Question

CMS Corporation's balance sheet as of today is as follows:

Long-term debt (bonds, at par)	$10,000,000
Preferred stock	2,000,000
Common stock ($10 par)	10,000,000
Retained earnings	4,000,000
Total debt and equity	$26,000,000

The bonds have an 4.3% coupon rate, payable semiannually, and a par value of $1,000. They mature exactly 10 years from today. The yield to maturity is 12%, so the bonds now sell below par. What is the current market value of the firm's debt?

Select the correct answer.

a. $5,586,184

b. $5,585,483

c. $5,584,080

d. $5,584,782

e. $5,586,885

A 25-year, $1,000 par value bond has an 8.5% annual coupon. The bond currently sells for $1,025. If the yield to maturity remains at its current rate, what will the price be 5 years from now?

Select the correct answer.

a. $1,019.58

b. $1,022.19

c. $1,020.45

d. $1,023.06

e. $1,021.32

5-year Treasury bonds yield 3.7%. The inflation premium (IP) is 1.9%, and the maturity risk premium (MRP) on 5-year bonds is 0.4%. What is the real risk-free rate, r*?

Select the correct answer.

a. 1.21%

b. 1.40%

c. 1.59%

d. 1.02%

e. 0.83%

A stock is expected to pay a dividend of $0.75 at the end of the year. The required rate of return is r_s = 10.5%, and the expected constant growth rate is g = 5.5%. What is the stock's current price?

Select the correct answer.

a. $17.44

b. $16.22

c. $15.00

d. $18.66

e. $19.88

A stock just paid a dividend of D₀ = $1.50. The required rate of return is r_s = 11.0%, and the constant growth rate is g = 4.0%. What is the current stock price?

Select the correct answer.

a. $21.75

b. $21.21

c. $22.29

d. $22.02

e. $21.48

$31.00 per share is the current price for Foster Farms' stock. The dividend is projected to increase at a constant rate of 5.50% per year. The required rate of return on the stock, r_s, is 9.00%. What is the stock's expected price 3 years from today?

Select the correct answer.

a. $34.50

b. $34.13

c. $35.24

d. $34.87

e. $33.76

Answer 1

1. We shall use the financial calculator in order to solve this problem:

Coupon rate = 4.3 / 2 = 2.15% (Since the payments are semi annually)

Now we shall plug the below figures in the financial calculator:

N = 20 years ( 10 x 2 , since the payments are semi annual)

I/Y = 6 (12 / 2, since the payments are semi annual)

FV = $ 1000

PMT = 1000 x 2.15% i.e. $ 21.50

CPT PV = $ 558.4080

This is the value of 1 bond. In order to compute the value of 10,000 bonds (i.e. 10,000,000 / 1,000), we need to multiply it by 10,000 which will give us the value to be $ 5,584,080 i.e. option c is the correct answer.

2. In this part we shall first calculate Yield to Maturity i.e. I/Y by using the financial calculator as follows:

N = 25

PV = $ - 1,025

FV = $ 1,000

PMT = 8.5% x 1000 = $ 85

CPT I/Y = 8.2606 %

Now for determining price after 5 years we shall plug the below numbers in the financial calculator as follows:

N = 20 (Since 5 years has elapsed from 25 years)

FV = $ 1,000

I/Y = 8.2606

PMT = 8.5% x 1000 = $ 85

CPT PV = $ 1,023.06, i.e. option d is the correct answer

3. Real Risk Free Rate = 5 year Treasury bond yield - Inflation Premium - Maturity Risk Premium

= 3.7% - 1.9% - 0.4%

= 1.4% i.e. option b is the correct answer.

4. We shall use the following formula in order to compute the price:

[ Expected Dividend / (Required rate of return - Growth rate) ]

Expected dividend = $ 0.75

Required rate of return = 10.5 % or 0.105

Growth Rate = 5.5% or 0.055

By plugging these figures in the above mentioned formula we shall get:

= [ $ 0.75 / ( 0.105 - 0.055) ]

= $ 15 i.e. option c is the correct answer

5. We shall use the following formula in order to compute the price:

[ Dividend just paid ( 1 + growth rate ) / (Required rate of return - Growth rate) ]

Dividend just paid = $ 1.50

Growth rate = 4% or 0.04

Required rate of return = 11% or 0.11

By plugging these figures in the above mentioned formula we shall get:

= [ $ 1.50 ( 1 + 0.04 ) / ( 0.11 - 0.04) ]

= $ 22.29 i.e. option c is the correct answer.

6. In order to solve this part, we first need to calculate the dividend by using the below formula

Current Price = [ Dividend at end of year 1 / (Required rate of return - Growth rate ) ]

31 = [ Dividend at end of year 1 / ( 0.09 - 0.055) ]

Dividend at end of year 1 = $ 1.085

Dividend at end of year 2 = 1.085 x 1.055 (i.e. dividends are increasing at at rate of 5.5% or 0.055 per year) i.e. 1.1447

Dividend at end of year 3 = 1.1447 x 1.055 = $ 1.2077

Now the stocks expected price three years from today shall be

= [ 1.2077 / ( 0.09 - 0.055 ) ]

$ 34.50 i.e. option A is the correct answer

Feel free to ask in case of any query relating to this question.