- Length: 5 pages
- Subject: Economics
- Type: Term Paper
- Paper: #19764825

Since Billy Bob held the investment for 54 years, the annual rate of return is best calculated using the compound rate of return formula:

(Future Value / Present Value) ^ (1 / n) -- 1, where n = number of years.

Filling the data into the above formula:

Billy Bob's return on his investment in Ben's Barbeque is 1.78% per year.

Yellow Fruit Company's bonds are currently selling for $1,157.75 per $1,000 par-value bond. The bonds have a 10% coupon rate and will mature in 10 years. What is the approximate yield to maturity of the bonds?

ANSWER:

Using the following formula:

c (1 + r)-1 + c (1 + r)-2 + . . . + c (1 + r)-n + B (1 + r)-n = P

where c = annual coupon payment (in dollars, not a percent) = $100

n = number of years to maturity = 10

B = par value = $1,000

P = purchase price = $1,157.75

Using our data for Yellow Fruit Company, we get:

100(1+r)-1 + 100(1+r)-2 + 100(1+r)-3 + 100(1+r)-4 + 100(1+r)-5 + 100(1+r)-6 + 100(1+r)-7 + 100(1+r)-8 + 100(1+r)-9 + 100(1+r)-10 + 1000(1+r) -10 = $1,157.75

Solving for r, the approximate yield to maturity for the Yellow Fruit Company's bonds is 7.683%.

Question 2: Bar T. Ranches, Inc. is considering buying a new helicopter for $350,000. The company's old helicopter has a book value of $85,000, but will only bring $60,000 if it is sold. The old helicopter can be depreciated at the rate of $13,500 per year for the next four years. The new helicopter can be depreciated using the 5-year MACRS schedule. The new helicopter is expected to save $62,000 after taxes through reduced fuel and maintenance expenses. Bar T. Ranches is in the 34% tax bracket and has a 12% cost of capital.

a. What is the cash inflow from selling the old helicopter?

Depreciation on the old equipment is $54,000 ($13,500 * 4 years). Depreciation on the new equipment is $306,635 for the same four-year period, and is calculated using the 5-year MACRS schedule. The assumption was made to use the MACRS Mid-Quarter convention since this problem was being solved in February, 2005 and the equipment purchase decision would be made in the first quarter of the year. The schedule used was:

Year

5-year depreciation rate for recovery period

New Equipment Depreciation

1

35.00%

$122,500

2

26.00

91,000

3

15.60

54,600

4

11.01

38,535

5

11.01

38,535

6

1.38

4,830

(source: www.irs.gov)

Replacing the old equipment results in a decrease in expenses and an increase in depreciation expense. Since the depreciation expense is a noncash expense that is recouping the cost of the investment, it is added back to profits to obtain the cash flow generated by the investment. Calculations are shown in the following table:

Present Helicopter

New Helicopter

Net Change

Depreciation

$54,000

$306,635

$252,635

Decrease in Expenses

$0

$248,000

$248,000

Cash Flow

$54,000

$554,635

$500,635

b. What is the net cost of the new helicopter?

ANSWER: The new helicopter costs $350,000, but the firm is able to sell the old equipment for $60,000, so the net outlay to replace the old equipment is reduced to $290,000. The decision as to whether to replace the existing equipment therefore depends on the present value of the increased cash flows and the present value of the $290,000 expenditure required to make the investment. The net present value of the investment is:

$500,635

Expected Cash Flow

60,076

Cost of Capital

$440,559

Present Value

290,000

Cost of initial investment less salvage value

$150,559

Net Present Value

Question 3: Mud Construction Co. is considering buying new equipment with a cost of $625,000 and a salvage value of $50,000 at the end of its useful life of ten years. The equipment is expected to generate additional annual cash flow for ten years with the following possibilities:

Probability

Cash Flow

.15

$60,000

.25

$85,000

.45

$110,000

.15

$130,000

a. What is the expected cash flow?

ANSWER: The expected cash flow is calculated as:

.15*60,000 + .25*85,000 + .45*110,000 +…