1. Quiz 3 solution sketches 11:00 Lecture, Version A Note for multiple-choice questions: Choose the closest answer

2. Stock Returns A stock can be purchased today for $100. The next dividend of $4 will be paid one year from today. The value of the stock one year from today will be $98. What is the total dollar return over the next year for owning 10 shares of this stock?

3. Stock Returns Total dollar return per share = 4 + (98-100) = $2 Total dollar return for 10 shares = $20

4. Average Rates of Return Use the following information for the next two questions: On Oct. 31, 2013, the Dow Jones was at 15,545.75. On Oct. 31, 2003, the Dow Jones was at 9,801.12. (Please note that this may or may not be enough information to answer each question.)

5. Average Rates of Return What is the geometric average rate of return over this 10-year period? Geom. avg =(1+holding period return) 1/n –1 = (15,545.75/9,801.12) 1/10 – 1 = (1.58612) 1/10 – 1 = 1.0472096 – 1 Geom. avg = 4.72096%

6. Average Rates of Return We need individual year returns to be able to calculate the arithmetic mean, so there is not enough information to answer this question.

7. Loan Amortization Goliath Gladwell will borrow $60,000 on Jan. 1, 2014. He will make 12 equal yearly payments, on Oct. 1 of years 2015-2026, to completely pay back the loan. How much will each payment be if the EAR is 10%?

8. Loan Amortization If paid on Jan. 1, 2015-2026: 60,000 = C/.1 * [1 – 1/1.1 12 ] 60,000 = 6.8137 * C C = 8,805.80 Add 9 months of interest to account for payments on Oct. 1: 8,805.80 * (1.1) 3/4 = $9,458.30

9. Growing Perpetuity Mortimer will receive $1,000 today. He will receive 8% more each subsequent year. If his effective annual discount rate is 20%, what is the PV of this stream of payments? PV = 1,000 + (1,000 * 1.08)/(.2 -.08) PV = 1,000 + 1,080/.12 PV = $10,000

10. Expected NPV Sallie is trying to invent a new type of tent. The invention costs $1 million to develop, which must be paid whether or not it is successful. If the invention is successful, she will sell $20 million in tents (in PV), and the cost to produce the tents is $8 million (in PV). If the invention does not succeed, the respective PVs for tent sales are $3 million and $2.8 million.

11. Expected NPV If the invention is successful with 10% probability, what is the expected NPV of Sallie’s tent business? (in $Millions) NPV = -1 +.1 * (20 – 8) +.9 * (3 – 2.8) NPV = -1 + 1.2 + 1.8 NPV = 0.38, so NPV is $380,000

12. Bond Yields Bruce is quoted a price for a bond of $1,000. This bond has a face value of $900 and pays a 12% coupon once per year. Two coupons will be paid. One coupon will be later today and the other will be paid one year from today. If the bond matures in one year, what is the yield of this bond (expressed as an effective annual interest rate)?

13. Bond Yields 1,000 = 900(.12) + 900(1.12)/(1+r) 892 = 1008/(1+r) 1+r = 1008/892 = 1.13004 r = 13.004%

14. Real Rate of Return In 1981, large-company stocks had an effective annual return of -4.92%. The Consumer Price Index, which is used as a measure of inflation, was 8.92%. What is the real effective annual return of large-company stocks in 1981? (1+real)*(1+inflation) = (1+nominal) (1+real)*(1.0892) = 0.9508 Real = 0.9508/1.0892 – 1 = -12.707%

15. Cash Cow & Retained Earnings Cow Bell Boots, Inc. is currently a cash cow. Without any re-investment of their earnings, they will earn $8 per share every year forever. The effective annual discount rate for owning this stock is 10%. Assume that the next dividend payment will be made in 1 year.

16. Cash Cow & Retained Earnings Suppose that Cow Bell Boots could retain all of its earnings 4 years from today, and earn 20% on these earnings over the following year. (a) What is the PV of this stock if it continues to act as a cash cow? PV = 8/.1 = $80

17. Cash Cow & Retained Earnings (b) Should Cow Bell Boots retain its earnings 4 years from today? Why/why not? Yes, because either: NPV is positive Rate of return (20%) > Discount rate (10%)

18. Cash Cow & Retained Earnings (c) How much does the present value of Cow Bell Boots change if the company retains its earnings 4 years from today? NPV of retaining earnings = -8/1.1 4 + 8(1.2)/1.1 5 = 0.4967