Problem 7-21
a. The initial investment would be equal to the plant and equipment
expenditure of $50,000 plus the working capital for the first-year.
The working capital for the first-year is defined as 20% of the
revenues of year 1, so it is equal to $8,000. Therefore, the total
initial investment is $58,000. The working capital requirement for
years 2 and 3 is $6000, $4000, respectively. Because the business
ends at the end of Year 4, there is a return of $20,000 in working
capital then.
b. Straight-line depreciation over four years means that the plant
and equipment will be depreciated in equal amounts over four years. A
salvage value of zero means that the plant and equipment will be
completely depreciated after four years. Therefore, the annual
depreciation is equal to $50,000 divided by four or $12,500 per year.
The tax payment per period is equal to the (revenue minus the expenses
minus the depreciation) multiplied by 40%. Working capital is not an
expense, so it is not used in this calculation. In the third and
fourth years, the depreciation plus the expenses exceeds the revenue,
so there is no tax payment due. The taxes for year one are $4600, for
year two are $2200, and for years three and four are zero dollars,
respectively.
The cash flow in each year is determined by taking the revenue minus
the expenses minus the working capital used minus the tax payment.
Depreciation is a noncash expense, so it does not affect cash flow.
The cash flow for year zero is -$58,000, for year one is $13,400, for
year two is $11,800, for year three is $10,000, and for year four is
$26,000.
c. The net present value is calculated by subtracting the initial
investment amount from the sum of the cash flow for each period
divided by (1 + i)^n where i is the cost of capital and n is the
period. The net present value for the project is -$10,794.62.
Generally, one wishes to avoid projects with negative net present
values.
d. The internal rate of return is the value of i for which the net
present value equation equals zero. An iterative approach is required
to solve this one. My Hewlett-Packard calculator calculates an
internal rate of return of approximately 1.95%. If the cost of
capital were less than 1.95%, then the project would have a positive
net present value.
Here is a table of computed values:
Year 0 1 2 3 4
Plant -$50,000
Revenue $40,000 $30,000 $20,000 $10,000
Expenses -$16,000 -$12,000 -$8,000 -$4000
Working Capital -$8,000 -$6,000 -$4000 -$2000 $20,000
Depreciation -$12,500 -$12,500 -$12,500 -$12,500
Tax Payment -$4600 -$2200 $0 $0
Cash Flow -$58,000 $13,400 $11,800 $10,000 $26,000
Present Value -$10,794.62
Internal Rate of Return 1.95%
Problem 6-20
a. The net present value of a series of cash flows is calculated by
the formula NPV = -I + C(n)/(1 + r)^n where C(1) is the cash flow in
period n, I is the initial investment, and r is the interest-rate
Rate NPV A NPV B
0 4000 5000
2 3071.066 3558.058
4 2200.728 2224.909
6 1384.096 990.4821
8 616.7759 -154.194
10 -105.184 -1217.13
12 -785.35 -2205.49
14 -1426.94 -3125.71
16 -2032.88 -3983.56
18 -2605.82 -4784.23
20 -3148.15 -5532.41
As you can see, the net present value of Project B is higher than that
of Project A for interest rates of 4% or less. Project A is preferred
for interest rates of 6% or more, although Project A becomes
potentially unattractive for interest rates of 10% or higher.
One project is preferred over another if it's net present value is
greater than that of the other Project (it has a higher POSITIVE net
present value or has a lesser NEGATIVE net present value). Since the
net present value of Project B is greater than the net present value
of Project A, it is preferred for discount rates of 0% to 4%. For
discount rates of 6% to 20%, Project A is preferred because it has a
greater net present value (it is less negative in those cases where
both are negative) then does Project B. However, in general, one tries
to avoid projects with zero or negative net present values.
b. The Internal Rate of Return is the value of r for which the Net
Present Value is zero. In this case, it can be solved using simple
algebra. The Internal Rate of Return for Project A is 9.7%, and the
Internal Rate of Return for Project B is 7.72%. This makes sense
based on what we saw above where Project B had a slightly negative net
present value at 8% and Project A had a slightly negative net present
value at 10%.
Problem 11-10
The Weighted Average Cost of Capital is calculated using the formula
r* = rD (1-TC) D/V + rE (E/V) where r* is the weighted average cost of
capital, rD is the firm's current borrowing rate, TC is the firm's
marginal income tax rate, rE is the expected rate of return on the
firm's stock, D is the market value of the firm's debt, E is the
market value of the firm's equity, and V is the total market value of
the firm (D + E).
From the problem, we know that rE is 15% and TC is 40%.
D is determined by multiplying the par value of $5 million by the 110%
premium currently prevailing in the market, which equals $5,500,000.
rD is determined by dividing the yield to maturity on the bonds of 9%
by the 110% premium currently prevailing in the market, which equals
8.18%.
E is determined by dividing the firm's book value of the equity by the
book value per share and then multiplying the result by the price per
share. $10 million book value/$20 book value per share = 500,000
shares outstanding. 500,000 shares*$30 per share = $15 million.
V is determined by adding D and E, which equals $20,500,000.
Plugging the above values into the Weighted Average Cost of Capital
formula given above results in an r* of 12.29%.
Sincerely,
Wonko |
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