Question

1. Scott will deposit $10,600 every other year beginning one year from today and ending in year 9. He will have $ ____ in his account 20 years from today. Assume a discount rate of 5% p.a.

a. 105,472.04

b. 107,037.63

c. 108,314.30

d. 109,136.41

e. 111,235.18

2. Jennifer works for FHG, Inc. She has just been told that the company plans to pay a dividend of $3.20 exactly one year from today (i.e., D₁ = 3.20). If dividends are expected to grow at 4.10% each year thereafter, and if Jennifer believes that appropriate discount rate for FHG, Inc. stock is 12%, then she will calculate that the stock is currently worth $______.

a. 40.51

b. 41.56

c. 42.28

d. 43.84

e. 44.24

3. Alexis believes that the WRT Company will pay a dividend of $3.00 next year, $3.60 in year 2 and $3.90 in year 3. She believes that dividends will then grow at a constant rate of 3.90% forever. If the appropriate discount rate is 12%, then she values WRT Company stock at $ _____.

a. 40.48

b. 41.11

c. 42.41

d. 43.01

e. 43.93

4. Victoria is interested in adding some KLM, Inc. stock to her investment portfolio. She observes that the stock just paid a dividend of $4.00. Based on her estimates, dividends will grow at 20% for the next two years and 5% forever after that. Assuming a discount rate of 11.2%, Victoria knows that KLM, Inc. stock is worth $______.

a. 82.50

b. 83.62

c. 84.14

d. 85.10

e. 87.86

PLEASE SHOW YOUR WORK!

Answer 1

1. Let us first try to find out the present value of the deposits.

PV = (10600/1.05) + (10600/1.05³) + (10600/1.05⁵) + (10600/1.05⁷) + (10600/1.05⁹) = 41923.37

Future value of the above amount after 20 years = 41923.37 * 1.05²⁰ = 111235.18

2. Value of the stock = D₁ / (K_e-g) = 3.20 / (0.12-0.041) = 40.51

3. Present value of the dividends for the first 3 years = (3/1.12) + (3.6/1.12²) + (3.9/1.12³) = 8.32

Value of perpetuity at the end of the 3 years = 3.9 * (1+0.039) / (0.12-0.039) = 50.026

Present value for the above amount = 50.026 / 1.12³ = 35.61

Hence, value of the stock = 35.61+8.32 = 43.93

4. Present value of the dividends for the first two years = (4*1.2/1.112) + (4*1.2²/1.112²) = 8.975

Value of the perpetuity at the end of 2 years = 4*1.2²*1.05 / (0.112-0.05) = 97.55

Present value of the above amount = 97.55 / 1.112^{2 =} 78.89

Hence, value of the stock = 78.89+8.975 = 87.86