FIN 401 Lab 1

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School

Toronto Metropolitan University *

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401

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Finance

Date

Feb 20, 2024

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FIN 401 LAB 1 Q2: You plan to deposit $300 in a bank account now and $800 at the end of one year. If the account earns 2% interest per year, what will the balance be in the account right after you make the second deposit? ANSWER: FVn = Co x (1 + r)^n FV1 = 300 x (1+ 0.02)^1 FV1 = 306 Find the sum of the 2 values at time 1: → 306 + 800 = 1,106 Q3: You have just received a windfall from an investment you made in a friend's business. She will be paying you $ 11,754 at the end of this year, $23,508 at the end of next year, and $35,262 at the end of the year after that (three years from today). The interest rate is 10.7% per year. ANSWER: a. What is the present value of your windfall? = $55,795 b. What is the future value of your windfall in three years (on the date of the last payment)? PV= 55,795, PMT = 0, N= 3, I/Y= 10.7 → CPT FV= 75,690 Q4: You want to endow a scholarship that will pay $9,000 per year forever, starting one year from now. If the school's endowment discount rate is 9%, what amount must you donate to endow the scholarship? ANSWER: PV = C / r PV = 9,000 / 0.09 PV = 100,000 Q5: What is the present value of $6,000 paid at the end of each of the next 81 years if the interest rate is 10% per year? ANSWER: N = 81, PMT = 6,000, I/Y= 10, FV= 0 → CPT PV = $59,973.37 Q6: You are thinking about buying a savings bond. The bond costs $165 today and will mature in 10 years with a value of $340. What annual interest rate will the bond earn? ANSWER: PV= +/- 165, N= 10, FV= 340, PMT= 0 → CPT I/Y= 7.50% Q7: Your company wants to raise $9.5 million by issuing 25-year zero-coupon bonds. If the yield to maturity on the bonds will be 6% (EAR), what total face value amount of bonds must you issue? ANSWER: PV= 9,500,000, I/Y= 6, PMT= 0, N= 25 → CPT FV= 40,772,771.84 Q8: The following table summarizes prices of various default-free zero-coupon bonds a. Compute the yield to maturity for each bond. Year 1 = N= 1, PV = 96.06, PMT = 0, FV= 100 → CPT I/Y= 4.10% Year 2 = N= 2, PV= +/- 91.57, PMT= 0, FV= 100 → CPT I/Y= 4.50% Year 3 = N= 3, PV= +/- 86.96, PMT = 0, FV = 100 → CPT I/Y = 4.77% Year 4 = N= 4, PV= +/- 82.11, PMT = 0, FV= 100 → CPT I/Y = 5.05% Year 5 = N= 5, PV= +/- 77.05, PMT = 0, FV= 100 → CPT I/Y= 5.35% b. Plot the zero-coupon yield curve (for the first five years). c. Is the yield curve upward sloping, downward sloping, or flat? - UPWARD SLOPING Q9: For each of the following pairs of Government of Canada Bonds, identify which will have the higher price as a percentage of the face value. a. A three-year zero-coupon bond or a five-year zero-coupon bond? - A 3-year, b/c the FV is received sooner, the PV is higher b. A three-year zero-coupon bond or a three-year 4% coupon bond? 1

