Quiz 3 solution sketches

1. Quiz 3 solution sketches 1:00 Lecture, Version A Note for multiple-choice questions: Choose the closest answer

2. Finite PV • Someone tells you that there is a stock that will have an annual growth rate of dividend payments of 55%, and the annual discount rate for the stock is 40%. Which of the following statements is correct? (Assume that dividends are paid annually starting one year from today.)

3. Finite PV • A: The stock is finitely valued if we assume that dividends will be paid forever. • No (g>r means infinite PV of perpetuity) • B: The stock is finitely valued if we assume that dividends will be paid only for 100 years. • Yes (each PV is finite)

4. Finite PV • C: No stock can ever have dividend growth of 55% from one year to the next. • No, high growth rate is possible in any year • D: The PV of the stock is $0. • No, PV is positive since the dividend>0. • E: Both (A) and (B) • No, because (A) is false.

5. Sample Standard Deviation • A sample of 3 stocks has rates of return of 8%, 5%, and 2%. What is the standard deviation of this sample? • Avg = (8 + 5 + 2)/3 = 5% • Variance= 1/2*[(.08-.05)2 + (.05-.05)2 + (.02-.05)2]= 1/2*[.0018] = .0009 • S.D. = (.0009)1/2 = .03 • S.D. = 3%

6. Expected NPV • Mariah plans to open a new car dealership. She will buy a plot of land today for $900,000. She will have to spend $800,000 for cars today. Starting one year from today, she will have positive cash flows (undiscounted) of $200,000 every year. The last of these positive cash flows will be 10 years from today.

7. Expected NPV • There is a clause in the contract that 10 years from today, the land must be sold to a university. If economic times are good, the plot will sell for $2 million. If not, the plot must be sold for $900,000. If the effective annual discount rate is 5% and you believe the probability of good economic times is 50%, what is the NPV of this investment?

8. Expected NPV • (in $millions) • NPV = -0.9 – 0.8 + .2/.05 (1 – 1/1.0510) + 0.5 *2*(1/1.0510) + 0.5*0.9(1/1.0510) • NPV = 0.7345 • NPV = $734,500

9. Semiannual Bond Coupons • A bond pays coupons of $60 annually, starting six months from today, until the bond matures (with the last coupon on the maturity date). The bond will mature 3½ years from today and pay a face value of $500. What is the PV of this bond if the appropriate effective annual interest rate for this bond is 8%?

10. Semiannual Bond Coupons • PV = 60/(1.08)1/2 + 60/(1.08)3/2 + 60/(1.08)5/2 +560/(1.08)7/2 • PV = $588.46

11. Zero-Coupon Bond Value • A zero-coupon bond will mature 5 years from today. The promised payment at maturity is $10,000. The current market rate (as an effective annual interest rate) is 12%. What is the current value of owning this bond? • X * (1.12)5 = 10,000 • X = 10,000/(1.12)5 • X = $5674.27

12. Change in Bond Value • You currently own a zero-coupon bond with maturity date in 18 months. The bond will pay $3,000 on the maturity date. The effective annual rate of return for this bond at the beginning of today is 9%. At the end of the day the rate drops to 8%. How much does the value of the bond change today?

13. Change in Bond Value • PV @ 9% = 3000/(1.09)3/2 = $2,636.22 • PV @ 8% = 3000/(1.08)3/2= $2,672.92 • r decreases  PV increases • Change in PV = 2672.92 – 2636.22 • Change in PV = $36.70

14. Payback Period Method • Use the undiscounted payback period method, with the cutoff date 10 years, 4 months from now. (In other words, the payback period is 10 years, 4 months.) The effective annual discount rate is 37.934%. Which of the following offers should be picked if someone uses this method?

15. Payback Period Method • A: A one-time payment of $5,000 today • B: $600 every year forever, starting 1 year from now • C: $1,100 every 2 years, starting today • D: $8,000 every 10 years, starting 8 years from now • E: $20,000 every 20 years, starting 11 years from now

16. Payback Period Method • Undiscounted future value at 10y 4m: • A: $5,000 • B: $600 * 10 = $6,000 • C: $1,100 * 6 = $6,600 • D: $8,000 • E: $0 (first payment not until year 20) • Using the undiscounted payback period method, one should choose option D

17. Price-to-Earnings Ratio • Stocks A and B have the same annual discount rate, and would each pay the same dividend if they acted as cash cows. Stock A has no growth opportunities with positive NPV. Stock B has many growth opportunities with positive NPV. Which of the following statements is true if both companies maximize the value of their stock?

18. Price-to-Earnings Ratio • A: Stock A will have a lower price-to-earnings ratio than Stock B • B: Stock A will have a higher price-to-earnings ratio than Stock B • C: Both stocks will have the same price-to-earnings ratio • D: Stock A will have a higher price-to-earnings ratio than Stock B if the growth opportunities are small enough • E: None of the above

19. Price-to-Earnings Ratio • Price per share / Earnings per share= 1/R + NPVGO/EPS • 1/R is positive and the same for both • NPVGO is positive for B and zero for A • A’s P-E ratio < B’s P-E ratio, so the correct response is A

20. Growing Dividends • Goliath Galloping Ghost, Inc. will pay its first dividend two years from today, and will pay annually thereafter forever. The first dividend payment (in 2 years) is $5 per share. Each of the next two dividend payments will be 30% higher than the previous payment. After that, dividend payments will grow at 6% per year forever.

21. Growing Dividends • What is the PV of this stock if the effective annual interest rate is 13%? • Year 2: PV = 5/1.132 = $3.92 • Year 3: PV = 5*1.3/1.133= $4.50 • Year 4: PV = 5*1.32/1.134 = 8.45/1.134 = $5.18 • Years 5+: FV in year 4 = 8.45*1.06/(.13 – .06) = $127.96 • Years 5+: PV = 127.96/1.134= $78.48 • Sum of PVs = $92.08