPM) discussed in Chapter 13. By incorporating these assumptions, we can streamline the calculation process for determining the present value of dividends.

 

For dividends that grow at a constant rate, the Net Present Value (NPV) of dividends can be calculated as:

P₀ = D₁ / (r - g)

where:

  • P₀ = Present Value or Market Price,
  • D₁ = Dividend expected in the first year,
  • r = Discount rate (required rate of return),
  • g = Growth rate of dividends.

 

   

 

https://www.nasdaq.com/market-activity/stocks/wmt

 

image170.jpg

 

What information does each item in the table convey or represent?

 

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

 

image171.jpg

 

 

 

 

Part II: Constant Dividend Growth-Dividend growth model

Calculate stock prices

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

Po= https://www.jufinance.com/fin509_19s/index_files/image013.gif 

Po= https://www.jufinance.com/fin509_19s/index_files/image015.gif +https://www.jufinance.com/fin509_19s/index_files/image017.gif

Po= https://www.jufinance.com/fin509_19s/index_files/image015.gif +https://www.jufinance.com/fin509_19s/index_files/image019.gif +https://www.jufinance.com/fin509_19s/index_files/image021.gif

Po= https://www.jufinance.com/fin509_19s/index_files/image015.gif +https://www.jufinance.com/fin509_19s/index_files/image019.gif +https://www.jufinance.com/fin509_19s/index_files/image023.gif+https://www.jufinance.com/fin509_19s/index_files/image025.gif

……

P₀ = D₁ / (r - g)

where:

  • P₀ = Present Value or Market Price,
  • D₁ = Dividend expected in the first year,
  • r = Discount rate (required rate of return),
  • g = Growth rate of dividends.

 

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

1. Present Value (P) Formulas:

P = D / (r - g) or P = D * (1 + g) / (r - g)

  • Where D is the dividend paid in the current period, and D is the dividend expected in the next period.

 

2. Required Rate of Return (r):

r = D / P + g = D * (1 + g) / P + g

  • Here, r represents the total return, which consists of:
    • Dividend Yield = D / P or D * (1 + g) / P
    • Capital Gain Yield = g

 

3. Growth Rate (g):

g = r - D / P = r - D * (1 + g) / P

  • This formula solves for the dividend growth rate g based on the required return and the dividend yield.

 

4. Dividend Formulas (D and D):

D = P * (r - g) and D = P * (r - g) / (1 + g)

 

5. Capital Gain Yield:

Capital Gain Yield = g = (P - P) / P

  • Where Pis the stock price one year later, calculated as:

P = D / (r - g)

 

6. Dividend Yield:

Dividend Yield = r - g = D / P = D * (1 + g) / P

 

7. Future Dividends (D, D, D, …):

D = D * (1 + g), D = D * (1 + g), D = D * (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? (answer:  15.71, 7%, 10%)

2.     The current market price of stock is $90 and the stock pays dividend of $3 (D1) with a growth rate of 5%. What is the return of this stock? How much is the dividend yield? Capital gain yield? (answer: 8.33%, 3.33%, 5%)

 

 

Part III: Non-Constant Dividend Growth

Calculate stock prices

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

Po= https://www.jufinance.com/fin509_19s/index_files/image013.gif 

Po= https://www.jufinance.com/fin509_19s/index_files/image015.gif +https://www.jufinance.com/fin509_19s/index_files/image017.gif

Po= https://www.jufinance.com/fin509_19s/index_files/image015.gif +https://www.jufinance.com/fin509_19s/index_files/image019.gif +https://www.jufinance.com/fin509_19s/index_files/image021.gif

Po= https://www.jufinance.com/fin509_19s/index_files/image015.gif +https://www.jufinance.com/fin509_19s/index_files/image019.gif +https://www.jufinance.com/fin509_19s/index_files/image023.gif+https://www.jufinance.com/fin509_19s/index_files/image025.gif

……

 

Non-constant dividend growth model

 

Equations

1. Market Price in Year nn (P):

When dividends start to grow at a constant rate from year nn:

P = Dₙ₊₁ / (r - g) = D * (1 + g) / (r - g)

where:

  • Dₙ₊₁ = Dividend in year n+1n+1
  • D = Dividend in year nn
  • r = Required rate of return (stock return)
  • g = Dividend growth rate
  • P = Market price of the stock in year nn

 

