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McGill University Faculty of Management Introduction to Finance (MGCR 341) Winter 2024 Intro to Finance (MGCR 341) Page 1 of 13 Sample Midterm SAMPLE MIDTERM - SOLUTIONS

Intro to Finance (MGCR 341) Page 2 of 13 Sample Midterm Question 1 If you invest $100 today at 10% APR compounded semiannually. How much will you have in 20 years? (a) $265 (b) $300 (c) $305 (d) $673 (e) $704 Solution: (e) % 25 . 10 1 ) 05 . 1 ( 2 = − + = EAR 704 $ ) 1025 . 1 ( 100 20 20 = + = FV Question 2 Veatriki has just won the lotto. The prize entitles Veatriki to 20 annual payments of $1,000,000 and the payments will start right away. If the interest rate is 10%, what is the current value of the prize? (a) 8,513,564 (b) 9,364,920 (c) 10,524,333 (d) 20,000,000 (e) 20,220,000 Solution: (b) 920 , 364 , 9 $ ) 1 . 1 ( 1 1 1 . ) 1 . 1 ( 000 , 000 , 1 20 0 =         + − + = PV Question 3 Mary deposited $100 in a bank account 20 years ago. It turns out that today she has $219 in the account. What annual interest has she earned? (a) 3% (b) 4% (c) 5% (d) 6% (e) 7% Solution: (b)

Intro to Finance (MGCR 341) Page 3 of 13 Sample Midterm % 4 1 100 219 20 = − = r Question 4 How much must be invested today in order to receive five annual payments of $1,000, if the first payment is collected two years from today and the interest rate is 10%? (a) $1,610.51 (b) $3,446.17 (c) $3,790.79 (d) $4,545.45 Solution: (b) 0 1 2 3 4 5 6 1000 1000 1000 1000 1000 PVA 1 ( ) 3791 ) 791 . 3 ( 1000 1 . 1 1 1 1 . 1000 5 = =         + − = PVA 0 = PVA 1 /1+r = 3791/1.1 = 3446.36 Question 5 Which of the following is NOT a true statement? (a) Present values and discount rates move in the opposite directions from one another. (b) On monthly compounded loans, the EAR will exceed the APR. (c) Future values increase with increases in interest rates. (d) All else equal, the longer the term of a loan the lower will be the total interest you pay on it. Solution: (d) Question 6 AES.com plans to start paying dividends in three years. At that time AES.com will start paying an annual dividend per share of $10 in perpetuity. If the required rate of return is 8%, what is the current price per share of AES.com? (a) $107 (b) $125 (c) $156 r = 10%

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Intro to Finance (MGCR 341) Page 4 of 13 Sample Midterm (d) $187 (e) $192 Solution: (a) 107 $ 08 . 10 ) 08 . 1 ( 1 2 0 = + = P Question 7 Forest Inc. is a major producer of wood. Forest has just paid a dividend per share of $10 this year. Unfortunately, because wood prices going down, in the following years, the dividend per share will decrease at a constant rate of 1%. If the required rate of return is 4%, what is the current price per share of Forest Inc.? (a) –$333 (b) $198 (c) $200 (d) $212 (e) $333 Solution: (b) 198 $ ) 01 . ( 04 . 9 . 9 0 = − − = P Question 8 The bonds of Microhard, Inc. carry a 10% annual coupon, have a $1,000 face value, and mature in four years. Bonds of equivalent risk yield 7%. What is the market value of Microhard's bonds? (a) $1,011.20 (b) $1,087.25 (c) $1,095.66 (d) $1,101.62 (e) $1,160.25 Solution: (d) ( ) ( ) 62 . 101 , 1 $ 07 . 1 000 , 1 07 . 1 1 1 07 . 1 . 000 , 1 4 4 0 = + +         + − × = P 9 . 9 ) 01 . 1 ( 10 ) 1 ( 0 1 = − = + = g D D

Intro to Finance (MGCR 341) Page 5 of 13 Sample Midterm Question 9 If the required return on a bond does not change from one year to the next, then ____________ over the same period. (a) the price of a premium bond will rise (b) the price of a discount bond will fall (c) the price of a bond selling at par will remain unchanged (d) the price of a bond selling at par will rise Solution: (c) Question 10 Your broker offers you the opportunity to purchase a bond with coupon payments of $90 per year and a face value of $1,000. If the yield to maturity on similar bonds is 8%, this bond should: (a) Sell for the same price as the similar bond regardless of their respective maturities. (b) Sell at a premium. (c) Sell at a discount. (d) Sell for either a premium or a discount but it's impossible to tell which. (e) Sell for par value. Solution: (b) Question 11 Suppose you are trying to price a bond. Which ONE of the following is FALSE ? (a) The lower the discount rate, the more valuable the coupon payments are today. (b) Bonds with high coupon payments are generally (all else the same) more sensitive to changes in interest rates than bonds with lower coupon payments. (c) When market interest rates rise, bond prices will fall, all else the same. (d) Bonds with long maturities are generally (all else the same) more sensitive to changes in interest rates than bonds with shorter maturities. (e) All else the same, bonds with larger coupon payments will have a higher price today. Solution: (b)

