Question

Photochronograph Corporation (PC) manufactures time series photographic equipment. It is currently at its target debt−equity ratio of .80. It’s considering building a new $45 million manufacturing facility. This new plant is expected to generate aftertax cash flows of $5.7 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 7.5 percent of the amount raised. The required return on the company’s new equity is 14 percent. 2. A new issue of 20-year bonds: The flotation costs of the new bonds would be 5 percent of the proceeds. If the company issues these new bonds at an annual coupon rate of 8 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 35 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 answer to the nearest whole dollar amount, e.g., 32.)

What is NPV

Answer 1

To find - Net Present Value of the project.

The methodology used = Perpetuity cash flow / Weighted average cost of capital deducted from Initial Investment and then, the floatation costs of the capital raised have been deducted from the NPV.

After-tax cash flow (Perpetuity) = 5.7 million

Methods used to raise capital =
1) Issued equity at a 14% rate of return and floatation cost of 7.5%
2) Bonds issued at an 8% rate of return and floatation cost of 5%
3) Trade payables at WACC

Debt to Equity ratio = 0.8

Investment = 45 million

WACC = (cost of equity * % of equity) + (cost of debt * % of debt * 1-tax rate)

Total Capital used =
Equity = 25 million
Debt = 20 million (17.39 million as long term debt and 2.61 as trade payables)
(Based on the 'trade payables to long term debt ratio os 0.15)

Total Capital Raised =
Equity = 25 million
Debt = 17.39 million
Total = 42.39 million

Amount of Equity = 25 million
Based on the debt to equity ratio of 0.8.
(45 million / 1.8) = 25 million)
Cost of equity = 14%
Therefore, the weighted cost of equity = 0.589 * 14% = 8.246%
(Weight calculation = Equity amount / total capital raised = 25/43.29 = 58.9%)

Amount of long term Debt raised = 17.39 million
Based on the debt to equity ratio of 0.8%.
((45 million * 0.8) // 1.8) = 20 million)
Cost of equity = 8%
Therefore, the weighted cost of equity = 0.41 * 8% =3.288%
(Weight calculation = Debt amount raised / total capital raised = 17.39/43.29 = 41.02%)

Total Firm WACC = 8.246% + 3.288% = 11.534%

==> Now, the trade payables component has to be added to the overall firm WACC. And this will be calculated by keeping Total Capital (45 million) used in the equation (mentioned above).

Amount of Trade Payables used = 2.61 million
Cost of Trade Payables = (Firm WACC) = 11.534%

FINAL WACC of the firm will be calculated considering all the 3 sources of capital, i.e., Equity raised, Debt raised and Trade Payables employed.

Total Capital = 45 million
Equity = 25 million = weight of 55.56% at 8.246%
Long term Debt = 17.39 million = weight of 38.64% at 3.288%
Trade Payables = 2.61 million = weight of 5.8% at 11.534%

Therefore, WACC = (0.5556 * 8.246%) + (0.3864 * 3.288%) + (0.058 * 11.534%) = 6.52%

NPV = Perpetuity cash flow / Weighted average cost of capital deducted from Initial Investment and then, the floatation costs of the capital raised have been deducted from the NPV.

Floatation costs for:
Equity = 25 million * 7.5% = 1,875,000
Debt = 17.39 million * 5% = 869,500
Total Floatation cost = 2,744,500

NPV (before adjusting for floatation cost) = (5700000 / 6.52%) - 45,000,000 = 42,423,313
NPV (after adjusting for floatation cost) = 42,423,313 - 2,744,500 = 39,678,813.

Hence, The NPV of the project is $39,678,813.

(NOTE: As floatation costs are a one-time payment made to the third parties, these costs are deducted from the NPV rather than incorporating these costs in the cost of capital calculations).