FIN 401 LAB 1 - The 4% coupon bond, b/c the 4% coupon bond pays interest payments; whereas the 0 coupon bond is a pure discount bond c. A two-year 5% coupon bond or a two-year 6% coupon bond? - The 6% coupon bond, b/c the coupon (interest) payments are higher, even though the timing is the same Q10: The yield to maturity of a $1,000 bond with a 7.2% coupon rate, semi-annual coupons, and two years to maturity is 7.7% APR, compounded semi-annually. What must its price be? ANSWER: APR = 7.7 / 2 = 3.85 N = 2 x 2 = 4, I/Y = 3.85, FV = 1,000, PMT = 1,000 x 7.2% = 72 / 2 = 36 → → CPT PV = $990.89 Q11: If you own 11,000 shares of stock of Brookfield Asset Management and it pays a dividend of $0.29 per share, then what is the total dividend you will receive? ANSWER: Dividend = Dividend per share x Number of Shares Dividend = 0.29 x 11,000 = $3,190 Q12 : Assume Evco, Inc. has a current stock price of $53.62 and will pay a $2.10 dividend in one year; its equity cost of capital is 13%. To justify its current price, what price must you expect Evco stock to sell for immediately after the firm pays the dividend in one year? ANSWER: 𝑃𝑜 = ?𝑖𝑣1 + 𝑃1 1 + 𝑟? Where: Po = current stock price, rE= equity cost of capital, Div1 = dividend to be paid in 1 year, P1= the stock price in 1 year 53. 62 = 2.10 + 𝑃1 1 + 0.13 P1 = ( 53.62 x 1.13) - 2.10 P1 = 60.5906 - 2.10 P1 = $58.49 Q13: You just purchased a share of Northstar Sports for $97.94. You expect to receive a dividend of $5.20 in one year. If you expect the price after the dividend is paid to be $100.05, what total return do you expect to earn over the year? What do you expect to be your dividend yield? What do you expect to be your capital gain rate? a. If you expect the price after the dividend is paid to be $100.05, what total return do you expect to earn over the year? rE = 5.20 + 100.05 / 97.94 - 1 rE = 105.25 / 97.94 -1 rE = 0.07463753 OR 7.46% → Your expected total return to earn over the year is 7.46% b. What do you expect to be your dividend yield? Div Yield = 5.20 / 97.94 = 5.31% c. What do you expect to be your capital gain rate? Cap. Gain Rate = 100.05 - 97.94 / 97.94 = 2.15% Q14: Assume Coleco pays an annual dividend of $1.41 and has a share price of $35.25. It announces that its annual dividend will increase to $1.61. If its dividend yield is to stay the same, what should its new share price be? Dividend Yield = 1.41 / 35.25 = 4% Po = 1.61 / 4% = $40.25 2

FIN 401 LAB 1 Q15: Anle Corporation has a current stock price of $20.55 and is expected to pay a dividend of $1.15 in one year. Its expected stock price right after paying that dividend is $22.43. a. What is Anle's equity cost of capital? rE= 1.15 + 22.43 / 20.55 -1 rE = 14.74% b. How much of Anle's equity cost of capital is expected to be satisfied by dividend yield and how much by capital gain? Dividend Yield = 1.15 / 20.55 Dividend Yield = 5.60% Capital Gain Rate = 22.43 - 20.55 / 20.55 Capital Gain Rate = 9.15% Q16: Achi Corp has preferred stock with an annual dividend of $3.11. If the required return on Achi's preferred stock is 8.1%, what is its price? ANSWER: Po = Div1 / rE - g Po = 3.11 / 8.1% Po = $38.40 Q17 : Ovit, Inc. has preferred stock with a price of $21.32 and a dividend of $1.39 per year. What is its dividend yield? ANSWER: Dividend Yield = Div1 / Po Dividend Yield = 1.39 / 21.32 Dividend Yield = 6.52% Q18: Summit Systems will pay an annual dividend of $1.41 this year. If you expect Summit's dividend to grow by 6.8% per year, what is its price per share if the firm's equity cost of capital is 12%? ANSWER: Po = Div1 / rE - g Po = $1.41 / 0.12 - 0.068 Po = 1.41 / 0.052 Po = $27.11 Q19: Assume Gillette Corporation will pay an annual dividend of $0.66 one year from now. Analysts expect this dividend to grow at 11.5% per year thereafter until the sixth year. Thereafter, growth will level off at 1.9% per year. According to the DDM, what is the value of a share of Gillette stock if the firm's equity cost of capital is 7.7%? ANSWER: 3

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