Question

Photochronograph Corporation (PC) manufactures time series photographic equipment. It is currently at its target debt−equity ratio of .85. It’s considering building a new $58 million manufacturing facility. This new plant is expected to generate aftertax cash flows of $7 million in perpetuity. The company raises all equity from outside financing. There are three financing options: 1. A new issue of common stock: The flotation costs of the new common stock would be 8.8 percent of the amount raised. The required return on the company’s new equity is 13 percent. 2. A new issue of 20-year bonds: The flotation costs of the new bonds would be 4.0 percent of the proceeds. If the company issues these new bonds at an annual coupon rate of 7 percent, they will sell at par. 3. Increased use of accounts payable financing: Because this financing is part of the company’s ongoing daily business, it has no flotation costs, and the company assigns it a cost that is the same as the overall firm WACC. Management has a target ratio of accounts payable to long-term debt of .20. (Assume there is no difference between the pretax and aftertax accounts payable cost.) What is the NPV of the new plant? Assume that PC has a 40 percent tax rate. (Enter your answer in dollars, not millions of dollars, e.g. 1,234,567. Do not round intermediate calculations and round your final answer to the nearest whole dollar amount, e.g., 32.) NPV

Answer 1

Step 1: Calculate Accounts Payable Weight and Long-Term Debt Weight

The accounts payable and long-term debt weight is calculated as below:

Accounts Payable Weight = Proportion of Accounts Payable/(Proportion of Accounts Payable + Proportion of Long Term Debt) = .20/(.20+1) = 16.67%

Long-Term Debt Weight = Proportion of Long-Term Debt/(Proportion of Accounts Payable + Proportion of Long Term Debt) 1/(.20+1) = 83.33%

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Step 2: Calculate WACC

The WACC can be arrived with the following equation

WACC = Weight of Equity*Cost of Equity + Weight of Debt*[Accounts Payable Weight*WACC + Long-Term Debt Weight*Cost of Long-Term Debt*(1-Tax Rate)

Substituting values in the above formula, we get,

WACC = 1/(1+.85)*13% + .85/(1+.85)[.20/1.20*WACC + 1/1.20*7%*(1-40%)]

WACC = .0703 + .4595*[.20/1.20*WACC + .035]

WACC = .0703 + .0766WACC + .0161

Rearranging values, we get,

WACC - .0766WACC = 0.0864

WACC = 0.0864/(1-.0766) = 9.35%

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Step 3: Calculate Weighted Average Flotation Cost

The flotation cost is determined as follows:

Weighted Average Flotation Cost = Weight of Equity*Flotation Cost of Equity + Weight of Debt*[Accounts Payable Weight*Flotation Cost + Long-Term Debt Weight*Flotation Cost of Long-Term Debt

Substituting values in the above equation, we get,

Weighted Average Flotation Cost = 1/(1+.85)*8.8% + .85/(1+.85)[.20/1.20*0 + 1/1.20*4%]

Solving further, we get,

Weighted Average Flotation Cost = .0476 + .4595*(0 + .0333) = 6.29%

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Step 4: Calculate Amount Needed to be Raised

The amount needed to be raised is derived as below:

Amount Needed to be Raised = 58,000,000/(1-6.29%) = $61,891,943.86

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Step 5: Calculate NPV

The NPV is determined as follows:

NPV = Amount Needed to be Raised + Annual After-Tax Inflow/WACC = -61,891,943.86 + 7,000,000/9.35% = $12,964,602.83 (answer)

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Notes:

There can be a slight different in final answer on account of rounding off values.