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¶ … Billy Bob bought 100 shares of Stock in Ben's Barbeque, Inc. For $37.50 per share. He sold them in January, 2004 for a total of $9,715.02. What is Billy Bob's annual rate of return?
Since Billy Bob held the investment for 54 years, the annual rate of return is best calculated using the compound rate of return formula: 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:
(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
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 + .15*130,000 = $99,250 annual cash flow
$99,250 * 10 years = $992,500 total expected cash flow
b. If the company's cost of capital is 10%, what is the expected net present value?
ANSWER: Net Present Value is calculated as the expected cash flow less the cost of capital, giving present value, and then subtracting the cost of the initial investment. The NPV for Mud's project is:
$992,500
Expected Cash Flow
(99,250)
Cost of Capital
$893,250
Present Value
(575,000)
Cost of initial investment less salvage value
$318,250
Net Present Value
c. Should the company buy the equipment?
ANSWER:…
References
Block, S. And Hirt, G. (2005). Foundations of Financial Management, Eleventh Edition. New York, NY: McGraw-Hill Irwin.
Mayo, H. (1982). Finance. New York, NY: CBS College Publishing.
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