Intro to Finance (MGCR 341) Page 6 of 13 Sample Midterm Question 12 The annual coupon of a bond divided by its face value is called the bond's: (a) Coupon. (b) Face value. (c) Maturity. (d) Yield to maturity. (e) Coupon rate. Solution: (e) Question 13 The rate at which the stock price is expected to appreciate (or depreciate) is the: (a) Current yield. (b) Total yield. (c) Dividend yield. (d) Capital gains yield. (e) Earnings yield. Solution: (d) Question 14 Which ONE of the following is TRUE about the differences between debt and common stock? (a) Debt is ownership in a firm but equity is not. (b) Creditors have voting power while stockholders do not. (c) Interest payments are a liability while dividend payments are not. (d) Bondholders can also own equity, but not vice versa. Solution: (c) Question 15 What would you pay for a share of ABC Corporation stock today if the dividend next year will be $2 per share, your required return on equity investments is 12%, and the stock is expected to be worth $110 one year from now? (a) $95 (b) $100 (c) $110 (d) $115

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Intro to Finance (MGCR 341) Page 7 of 13 Sample Midterm (e) $120 Solution: (b) 100 $ 12 . 1 110 2 0 = + = P Question 16 Suppose that you have just purchased a share of stock for $22.50. The most recent dividend was $1.50 and dividends are expected to grow at a rate of 5% indefinitely. What must your required return be on the stock? (a) 5.00% (b) 7.00% (c) 10.25% (d) 12.00% (e) 13.67% Solution: (d) % 00 . 12 05 . 5 . 22 5 . 1 ) 05 . 1 ( ) 1 ( 0 0 = + × + = + + = g P D g r Question 17 The total return on a share of common stock is comprised of a ________________. (a) capital gains yield and a dividend growth rate (b) capital gains growth rate and a dividend growth rate (c) dividend payout ratio and a required rate of return (d) dividend yield and the present dividend (e) dividend yield and a capital gains yield Solution: (e) Question 18 You just voted to elect the board of directors. You must own: (a) Preferred stock (b) Debentures (c) Common stock (d) T-Bills (e) Bonds Solution: (c)

Intro to Finance (MGCR 341) Page 8 of 13 Sample Midterm Question 19 You have just arranged a $15,000 loan from your bank at an EAR of 10%. The loan calls for annual payments of $1,000 over the next 14 years, and a final payment 15 years from today that will liquidate the loan. How big will the final payment be? (a) $2,333 (b) $26,335 (c) $27,228 (d) $31,886 (e) $40,325 Solution: (d) ( ) ( ) 886 , 31 $ 1 . 1 1 . 1 1 1 1 . 000 , 1 000 , 15 15 15 15 14 = ⇒ +         − = C C Question 20 Moore Money Inc. just paid a dividend of $2. The required return on the stock is 15%. If it has the following expected dividend growth rates what should the stock sell for? Year Growth 1& 2 15% 3 12% 4 and on 6% (a) $22.45 (b) $26.17 (c) $27.79 (d) $28.89 (e) $29.68 Solution: (d) ( ) ( ) ( ) 89 . 28 $ 06 . 15 . ) 06 . 1 ( ) 12 . 1 ( ) 15 . 1 ( 2 15 . 1 1 15 . 1 ) 12 . 1 ( ) 15 . 1 ( 2 15 . 1 ) 15 . 1 ( 2 15 . 1 ) 15 . 1 ( 2 2 3 3 2 2 2 0 = − × × × + × × + × + × = P

Intro to Finance (MGCR 341) Page 9 of 13 Sample Midterm PROBLEM 1 (15 POINTS) To insure you, Assurances Nochance Ltd offers the following plan: you will pay 20 annual payments of $8,000 starting one year from today. Then, in year 21, you or your heirs will receive a pension for the following 15 years. The discount rate used by the company to calculate your pension is 6%. (a) What is the size of your annual pension? (10 POINTS) (b) If you could take a one-time lump sum payment 25 years from today instead of the pension, how high would the equivalent lump sum payment have to be? (5 POINTS) (a) What is the size of your annual pension? 0 1 2 3 ……… 20 21 22 ……..… 35 8,000 8,000 8,000 …….. 8,000 Pension Pension …… Pension Structure: In Year 20, the future value of the $8,000 deposits should be equal to the then present value of the pension payments Step 1: Calculate the present value (at t=0) of all the $8,000 payments: 𝑃𝑃𝑃𝑃 0 = 8,000 × � 1 0 . 06 − 1 ( 1+0 . 06 ) 20 � = 91,759.20 Step 2: Calculate the future value (at t=20) of all the $8,000 payments: 𝐹𝐹𝑃𝑃 20 = 91,759.20 × (1.06) 20 = 294,284.20 Step 3: Calculate the present value in Year 20 of the Pension payments 𝑃𝑃𝑃𝑃 20 = 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 × � 1 0 . 06 − 1 ( 1+0 . 06 ) 15 � = 9.7122 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 Step 4: Equate the value in Step 2 to Step 3: 294,284.20 = 9.7122× Pension ⇒ Pension = $ 30,300.47

