SM132 final exam practice - Fall 2020 PDF

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Practice questions for the exam. I have shown all the processes....

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SM132 Fall 2020 Final Exam Practice Problems Notes  The weekly practice problem sets are taken from old exams – you should use them in conjunction with these problems to study  The exam will be cumulative so you should also use the practice problems from both midterms to study The answer key is at the end of this document 1. Which one of the following bonds will trade at a premium? A) B) C) D)

A zero coupon bond that was purchased before interest rates fell sharply A bond with a coupon of 8.6% and a yield to maturity of 9.0% A zero coupon bond that was purchased before interest rates increased sharply None of the bonds above will trade at a premium

*** Use this table for the following question ***

Rating:

AAA

AA

A

BBB

Yield

2.40%

2.60%

3.20%

4.80%

2. Given the table above which shows typical yields for 5 years bonds of varying credit ratings, what is the most likely credit rating of your company if your 5-year, semiannual bonds with a face value of $5,000 and a coupon rate of 7% are trading at a price of $5,483.86? Find yield: PMT:175, PV=5483.86, FV= 5000, N=10, r=2.4. 2.4*2= 4.8 Anwser=BBB 3. Which of the following bonds is the most sensitive to a change in interest rates. Each bond is semiannual, $10,000 face value. A) B) C) D)

Bond A Bond B Bond C Bond D

Coupon Rate 4.3% 6.0% 5.2% 15.0%

Maturity 8 Years 8 Years 7 Years 7 Years

4. A bank pays interest quarterly with an EAR of 8.0%. How much interest will you receive in the first quarter if you deposit $500 into this account?

SM132 Fall 2020 Final Exam Practice Problems (1.08)^(1/4) -1= 0.019427 0.019427*500= 9.7132 5. A stock is bought for $22.00 and sold for $26.00 one year later, immediately after it has paid a dividend of $1.50. What was the realized rate of return on this stock expressed as a percent return (xx.x%) (1.5/22)+ (4/22)=0.25=25% r= rate of return? 6. Sampson & Team Inc. had share price at the start of the year of $26.20, is expected to pay a dividend of $0.56 at the end of the year, and has an equity cost of capital of 17.0%. What is the expected share price at the end of the year, just after it pays its dividend? PV= (Dividend + P1)/ (1+r)-----

研究下这个 formula，对比下 Perpetuity 的 C/r

PV*(1+r)= 26.20*1.17-0.56= 30.094 7. You expect TMZ Industries will have earnings per share of $5.00 this year and will pay out $2.00 of these earnings to shareholders in the form of a dividend. TMZ’s cost of equity capital is 17.0% and its share price is $50.00. What growth rate in earnings is the market expecting? PV= (Dividend + P1)/ (1+r) P1=50*1.17-2= 56.5 Growth rate in earning means capital growth yield= 6.5/50= 13% 8. Reddit Corp. is expected to pay a dividend of $1.20 at the end of the coming year. It is expected to sell for $42.00 at the end of the year. If its equity cost of capital is 14%, what is the expected capital gain from the sale of the stock at the end of the coming year? PV= (Dividend + P1)/ (1+r) PV=(1.2+42)/1.14= 37.8947 42-37.8947=4.10526 9. Summer Vacations To Go, Inc (“SVTG”) is expected to pay a dividend of $3 in one year and a

dividend of $6 in two years. In two years, the stock is expected to sell for $60 right after it pays the $6 dividend. If their equity cost of capital is 12%, what would you expect to be the current price of a share of SVTG’s stock? PV= (C1/(1+r)) + C2/(1+r)^2 PV= 3/1.12 + 6+60/1.12^2= 55.29 Use this Balance Sheet for the following question. The company has 10 million shares outstanding. The stock is currently trading on the NYSE at a price of $5 per share.

