Question

1. A Life Insurance company offers a perpetuity that pays annual payments of $20,000. This contract sells for $320,000 today. What is the interest rate?

2. Noly Corp. issued preferred stock at $1,000 with a 5.8% dividend. The current rate of return investors require is 6.0%. What is the maximum price investors would be willing to buy for the preferred stock?

3. Crinkle Inc. is selling a product that it expects will generate cash flows of $715,000 every year. The company’s required rate of return is 12.8%. What is the value of this product to the company?

4. For her retirement, Rebecca plans to invest $8,000 each year for 15 years. If she earns 7% per year and invests monthly starting now, how much will she have when she retires?

Answer 1

Solution 1:

Given that Annual payments, A = $20,000 and Present value, PV = $320,000

The interest rate, I would e

PV = A/I

$320,000 = $20,000/I

I = $20,000/$320,000

I = 0.0625 or 6.25%

Solution 2:

Given that Face value of preferred stock = $1,000, Dividend rate = 5.8% and current rate of return, k = 6%

The maximum price, P would be

k = Dividend/P0

0.06 = (0.058*1000)/P0

0.06 = 58/P0

P0 = $58/0.06

P0 = $966.67

Solution 3:

Given that Cash flow, CF = $715,000 and Rate of return,k = 12.8%

Value of the company = CF/k

Value of company = $715,000/0.128

Value of company = $5,585,937.5

Solution 4:

Given that Annual payment, A = $8,000, Number of years, n = 15 and Interest rate, I = 7%

The future value, FV would be

FV = A (FVIFA @ I, n)

FV = $8,000 (FVIFA @ 7%, 15)

FV = $8,000 [(1.07^15-1)/0.07]

FV = $8,000 (25.1290)

FV = $201,032.18