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Intro to Finance (MGCR 341) Page 10 of 13 Sample Midterm PROBLEM 1 CONTINUED Use this space to continue working on Problem 1 (b) If you could take a one-time lump sum payment 25 years from today instead of the pension, how high would the equivalent lump sum payment have to be? Structure: Today, the present value of the lump sum payment must be equal to the present value of the $8,000 annuity Step 1: Calculate the present value (at t=0) of all the $8,000 payments: 𝑃𝑃𝑃𝑃 0 = 8,000 × � 1 0 . 06 − 1 ( 1+0 . 06 ) 20 � = 91,759.20 Step 2: Calculate the present value (at t=0) of the Lumpsum: 𝑃𝑃𝑃𝑃 0 = 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑃𝑃𝐿𝐿𝐿𝐿 (1.06) 25 Step 3: Equate the value in Step 1 to Step 2: 91,759.20 = 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 ( 1 . 06 ) 25 ⇒ 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑃𝑃𝐿𝐿𝐿𝐿 = $393,818.60

Intro to Finance (MGCR 341) Page 11 of 13 Sample Midterm PROBLEM 2 (10 POINTS) Bond MGCR is a $1,000 par, 4-year, 7.5 % semi-annual coupon bond. Assume a required return of 6%. (a) Calculate the current price of the bond. (6 POINTS) (b) Calculate the current yield of the bond. (4 POINTS) 0 1 2 ……. ……. … .... 8 37.50 37.50 …….. …….. …………………. 37.50+1,000 𝑃𝑃𝑃𝑃 0 = 37.50 0.03 � 1 − 1 (1 + 0.03) 8 � + 1,000 (1 + 0.03) 8 = 1,052.65 Current yield = Annual coupon Price = 75 1,052.65 = 7.12% r=3%

Intro to Finance (MGCR 341) Page 12 of 13 Sample Midterm PROBLEM 3 (20 POINTS) Assume that McGill Inc. is expected to experience supernormal growth of 25 percent for the next 2 years, followed by 15 percent for the year after, and then to return to its long-run constant growth rate of 4 percent. McGill Inc. most recent dividend was $1.25. The investor’s required rate of return is 11%. (a) Calculate the current price of the stock. (10 POINTS) (b) What is the expected dividend yield and capital gains yield in Year 1? (5 POINTS) (c) What is the expected dividend yield and capital gains yield in Year 4? (5 POINTS) (a) Calculate the current price of the stock. g 2 =25% g 4 =4% g 1 =25% g 3 =15% 0 1 2 3 4 5 ...... …….. ∞ DIV 0 = 1.25 DIV 0 = 1.25 DIV 1 = DIV 0 (1 + g 1 ) = 1.25×1.25=1.5626 DIV 2 = DIV 1 (1 + g 2 ) = 1.5625×1.25=1.9531 DIV 3 = DIV 2 (1 + g 3 ) = 1.9531×1.15=2.2461 DIV 4 = DIV 3 (1 + g 4 ) = 2.2461×1.04=2.3359 P 3 = DIV 4 /(r- g) = 2.3359/(0.11-0.04)=33.3705 𝑃𝑃 0 = 𝐷𝐷𝐷𝐷𝐷𝐷 1 ( 1+𝑟𝑟 ) + 𝐷𝐷𝐷𝐷𝐷𝐷 2 ( 1+𝑟𝑟 ) 2 + 𝐷𝐷𝐷𝐷𝐷𝐷 3 +𝑃𝑃 3 ( 1+𝑟𝑟 ) 3 = 29.04 (b) What is the expected dividend yield and capital gains yield in Year 1? Dividend yield in Year 1 = DIV 1 /P 0 = 1.5626/29.04 = 5.38% Capital gains yield in Year 1 = total return – dividend yield = 11% - 5.38% = 5.62% r=11%

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Intro to Finance (MGCR 341) Page 13 of 13 Sample Midterm PROBLEM 3 CONTINUED Use this space to continue working on Problem 3 (c) What is the expected dividend yield and capital gains yield in Year 4? Dividend yield in Year 4 = DIV 4 /P 3 = 2.3359/33.3705 = 6.999% ≈ 7% Capital gains yield in Year 1 = total return – dividend yield = 11% - 7% = 4% Good luck for the midterm! I am certain we will do great. 