BALANCE SHEET ($, millions)

SM132 Fall 2020 Final Exam Practice Problems Assets Current Assets Long-Term Assets Net Property, Plant and Equipment Total Long-Term Assets

Liabilities Current Liabilities

89

121 121

210

Total Assets

49

Long-Term Liabilities Long-Term Debt Total Long-Term Liabilities

128 128

Total Liabilities

177

Stockholders' Equity

33

Total Liabilities and Stockholders' Equity

210

10.What is the market capitalization of the company’s stock? 10M*5= 50M *** BEGIN QUESTROM CORPORATION BOND PROBLEMS *** Rating: Yield

US Treasury 3.00%

A 4.00%

BBB 6.00%

BB 10.00%

11. You begin your job as a credit analyst and decide to make your first investment. You invest in the 10 year bonds of Questrom Corporation, a BB-rated company. If your bonds pay coupons twice a year with a coupon rate of 9.0%, what is the price of one bond if the face value is $100? N=20, i=10%/2= 5% , FV=100, PMT=4.5%*100= 4.5. PV=? PV=93.7688 12. Immediately after you purchase these bonds, Standard & Poor’s decides to upgrade Questrom Corp. to a BBB-rating! What is the new price of your bonds? N=20, i=6%/2= 3% , FV=100, PMT=4.5%*100= 4.5 PV=? PV= 122.316 13. What was the percentage change in the price of your bonds? (122.316-93.7688)/ 93.7688=0.304442

*** END QUESTROM CORPORATION BOND PROBLEMS ***

*** BEGIN COCA-COLA PROBLEMS ***

SM132 Fall 2020 Final Exam Practice Problems Coca-Cola will pay an annual dividend of $0.75 one year from now. Analysts expect this dividend to grow at 8.75% per year for three years. Thereafter, growth will slow down to 3.0% per year and remain there for the foreseeable future. 14. What dividend will the company pay in each of the first 5 years? 0 Growth Dividen d

1

2 0.0875

3 0.0875

4 0.0875

5 0.03

$0.750

$0.816

$0.887

$0.965

$0.994

15. According to the dividend discount model, what is the value of a share of Coca-Cola stock today if the firm’s cost of equity capital is 9.0%? PV4= Div5/r-g= 0.994/9.0%-3.0%=16.5667 16.5667/1+0.09^4=11.7362 Pv=C* 1/(r-g) *(1-((1+g)/(1+r))^4)=2.74284 Pv=11/7362+2.74284=14.479 Or Using cf

*** END COCA-COLA PROBLEMS *** 16. Caribou Transport Inc (CTI) had a share price at the start of the year of $41.80, paid a dividend of $0.39 at the end of the year, and has an equity cost of capital of 23.0%. What share price would you expect CTI to have at the end of the year, just after it pays its dividend? PV= (Dividend + P1)/ (1+r) P1=PV*(1+r)-D1= 41.8*1.23-0.39= 51.024 17. You purchase a zero-coupon bond with a $1000 face value and 6 years left until maturity. If the YTM of this bond is 7.6% EAR, what is the price of this bond? EAR to Discount rate = (1+0.076)^(1/1)-1= 7.6% N=6, I=7.6%, FV=1000, PV=? PV= 644.35 18. Boston Dog Sleds Inc. (BDS) has a current stock price of $10 and is expected to trade for $11 in 1 year. If BDS’s equity cost of capital is 12%, what is their expected dividend in 1 year?

SM132 Fall 2020 Final Exam Practice Problems PV= (Dividend + P1)/ (1+r) D1=10*1.12-11=0.2

19. You receive $10,000 today and $20,000 every six months beginning six months from today for 10 years. If the interest rate is 5.5% (EAR), what is the present value (PV) of this stream of cash flows? Ear= (1+0.055)^(1/2)-1=0.027132 N=20, I=2.7132, PV=?, PMT=20000 Pv=305595.5037+10000=315595.5037 $315,595 20. Snowshoe Mountain Excursions (SMEx) had a share price at the start of the year of $96.12 and paid a dividend of $2.14 at the end of the year. If SMEx has an equity cost of capital of 14%, what price would you expect to pay for a share of stock just after it pays its dividend at the end of the year? PV= (Dividend + P1)/ (1+r) P1=96.12*1.14-2.14=107.437

