Chapter 13

1. A $1,000 bond has a coupon of 6 percent and matures after 10 years.

a. What would be the bond’s price if comparable debt yields 8 percent?

Price = $1,000 x 0.4632 + $1,000 x 6% x 6.7101

Price = $463.20 + $402.61

Price = $865.81

b.What would be the price if comparable debt yields 8 percent and the bond matures after five years?

Price = $1,000 x 0.6806 + $1,000 x 6% x 3.9927

Price = $680.60 + $239.56

Price = $920.16

c.Why are the prices different in a and b?

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

Yes; cash receipt can cover cash expenses

Second Scale:

Total Cost (Cash) = $2,500 + ($2.4 x 2,000 units) = $7,300

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

Yes; cash receipt can cover cash expenses

d.The anticipated levels of sales are
YearUnit sales
14,000
25,000
36,000
47,000
If management select the scale of production with higher fixed cost, what can it expect in years 1 and 2?

On Year 1, the management can expect lower profit using the scale with higher fixed cost. On Year 2, the management can expect indifference of profit between either scales of production.

On what grounds can management justify selecting this scale of operation?

The indifference point, which is shown in (b), should be the ground in selecting which scale of production should be used. If the management forecasted a sale below 5,000 units, it is better to use the first scale; if above 5,000 units, the second scale should be used and if equal to 5,000 units, either of the scales of production may be used.

If sales reach only 5,000 a year, was the correct scale of operation chosen?

Generally, yes. At 5,000 level of sales, neither scales of production is a wrong choice as either of the two may be used because they will just yield the same profit.

3. A firm has the following total revenue and total cost schedules:
TR = $2Q.
TC = $4,000 + $1.5Q

a. What is the break-even level of output?

Breakeven = $4,000 / ($2 – $1.50)

Breakeven = $4,000 / $0.5

Breakeven = 8,000 units

What is the level of profits at sales of 9,000 units?
Profit = (9,000 units x $2) – [$4,000 + ($1.50 x 9,000 units)]

Profit = $18,000 – $17,500

Profit = $500

b. As the result of a major technological breakthrough, the total cost schedule is changed to: TC = $6000 + $ 0.5Q.

What is the break-even level of output?

Breakeven = $6,000 / ($2 – $0.50)

Breakeven = $6,000 / $1.50

Breakeven = 4,000 units

What is the level of profits at sales of 9,000 units?

Profit = (9,000 units x $2) – [$6,000 + ($0.50 x 9,000 units)]

Profit = $18,000 – $10,500

Profit = $7,500

4. The manufacturer of a product that has a variable cost of $2.50 per unit and total fixed cost of $125,000 wants to determine the level of output necessary to avoid losses.

a.What level of sales is necessary to break even if the product is sold for $4.25?

Breakeven = $125,000 / ($4.25 – $2.50)

Breakeven = $125,000 / $1.75

Breakeven = 71,429 units

What will be the manufacturer’s profit or loss on the sales of 100,000 units?
Profit = (100,000 units x $4.25) – ($125,000 + (100,000 units x $2.50)

Profit = $425,000 – 375,000

Profit = $50,000

b.If fixed costs rise to $175,000, what is the new level of sales necessary to break even?
Breakeven = $175,000 / ($4.25 – $2.50)

Breakeven = $175,000 / $1.75

Breakeven = 100,000 units

c.If variable costs decline to $2.25 per unit, what is the new level of sales necessary to break even?
Breakeven = $125,000 / ($4.25 – $2.25)

Breakeven = $125,000 / $2.00

Breakeven = 62,500 units

d.If fixed costs were to increase to $175,000, while variable costs declined to $2.25 per unit, what is the new break-even level of sales?
Breakeven = $175,000 / ($4.25 – $2.25)

Breakeven = $175,000 / $2.00

Breakeven = 87,500 units

e. If a major proportion of fixed costs were noncash (depreciation), would failure to achieve the break-even level of sales imply that the firm cannot pay its current obligations as they come due?

No; it does not imply so.

Suppose $100,000 of the above fixed costs of $125,000 was depreciation expense, what level of sales would be the cash break-even of sales?

Cash Breakeven = $25,000 / ($4.25 – $2.50)

Cash Breakeven = $25,000 / $1.75

Cash Breakeven = 14,286 units