2. Present Value in Year 0 (P):

The present value P0PP0 of all future dividends up to year nn is:

P = NPV(r, D, D, …, D + P)

 

Or, equivalently:

P = D / (1 + r) + D / (1 + r)² + + (D + P) / (1 + r)

 

Calculator: Non-Constant Dividend Growth Calculator  https://www.jufinance.com/dcf/

 

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%) = 1413.13

value in year 0 (current value) =1017.56 = npv(15%, 75, 84, 96, 111, 120+1413.13)

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 = 1017.56 - 500 = 517.56 millions

stock price = 517.56 / 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, 2.8561+2.8561*(1+6.34%)) /(12% - 6.34%)) = 40

 

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

 

 

 

Part IV: How to pick stocks? (FYI)

·       FINVIZ.com

http://finviz.com/screener.ashx

use screener on finviz.com to narrow down your choices of stocks, such as PE<15, PEG<1, ROE>30%

 

·       Mutual Fund Selection Game  https://www.jufinance.com/game/mutual_fund_selection.html

·        FYI  ~ Step-by-Step Guide for Screening Mutual Funds:

1. Open the Mutual Fund Screener:

2. Choose Basic Search Criteria:

  • Start by simplifying the search. 

Key Criteria to Focus On:

  • Fund Family: This is the company managing the mutual fund (e.g., Vanguard, Fidelity).
  • Morningstar Rating: This is a star-based rating (from 1 to 5 stars). The more stars, the better the fund has performed relative to its risk level.
  • Category: You can select a category of funds, such as "Large Growth", "Bond Funds", or "Balanced Funds" to meet specific needs.

3. Set Up a Simple Screen:

Step-by-Step Filters for the screener:

  1. Fund Family:
    • You can select well-known fund families like Vanguard or Fidelity to screen for trusted, low-cost funds.
  2. Category:
    • Pick a category based on what youre looking for, such as:
      • Large Growth: Focuses on big companies expected to grow fast.
      • Bond Funds: Safer investments for income.
      • Balanced Funds: Mix of stocks and bonds for moderate risk.
  3. Morningstar Rating:
    • Choose a Morningstar Rating of 4 or 5 stars to focus on higher-rated funds.
  4. Expense Ratio:
    • The expense ratio is the annual fee mutual funds charge. Select Low to filter funds with low fees (less than 1%).

4. Run the Search:

  • After selecting your criteria, click Search.
  • The screener will provide a list of mutual funds that match your search filters.

5. Analyze the Results:

After you run the screen, a list of funds will appear. Here's how to interpret the most important columns:

  • Fund Name: This is the name of the mutual fund.
  • Morningstar Rating: The star rating (1 to 5 stars).
  • Expense Ratio: The annual fee expressed as a percentage (the lower, the better).
  • 1 Year Return / 5 Year Return: The performance of the fund over the past 1 or 5 years.

6. Key Points:

  • Morningstar Rating: Aim for 4-5 stars.
  • Expense Ratio: Look for expense ratios below 1% for cost efficiency.
  • Fund Returns: Compare the 1-year and 5-year returns to see how well the fund has performed.

Example:

Lets say you want to find a low-cost, well-rated balanced fund:

  • Fund Family: Select Vanguard or Fidelity.
  • Category: Choose Balanced Funds.
  • Morningstar Rating: Select 4 or 5 stars.
  • Expense Ratio: Select Low (below 1%).

Now, click Search, and the results will show a list of funds that match this criteria.

7. Choosing a Fund:

After the search, click on a funds name for more detailed information. Youll see details like:

  • Top Holdings: What the fund is invested in.
  • Risk: How risky the fund is compared to others in its category.
  • Fees: A breakdown of the total fees and expenses.

Additional Tips:

·        Start Simple: Focus on categories and ratings to avoid getting overwhelmed by too many options.

·        Expense Ratio: Always look at the fees! They can significantly impact long-term returns.

·        Performance: A funds historical performance isnt a guarantee of future returns, but its a useful indicator.

 

 

Part V: Behavior Finance (FYI)

Understanding behavioral finance is essential because it explains how psychological biases and emotions influence investors' decisions, often leading to irrational market behavior. By recognizing these tendencies, investors and analysts can make more informed choices, avoid common pitfalls, and better anticipate market trends driven by human behavior.

Anchoring   Game     Self-produced Video