Chapter 19

The price is different in a and b because a has longer period.

d. What are the current yields and the yields to maturity in a and b?

Current Yield:

a. $60 / $865.81 = 6.93%

b. $60 / $920.16 = 6.52%

Yield to Maturity (using Financial Calculator)

a. 8%

b. 8%

2.

a. A $1, 000 bond has a 7.5 percent coupon and matures after 10 years. If current interest rates are 10 percent, what should be the price of the bond?

Price = $1, 000 x 0.3855 + $1, 000 x 7.5% x 6.1446

Price = $385.50 + $460.85

Price = $846.35

b. If after six years interest rates are still 10 percent, what should be the price of the bond?

Price = $1, 000 x 0.6830 + $1, 000 x 7.5% x 3.1699

Price = $683 + $237.74

Price = $920.74

c. Even though interest rates did not change in a and b, why did the price of the bond change

The price of the bond changed because certain time period passed.

d. Change the interest in a and b to 6 percent and rework your answers. Even though the interest rate is 6 percent in both calculations, why are the bond prices different?

a.

Price = $1, 000 x 0.5584 + $1, 000 x 7.5% x 7.3601

Price = $558.40 + $552.01

Price = $1, 110.41

b.

Price = $1, 000 x 0.7921 + $1, 000 x 7.5% x 3.4651

Price = $792.10 + $259.88

Price = $1, 051.98

Bond prices are still different because the time period remains different.

4. Black stone, inc. has a five-year bond outstanding that pays $60 annually. The face value of each bond is $1, 000, and the bond sells for $890.

a. What is the bond’s coupon rate?

Coupon Rate = $60 / $1, 000 = 6%

b. What is the current yield?

Current Yield = $60 / $890 = 6.74%

c. What is the yield to maturity?

Using Financial Calculator: 8.814%

9. A bond has the following features:

• coupon rate interest: 8%
• principal: $1, 000
• term to maturity: 10 years

a. what will the holder receive when the bond matures? The principal of $1, 000

b. If the current rate of interest on comparable debt is 12 percent, what should be the price of this bond?

Price = $1, 000 x 0.3220 + $1, 000 x 8% x 5.6502

Price = $322 + $452.02

Price = $774.02

Would you expect the firm to call this bond? Why?

No; because the price of the bond is lower than the par (principal) value.

c. If the bond has a sinking fund that requires the firm to set aside annually with a trustee sufficient funds to retire the entire issue at maturity, how much must the firm remit each year for 10 years if the funds earn 9 percent annually and there is $10 million outstanding?

FV = Annual Payments x FV of Annuity Factor @9% for 10 years

$10, 000, 000 = Annual Payment x 15.19293

Annual Payment = $10, 000, 000 / 15.19293

Annual Payment = $658, 200.89

The firm should set aside $658, 200.89 at the end of each year.

Chapter 19

3. The management of a firm wants to introduce a new product. The product will sell for $4 a unit and can be produced by either of two scales of operation. In the first total cost are

TC = $ 3, 000 + 2.8Q.

In the second scale of operation, total costs are

TC = $ 5, 000 + 2.4Q.

a. What is the break-even level of output for each scale of operation?

First Scale:

Breakeven = $3, 000 / ($4 – $2.80)

Breakeven = $3, 000 / $1.2

Breakeven = 2, 500 units

Second Scale:

Breakeven = $5, 000 / ($4 – $2.40)

Breakeven = $5, 000 / $1.6

Breakeven = 3, 125 units

b. What will be the firm’s profits for each scale of operation if sales reach 5, 000 units?
First Scale:

Profit = ($4 x 5, 000 units) – [$3, 000 + (2.8 x 5, 000 units)]

Profit = $20, 000 – $17, 000

Profit = $3, 000

Second Scale:

Profit = ($4 x 5, 000 units) – [$5, 000 + (2.4 x 5, 000 units)]

Profit = $20, 000 – $17, 000

Profit = $3, 000

c. One half of the fixed costs are noncash (depreciation). All other expenses are for cash. If sales are 2, 000 units, will cash receipts cover cash expenses for each scale of operation?

First Scale:

Total Cost (Cash) = $1, 500 + ($2.8 x 2, 000 units) = $7, 100

Cash Sales = $4 x 2, 000 units = $8, 000