Test 2 solution sketches Spring 2012

Bob buys a treasury inflation- protected security Bob buys a treasury inflation-protected security (TIPS), an inflation-indexed bond, when it is first issued today. The bond has a REAL par value of $5,000 and a 2% real coupon. Inflation will be 4% in the next year, 5% in the following year, and 8% the year after that. For simplicity assume that all coupon payments are made on a YEARLY basis. The bond’s maturity date is THREE years from today.

Bob buys a treasury inflation- protected security (a) What will the nominal par value be for this bond ONE year from today? The nominal par value is par value with inflation factored in Nominal par value is $5,000 (1.04) $5,200 (b) How much will Bob receive from the nominal coupon payment TWO years from today? Nominal par value $5,000(1.04)(1.05) = $5,460 Coupon payment $5,460(0.02) = $109.20

Bob buys a treasury inflation- protected security (c) What will be the total of ALL nominal payments received by Bob THREE years from today? Par value will be received: $5,000(1.04)(1.05)(1.08) = $5, % coupon also received: $5,896.80(0.02) = $ Total: $6,014.74

Assuming an effective annual discount rate of 10%, solve… (a) Walla Walla Inc. will make 25 dividend payments of $20 per year for each share of stock owned, starting SIX years from now. These 25 dividend payments have a present value of X. Find X. Future value 5 years from now: Use the annuity formula (20/0.1)(1 – 1/ ) = $ To get present value, discount by 5 years $181.54/1.1 5 = $112.72

Assuming an effective annual discount rate of 10%, solve… (b) Belgique stock will pay $1 in dividends later today. Each subsequent year, the amount of the dividend will go up by 4% forever. What is the present value of all future dividend payments? Today’s dividend: $1 Dividend 1 year from today: $1.04 PV of all dividends paid after today’s PV = 1.04/(0.1 – 0.04) = $17.33 Total of all dividends paid: $1 + $17.33 = $18.33

Risk-free return is 4%, beta is 2.3, expected return of 12.05% Assume that the risk- free return in the market is currently 4%, and that a stock with beta (ß) of 2.3 has an expected return of 12.05% (a) What is the expected return on the market portfolio (as defined in lecture)? (b) What is the risk premium? Exp. Return = risk-free return + beta * (risk premium) 12.05% = 4% +2.3 * risk premium Risk premium = 3.5% (this answers (b)) Expected return on the market portfolio Risk-free rate + risk premium 4% + 3.5% = 7.5% (this answers (a))

Reddinator 3000 The Reddinator 3000 machine is purchased today for $5,000, and lasts SEVEN years. The Reddinator must also incur a maintenance expense of $1,400 each of TWO years, FOUR years, and SIX years from today. For your calculations, you can assume that the annual discount rate is 15%. (Note: All costs here are in real terms. This information has been incorporated into all of the above costs and discount rate.)

Reddinator 3000 (a) What is the equivalent annual cost of the Reddinator 3000? PV of costs = $5, ,400/ ,400/ ,400/ = $7, EAC calculation $7, = (EAC/.15)(1 – 1/ )  EAC = $1,794.12

Reddinator 3000 (b) If you made three equal rental payments -- TWO years from today, FOUR years from today, and SIX years from today -- that have the same combined present value as the present value of the combined purchase and maintenance costs for the Reddinator 3000, how much would each of these payments have to be? $7, = C/ C/ C/ C = $4,240.54

A sample of a stock’s returns over the past six years was 12%, 15%, -8%, 3%, -2%, and 28% (a) What is the arithmetic average return over the six year period? (12% + 15% – 8% + 3% – 2% + 28%)/6 8% (b) What is the geometric average return over the six year period? Sixth root of (1.12)(1.15)(0.92)(1.03)(0.98)(1.28) – %

A sample of a stock’s returns over the past six years was 12%, 15%, -8%, 3%, -2%, and 28% (c) What is the standard deviation of this sample? Variance of a sample is one-fifth of [(.12–.08) 2 + (.15–.08) 2 + (–.08–.08) 2 + (.03–.08) 2 + (–.02–.08) 2 + (.28–.08) 2 ] Standard deviation is the square root of the variance: , or %

A sample of a stock’s returns over the past six years was 12%, 15%, -8%, 3%, -2%, and 28% (d) If someone invested $100 in this stock six years ago, how much would this stock be worth today? $100(1.12)(1.15)(0.92)(1.03)(0.98)(1.28) $153.10