Question

Photochronograph Corporation (PC) manufactures time series photographic equipment. It is currently at its target debt–equity ratio of .56. It’s considering building a new $71.3 million manufacturing facility. This new plant is expected to generate aftertax cash flows of $7.88 million in perpetuity. There are three financing options: A new issue of common stock: The required return on the company’s new equity is 15.1 percent. A new issue of 20-year bonds: If the company issues these new bonds at an annual coupon rate of 7.3 percent, they will sell at par. Increased use of accounts payable financing: Because this financing is part of the company’s ongoing daily business, 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 .14. (Assume there is no difference between the pretax and aftertax accounts payable cost.) If the tax rate is 38 percent, what is the NPV of the new plant? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Calculating Weights of three sources of capital

Debt/Equity = 0.56 = 0.56/ 1

We know that Debt + Equity = total capital

So Debt/Total capital = Debt/(Equity + Debt) = 0.56 / 1.56 = 35.90%

Also, (Debt/Total Capital) + (Equity/Total capital) = 1

Equity/Total capital = 1 - (Debt/Total capital) = 1 - 35.90% = 64.10%

Therefore, Weight of equity in total capital = 64.10%

It is know that, accounts payable financing + long term debt = debt

We know that accounts payable / Long term debt = 0.14 = 0.14 / 1

Accounts payable financing / Debt = (0.14 / 1.14)

Accounts payable financing = Debt x (0.14/1.14)

Percentage of accounts payable financing in total capital = Percentage of debt in of total capital x (0.14 / 1.14) = 35.90% x (0.14/1.14) = 4.41%

Weight of accounts payable financing in total capital = 4.41%

Weight of accounts payable in total capital + Weight of Long term debt in total capital = Weight of debt in total capital

Weight of accounts payable in total capital + Weight of Long term debt in total capital = 35.90%

4.41% + Weight of Long term debt in total capital = 35.90%

Weight of Long term debt in total capital = 35.90% - 4.41% = 31.49%

Hence Weight of long term debt in total capital = 31.49%

Calculating WACC

Required rate of return on company' new equity = Cost of equity = 15.1%

If the bonds of a company are selling or trading at par, then it is known that Yield to maturity of bonds will be equal to annual coupon rate of bond.

As the company's bond will sell at par, therefore Cost of long term debt = YTM of bonds = Annual coupon rate = 7.3%

We know that, After tax cost of accounts payable financing = WACC of the company

Now

WACC of the company = (Weight of equity)(Cost of equity) + (Weight of Long term debt)(Cost of long term debt)(1-Tax rate) + (Weight of accounts payable financing)(After tax cost of accounts payable financing)

WACC = 64.10% x 15.1% + 31.49% x 7.3% x (1-38%) + 4.41% x WACC

WACC = 9.6791% + 1.4252% + 4.41%WACC

WACC - 0.0441WACC = 11.1043%

0.9559 WACC = 0.111043

WACC = 0.111043 / 0.9559 = 11.6165% = 11.6165%

Calculating NPV of the new plant

Perpetual after tax cash flow = $7.88 million = 7.88 x 1000000 = $7880000

Present value perpetuity = Cash flow / Discount rate

Now, present value of after tax cash flow discounted at WACC = Cash flow / WACC = 7880000 / 11.6165%

NPV of the new plant = - Initial investment + Present value of after tax cash flows discounted at WACC

NPV of the new plant = -71300000 + (7880000 / 11.6165%) = -71300000 + 67834545.6893 = -3465454.3107 = -3465454.31 (rounded to two decimal places)

Hence NPV of the new plant = -3465454.31