SM132 Fall 2020 Final Exam Practice Problems 21. You purchase a zero-coupon bond with a $5000 face value which matures in 10 years. The YTM when you purchased the bond was 6.3%. When you sell the bond 4 years later, the YTM is 6.3%. Which of the following are true statements? A) Your rate of return on your investment is 6.3% Ask why? B) The price at which you sold the bond is higher than the price at which you bought it C) You would need to know the price at which you bought the bond and the price at which you sold the bond in order to determine the rate of return on your investment D) A and B are true E) A and C are true 22. You expect to receive $600 every three months beginning fifteen months from today and expect to receive these payments forever. If the interest rate is 9% EAR, what is this stream of cash flows worth today? Ear to Discount rate (1+0.09)^(1/4)-1= 2.1778 PV4=C1/r= 600/2.1778%= 27550.7 27550.7/(1.021778)^4= 25275.9=25276 23. Terrier Nation has a $100 face value bond with a 5% coupon rate, paid quarterly. If the bond’s current yield to maturity is 6.1%, which of the following statements is true? A) B) C) D)

The bond price is $100 The bond price is greater than $100 The bond price is less than $100 You would need to know the maturity to determine the answer.

24. What is the coupon rate of a ten-year $3,000 bond with quarterly coupons and a price of $3,450 if it has a yield to maturity of 3.5% (APR)? N=40, I=3.5/4=0.875, FV=3000, PV=-3450, PMT=? PMT=39.63 39.63*4= 158.528 158.528/3000=5.2843%

SM132 Fall 2020 Final Exam Practice Problems 25. A $10,000 bond with semi-annual compounding was originally issued with an 8.4% coupon and ten years to maturity. What must the price of the bond be if there are 5 years remaining to maturity and a yield to maturity of 8% APR? N=10, I=4%, PV=?, PMT=4.2%*10000=420, FV=10000 PV=10162.2179 26. An investor bought a zero-coupon bond with $1000 face value and a ten-year maturity on December 1, 2010 for $505.62. She sold it after 5 years on December 1, 2015. If the YTM when she sold it was 5.6%, what price did she sell it for? N=5, I=5.6, FV=1000, PV=? PV=761.5184

*** Use this table for the following question ***

Rating:

AAA

AA

A

BBB

Yield

1.60%

2.20%

3.20%

4.00%

27. Given the table above which shows typical yields for 5 year bonds of varying credit ratings, what is the most likely credit rating of your company if your 5-year, semiannual bonds with a face value of $5,000 and a coupon rate of 5% are trading at a price of $5,412.81? A 28. Bull Dog Pretzels’ stock price is expected to be $74 next year (1 year from today) immediately after paying a dividend of $4.23. If its equity cost of capital is 18%, what is the expected capital gain if you sell the stock at the end of the coming year (1 year from today)? PV= (Dividend + P1)/ (1+r)

SM132 Fall 2020 Final Exam Practice Problems PV= (4.23+74)/1.18= 66.2966 74-66.2966=7.70 29. What is the yield to maturity of an eight year $1000 bond with a 8.6% coupon rate and semi-annual coupons if the bond is currently trading for $1173? N=16, I=?, PV=-1173, PMT=4.3%*1000= 43, FV=1000 I= 2.93%*2=5.86% Beginning Seaport Gondola Corporation bond issue [use this information for the following 3 problems] Seaport Gondola Corporation (SGC) wants to issue $20 million in 10 year bonds to build a gondola to transport commuters from South Station to the Seaport District. SGC plans to issue 10 year bonds with a face value of $1000 and a semi-annual 5% coupon. The following table summarizes the yield to maturity for 10 year semi-annual coupon corporate bonds with various credit ratings. Rating: YTM

AA 4.00%

A 5.00%

BBB 5.50%

BB 8.00%

30. Calculate the price of the bond if SGC has a BBB rating: N=20, I=2.75%, PV=?, PMT= 25, FV=1000 PV=961.93187 31. It turns out the bonds were issued at a price of $796.15. What was the likely credit rating? BB 32. What was the likely the credit rating if the bonds were issued at Par? A End Seaport Gondola Corporation bond issue 33. You expect Backcountry Helicopter Ski Tours (BHST) to have earnings per share of $15.00 in year 1 and to pay out $4.00 of these earnings to shareholders in the form of a dividend. BHST’s cost of equity capital is 14.0% and its share price is $80.00. What growth rate in earnings is the market expecting?

