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:
(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 + .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: The firm should buy the equipment because the present value of the new cash flows exceeds the cost of the investment.
QUESTION 4: Aero Company currently has net income of $3 million and 1 million common shares outstanding which sell for $20 per share. Aero has decided to issue new stock to raise $4,000,000 to expand its operations. Aero’s investment banker will sell the new shares for $18 per share with a spread of 7%. There will be a $60,000 registration cost.
a. Calculate the current EPS and PE ratio.
ANSWER: Using the EPS and PE formulas below:
Earnings per share =
Earnings available to common shareholder
Number of shares outstanding
Market Share Price
Earnings Per Share
Current earnings per share is equal to $3 ($3,000,000 / 1,000,000).
The P/E ratio is $6.67 ($20 / $3).
b. How many shares will have to be sold to net the $4,000,000 that Aero needs?
ANSWER: Because the investment banker is selling the shares with a spread of 7%, Aero only receives $16.74 per share. In addition, Aero needs to pay the registration cost of $60,000. Therefore, they need to sell 242,533 shares ($4,060,000 / $16.74) to net the $4,000,000 needed.
QUESTION 5: PG Corp has a bond outstanding with a par value of $1,000, an annual interest payment of $110, a market price of $1,200, and a maturity in 10 years. Determine the following:
a. Coupon rate
ANSWER: The coupon rate is 11% ($110 / $1,000).
b. Current yield
ANSWER: The current yield is 9.167% ($110 / $1,200).
c. Approximate yield to maturity.
ANSWER: Using the 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)
n = number of years to maturity
B = par value
P = purchase price
$110(1+r)-1 + $110(1+r)-2 + $110(1+r)-3 + $110(1+r)-4 + $110(1+r)-5 + $110(1+r)-6 + $110(1+r)-7 + $110(1+r)-8 + $110(1+r)-9 + $110(1+r)-10 + $1,000(1+r)-10 = $1,200
Solving for r we get an approximate yield to maturity of 8.017%.
QUESTION 6:
A. Explain how the price of a new security is determined.
ANSWER: Several factors go into determining the price of a new security. You can first look at the business and compare it to other like businesses. Calculating the price to earnings ratio will tell you how this company compares to the others. Additionally, you should look at how many interested buyers are looking to invest in this particular stock. The higher the demand, the higher the price can be, independent of what earnings the company actually has, similar to how it was a few years ago during the large dot com purchases. In this day and age, demand seems to be the primary driver for pricing stocks.
B. Shares of Darwin, Inc. sell for $20 per share. 40% of earnings are paid in dividends. What is the dividend yield? Earnings are $100,000, and there are 10,000 shares of stock outstanding.
ANSWER: Using the formula:
Dividend yield =
Dividends per Share
Market Share Price
Dividends per share is equal to $4 ($100,000 * 40% / 10,000). The dividend yield for Darwin, Inc. is 20% ($4 / $20).
QUESTION 7: Betsy Ross owns 918 shares of Flag Fabric Co. There are 13 directors to be elected. 31,000 shares of common stock are outstanding. There is cumulative voting.
a. How many votes can be cast for directors?
ANSWER: A total of 31,000 votes may be cast.
b. How many votes does Betsy control?
Betsy can cast 918 votes. Because Flag Fabric has cumulative voting, Betsy can cast her votes all for one director or she can spread them across the candidates.
c. What percentage of the vote does Betsy control?
ANSWER: Betsy controls 2.96% (918/31,000) of the total vote.
QUESTION 8: The stockholders’ equity portion of the balance sheet of Rollover Tire Company is as follows:
Common Stock (2,000,000 shares at $10 par)
$20,000,000
Paid-in-Capital in Excess of Par
17,000,000
Retained Earnings
33,000,000
$70,000,000
The current market value of Rollover stock is $20 per share. Show what the balance sheet would look like if Rollover declares a 10% stock dividend.
ANSWER: A stock dividend is a form of recapitalization and does not increase the assets of a company. A stock dividend merely transfers funds from retained earnings to common stock and paid-in-capital. When Rollover Tire Company issues the 10% stock dividend, 200,000 additional shares, with a value of $4,000,000 (200,000 shares * $20 per share), are issued. The $4,000,000 amount is subtracted from retained earnings and then $2,000,000 is transferred to common stock (calculated at $10 par price) and the remaining $2,000,000 balance is transferred to paid-in-capital. The resulting updated balance sheet is shown below:
Common Stock (2,200,000 shares at $10 par)
$22,000,000
Paid-in-Capital in Excess of Par
19,000,000
Retained Earnings
29,000,000
$70,000,000
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.
