Question

Photochronograph Corporation (PC) manufactures time series photographic equipment. It is currently at its target debt-equity ratio of .7. It’s considering building a new $70 million manufacturing facility. This new plant is expected to generate aftertax cash flows of $7.3 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 6.9 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 2.4 percent of the proceeds. If the company issues these new bonds at an annual coupon rate of 4 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 .10. (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 23 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

Calculating Weights of three sources of capital

Debt/Equity = 0.70 = 0.70 / 1

We know that Debt + Equity = total capital

So Debt/Total capital = Debt/(Equity + Debt) = 0.70 / 1.70 = 41.18%

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

Equity/Total capital = 1 - (Debt/Total capital) = 1 - 41.18% = 58.82%

Hence, Weight of equity = 58.82%

Now we will find the weight of long term debt and accounts payable financing

We know that Accounts payable financing + Long term debt = Debt

It is given that Accounts payable Financing / Long term debt = 0.10 = 0.10 / 1

Now we get, Accounts payable financing / Debt = (0.10 / 1.10)

Accounts payable financing = Debt x (0.10/1.10)

Accounts payable financing % of total capital = Debt% of total capital x (0.10 / 1.10) = 41.18% x (0.10 / 1.10) = 3.74%

Weight of accounts payable + Weight of Long term debt = 41.18%

3.74% + Weight of Long term debt = 41.18%

Weight of Long term debt = 41.18% - 3.74% = 37.44%

Calculating WACC

Cost of equity = Required rate of return on company' new equity = 13%

It is known that if the bonds of company are selling at par then yield to maturity of the bond is equal to annual coupon rate of the bond

So Cost of long term debt = YTM of bonds = Annual coupon rate = 4%

It is given that After tax cost of accounts payable financing = WACC

Now

WACC = (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 = 58.82% x 13% + 37.44% x 4% x (1-23%) + 3.74% x WACC

WACC = 7.6466% + 1.1531% + 0.0374WACC

WACC - 0.0374WACC = 8.7997%

0.9626WACC = 8.7997%

WACC = 8.7997% / 0.9626 = 0.087997 / 0.9626 = 9.1415%

Calculating Flotation costs

Total capital raised = Initial investment = 70 million = 70 x 1000000 = 70000000

Equity raised = Weight of Equity x Total capital raised = 58.82% x 70000000

Flotation cost of equity = Flotation cost % x Equity raised = 6.9% x 58.82% x 70000000 = 2841006

Long term issued = Weight of Debt x Total capital raised = 37.44% x 70000000

Flotation cost of Long term Debt = Flotation cost % x Long term capital issued = 2.4% x 37.44% x 70000000 = 628992

Calculating NPV

Perpetual after tax cash flow = $7.3 million = 7.3 x 1000000 = 7300000

We know that present value perpetuity = Cash flow / Discount rate

So present value of after tax cash flow discounted at WACC = Cash flow / WACC = 7300000 / 9.1415%

NPV of the new plant = - Initial investment - Flotation cost of equity - Flotation cost of Long term Debt + Present value of after tax cash flows discounted at WACC

NPV of the new plant = -70000000 - 28410006 - 628992 + (7300000 / 9.1415%)

NPV of the new plant = -70000000 - 28410006 - 628992 + 79855603.5661

NPV of the new plant = 6385605.5661 = 6385606 (rounded to nearest whole dollar)

Hence NPV of the new plant = 6385606