SM132 Fall 2020 Final Exam Practice Problems PV=D1+P1/1+r P1=80*1.14-4=87.2 (87.2-80)/80=9% 34. You purchased a zero-coupon bond with a $1000 face value with 6 years left until maturity at a 7.6% (EAR) yield to maturity. When you sell it exactly one year later, it has a 7% (EAR) yield to maturity. What was the return on your investment expressed as an EAR? N=6, I=7.6, FV=1000, PV= 644.3567 PV1=?, N=5, I=7, FV=1000, PV1=712.986 (712.986-644.3567)/ 644.3567=10.65%

Purchase: 644.35 Sell:712986

SM132 Fall 2020 Final Exam Practice Problems 35. Terrier Nation Inc. is expected to have earnings per share next year (year 1) of $20, which are expected to grow at 16%. They are planning to pay a dividend of $5 at the end of Year 4 (they do not expect to pay dividends in years 1, 2 and 3) and expect the growth rate to slow to 9%. After year 4, the dividend payout ratio and growth rate are expected to remain unchanged. If Terrier Nation’s equity cost of capital is 18%, what should the price of Terrier Nation’s stock be today? 1 0

0

0

20 23,2 26,912

5

5,45

31,2179 34,0275

5,45/18%-9%= 60,5556 60,5556+ 5= 65,5556 65,5556/(1,18)^4= 33,8128 36. Escape to the Sun Tours (E2ST) stock price is expected to be $89 4 years from today immediately after paying a dividend of $5. If its equity cost of capital is 14%, what price would you expect to pay for the stock today? (89+5)/1.14^4=55.66

SM132 Fall 2020 Final Exam Practice Problems

ANSWER KEY 1. Which one of the following bonds will trade at a premium? A) B) C) D)

A zero coupon bond that was purchased before interest rates fell sharply A bond with a coupon of 8.6% and a yield to maturity of 9.0% A zero coupon bond that was purchased before interest rates increased sharply None of the bonds above will trade at a premium

*** Use this table for the following question ***

Rating:

AAA

AA

A

BBB

Yield

2.40%

2.60%

3.20%

4.80%

2. Given the table above which shows typical yields for 5 years bonds of varying credit ratings, what is the most likely credit rating of your company if your 5-year, semiannual bonds with a face value of $5,000 and a coupon rate of 7% are trading at a price of $5,483.86? BBB 3. Which of the following bonds is the most sensitive to a change in interest rates. Each bond is semiannual, $10,000 face value. A) B) C) D)

Bond A Bond B Bond C Bond D

Coupon Rate 4.3% 6.0% 5.2% 15.0%

Maturity 8 Years 8 Years 7 Years 7 Years

4. A bank pays interest quarterly with an EAR of 8.0%. How much interest will you receive in the first quarter if you deposit $500 into this account? $9.71 5. A stock is bought for $22.00 and sold for $26.00 one year later, immediately after it has paid a dividend of $1.50. What was the realized rate of return on this stock expressed as a

SM132 Fall 2020 Final Exam Practice Problems percent return (xx.x%) 25% 6. Sampson & Team Inc. had share price at the start of the year of $26.20, is expected to pay a dividend of $0.56 at the end of the year, and has an equity cost of capital of 17.0%. What is the expected share price at the end of the year, just after it pays its dividend? $30.09

