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21. The total cost including flotation costs was:
Using the equation to calculate the total cost including flotation costs, we get:
(Amount raised)(1 – fT) = Amount needed after flotation costs
Now, we know the weighted average flotation cost. The equation to calculate the percentage flotation
costs is:
We can solve this equation to find the debt-equity ratio as follows:
We must recognize that the V/E term is the equity multiplier, which is (1 + D/E), so:
22. To find the aftertax cost of debt for the company, we need to find the weighted average of the four
debt issues. We will begin by calculating the market value of each debt issue, which is:
So, the total market value of the company’s debt is:
The weight of each debt issue is:
Next, we need to find the YTM for each bond issue. The YTM for each issue is:
P1 = $1,031.80 = $25(PVIFAR%,10) + $1,000(PVIFR%,10)
P2 = $1,128.00 = $35.50(PVIFAR%,16) + $1,000(PVIFR%,16)
P3 = $1,074.50 = $31.50(PVIFAR%,31) + $1,000(PVIFR%,31)
P4 = $1,027.50 = $29.50(PVIFAR%,50) + $1,000(PVIFR%,50)
The weighted average YTM of the company’s debt is thus:
And the aftertax cost of debt is:
23. a. Using the dividend growth model, the cost of equity is:
b. Using the CAPM, the cost of equity is:
c. When using the dividend growth model or the CAPM, you must remember that both are
24. First, we need to find the adjusted cash flow from assets (CFA*) for each year. We are given the
projected EBIT, depreciation, increase in NWC, and capital spending. Each of these accounts
increase at 18 percent per year. So, the CFA* for each of the next five years will be:
Year 1 Year 2 Year 3 Year 4 Year 5
EBIT $1,800,000 $2,124,000 $2,506,320 $2,957,458 $3,489,800
The cash flows will grow at 3 percent in perpetuity, so the terminal value of the company in Year 5
will be:
Terminal value5 = CFA*6/(WACC – g)
The value of the company today is the present value of the first five CFA*s, plus the value today of
the terminal value, or:
To find the value of equity, we subtract the value of the debt from the total value of the company,
which is:
Finally, the value per share is the total equity value divided by the shares outstanding, or:
25. The CFA* for each of the first five years will be the same as the previous problem. To calculate the
terminal value, we can use the price-sales ratio, which will be:
The value of the company today is the present value of the first five CFA*s, plus the value today of
the terminal value, or:
To find the value of equity, we subtract the value of the debt from the total value of the company,
which is:
Finally, the value per share is the total equity value divided by the shares outstanding, or:
Challenge
26. First, we need to find the adjusted cash flow from assets (CFA*) for each year. At the growth rates
given, the projected CFA* for each of the next five years will be:
Year 1 Year 2 Year 3 Year 4 Year 5
EBIT $3,622,500 $4,165,875 $4,790,756 $5,509,370 $6,335,775
Depreciation 318,000 381,600 457,920 549,504 659,405
The cash flows will grow at 3.5 percent in perpetuity, so the terminal value of the company in Year 5
will be:
Terminal value5 = CFA*6/(WACC – g)
The value of the company today is the present value of the first five CFA*s, plus the value today of
the terminal value, or:
Company value = $2,434,050/1.0925 + $2,791,133/1.09252 + $3,199,595/1.09253
To find the value of equity, we subtract the value of the debt from the total value of the company,
which is:
Finally, the value per share is the total equity value divided by the shares outstanding, or:
27. The CFA* for each of the first five years will be the same as the previous problem. To calculate the
terminal value, we can use the price-sales ratio, which will be:
The value of the company today is the present value of the first five CFA*s, plus the value today of
the terminal value, or:
To find the value of equity, we subtract the value of the debt from the total value of the company,
which is:
Finally, the value per share is the total equity value divided by the shares outstanding, or:
28. We can use the debt-equity ratio to calculate the weights of equity and debt. The debt of the company
has a weight for long-term debt and a weight for accounts payable. We can use the weight given for
Since the accounts payable has the same cost as the overall WACC, we can write the equation for the
WACC as:
Solving for WACC, we find:
We will use basically the same equation to calculate the weighted average flotation cost, except we
will use the flotation cost for each form of financing. Doing so, we get:
The total amount we need to raise to fund the new equipment will be:
Since the cash flows go to perpetuity, we can calculate the present value using the equation for the
PV of a perpetuity. The NPV is:
29. We can use the debt-equity ratio to calculate the weights of equity and debt. The weight of debt in
the capital structure is:
And the weight of equity is:
Now we can calculate the weighted average flotation costs for the various percentages of internally
raised equity. To find the portion of equity flotation costs, we can multiply the equity costs by the
percentage of equity raised externally, which is one minus the percentage raised internally. So, if the
company raises all equity externally, the flotation costs are:
The initial cash outflow for the project needs to be adjusted for the flotation costs. To account for the
flotation costs:
Amount raised(1 – .0531) = $51,000,000
If the company uses 60 percent internally generated equity, the flotation cost is:
And the initial cash flow will be:
Amount raised(1 – .0276) = $51,000,000
If the company uses 100 percent internally generated equity, the flotation cost is:
And the initial cash flow will be:
Amount raised(1 – .0106) = $51,000,000
30. The $2.7 million cost of the land three years ago is a sunk cost and is irrelevant; the $3.8 million
appraised value of the land is an opportunity cost and is relevant. The $4.1 million land value in five
MVD = 195,000($1,000)(1.06) = $206,700,000
The total market value of the company is:
Next we need to find the cost of funds. We have the information available to calculate the cost of
equity using the CAPM, so:
The cost of debt is the YTM of the company’s outstanding bonds, so:
And the aftertax cost of debt is:
The cost of preferred stock is:
a. The weighted average flotation cost is the sum of the weight of each source of funds in the
capital structure of the company times the flotation costs, so:
The initial cash outflow for the project needs to be adjusted for the flotation costs. To account
for the flotation costs:
So the cash flow at time zero will be:
There is an important caveat to this solution. This solution assumes that the increase in net
Total cost of NWC including flotation costs:
This would make the total initial cash flow:
b. To find the required return on this project, we first need to calculate the WACC for the
company. The company’s WACC is:
The company wants to use the subjective approach to this project because it is located overseas.
The adjustment factor is 2 percent, so the required return on this project is:
c. The annual depreciation for the equipment will be:
So, the book value of the equipment at the end of five years will be:
So, the aftertax salvage value will be:
d. Using the tax shield approach, the OCF for this project is:
OCF = [(P – v)Q – FC](1 – TC) + TCD
e. The accounting break-even sales figure for this project is:
QA = (FC + D)/(P – v)
f. We have calculated all cash flows of the project. We just need to make sure that in Year 5 we
add back the aftertax salvage value and the recovery of the initial NWC. The cash flows for the
project are:
Year Cash Flow
0 –$41,395,308
1 13,583,750
Using the required return of 10.74 percent, the NPV of the project is:
And the IRR is:
If the initial NWC is assumed to be financed from outside sources, the cash flows are:
Year Cash Flow
0 –$41,487,748
1 13,583,750
With this assumption, and the required return of 10.74 percent, the NPV of the project is:
And the IRR is:
31. With the assumptions given, the adjusted cash flows are a perpetuity, so we can discount the cash
flows using the perpetuity equation.
