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 $68 million manufacturing facility. This new plant is expected to generate aftertax cash flows of $6.1 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 7.2 percent of the amount raised. The required return on the company’s new equity is 11 percent. 2. A new issue of 20-year bonds: The flotation costs of the new bonds would be 2.2 percent of the proceeds. If the company issues these new bonds at an annual coupon rate of 5 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 .15. (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 21 percent tax rate. (Do not round intermediate calculations and enter your answer in dollars, not millions, rounded to the nearest whole dollar amount, e.g., 1,234,567.)

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) = .15/(.15+1) = .15/1.15 = 13.04%

Long-Term Debt Weight = Proportion of Long-Term Debt/(Proportion of Accounts Payable + Proportion of Long Term Debt) = 1/(.15+1) = 1/1.15 = 86.97%

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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)*11% + .85/(1+.85)[.15/1.15*WACC + 1/1.15*5%*(1-21%)]

WACC = .0595 + .4595*[.15/1.15*WACC + .0343]

WACC = .0595 + .0599WACC + .0158

Rearranging values, we get,

WACC - .0599WACC = .0753

WACC = .0753/(1-.0599) = 8.00%

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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)*7.2% + .85/(1+.85)[.15/1.15*0 + 1/1.15*2.2%]

Solving further, we get,

Weighted Average Flotation Cost = .0389 + .4595*(0 + .0191) = 4.77%

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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 = 68,000,000/(1-4.77%) = 71,406,712.73

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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 = -71,406,712.73 + 6,100,000/8.00% = $4,843,287.27 (answer)

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Notes:

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