SM132 Fall 2020 Final Exam Practice Problems 7. You expect TMZ Industries will have earnings per share of $5.00 this year and will pay out $2.00 of these earnings to shareholders in the form of a dividend. TMZ’s cost of equity capital is 17.0% and its share price is $50.00. What growth rate in earnings is the market expecting? 13% 8. Reddit Corp. is expected to pay a dividend of $1.20 at the end of the coming year. It is expected to sell for $42.00 at the end of the year. If its equity cost of capital is 14%, what is the expected capital gain from the sale of the stock at the end of the coming year? $4.11 9. Summer Vacations To Go, Inc (“SVTG”) is expected to pay a dividend of $3 in one year and a dividend of $6 in two years. In two years, the stock is expected to sell for $60 right after it pays the $6 dividend. If their equity cost of capital is 12%, what would you expect to be the current price of a share of SVTG’s stock? $55.29 Use this Balance Sheet for the following question. The company has 10 million shares outstanding. The stock is currently trading on the NYSE at a price of $5 per share.

BALANCE SHEET ($, millions) Assets Current Assets Long-Term Assets Net Property, Plant and Equipment Total Long-Term Assets

Total Assets

89

121 121

210

Liabilities Current Liabilities Long-Term Liabilities Long-Term Debt Total Long-Term Liabilities

128 128

Total Liabilities

177

Stockholders' Equity

33

Total Liabilities and Stockholders' Equity

210

10. What is the market capitalization of the company’s stock? $50 million

49

SM132 Fall 2020 Final Exam Practice Problems *** BEGIN QUESTROM CORPORATION BOND PROBLEMS ***

Rating: Yield

US Treasury 3.00%

A 4.00%

BBB 6.00%

BB 10.00%

11. You begin your job as a credit analyst and decide to make your first investment. You invest in the 10 year bonds of Questrom Corporation, a BB-rated company. If your bonds pay coupons twice a year with a coupon rate of 9.0%, what is the price of one bond if the face value is $100? 93.77 12. Immediately after you purchase these bonds, Standard & Poor’s decides to upgrade Questrom Corp. to a BBB-rating! What is the new price of your bonds? 122.32 13. What was the percentage change in the price of your bonds? 30.4% *** END QUESTROM CORPORATION BOND PROBLEMS ***

SM132 Fall 2020 Final Exam Practice Problems *** BEGIN COCA-COLA PROBLEMS *** Coca-Cola will pay an annual dividend of $0.75 one year from now. Analysts expect this dividend to grow at 8.75% per year for three years. Thereafter, growth will slow down to 3.0% per year and remain there for the foreseeable future. 14. What dividend will the company pay in each of the first 5 years? 0 Growth Dividen d

1

2 0.0875

3 0.0875

4 0.0875

5 0.03

$0.750

$0.816

$0.887

$0.965

$0.994

15. According to the dividend discount model, what is the value of a share of Coca-Cola stock today if the firm’s cost of equity capital is 9.0%?

0 Growth Dividend

1 $0.750

$14.47

2 0.0875 $0.816

3 0.0875 $0.887

4 0.0875 $0.965

5 0.03 $0.994

(0.965/(.09-.03) $16.08 $0.887 $0.750 $0.816 $16.96 *** END COCA-COLA PROBLEMS ***

16. Caribou Transport Inc (CTI) had a share price at the start of the year of $41.80, paid a dividend of $0.39 at the end of the year, and has an equity cost of capital of 23.0%. What share price would you expect CTI to have at the end of the year, just after it pays its dividend? $51.02 17. You purchase a zero-coupon bond with a $1000 face value and 6 years left until maturity. If the YTM of this bond is 7.6% EAR, what is the price of this bond? $644.36 18. Boston Dog Sleds Inc. (BDS) has a current stock price of $10 and is expected to trade for $11 in 1 year. If BDS’s equity cost of capital is 12%, what is their expected dividend in 1 year? $0.20

SM132 Fall 2020 Final Exam Practice Problems 19. You receive $10,000 today and $20,000 every six months beginning six months from today for 10 years. If the interest ...