Consider a project to produce solar water heaters. It requires a $10 million inv

Question

Consider a project to produce solar water heaters. It requires a $10 million investment and offers a level after-tax cash flow of $1.73 million per year for 10 years. The opportunity cost of capital is 11.75%, which reflects the projects business risk.

Suppose the project is financed with $7 million of debt and $3 million of equity. The interest rate is 7.75% and the marginal tax rate is 34%. The debt will be paid off in equal annual installments over the projects 10-year life. Calculate APV. (Do not round intermediate calculations. Roundup your answer to the nearest whole dollar.)

If the firm incurs issue costs of $600,000 to raise the $3 million of required equity. Calculate APV. (Do not round intermediate calculations. Roundup your answer to the nearest whole dollar.)

Suppose the project is financed with $7 million of debt and $3 million of equity. The interest rate is 7.75% and the marginal tax rate is 34%. The debt will be paid off in equal annual installments over the projects 10-year life. Calculate APV. (Do not round intermediate calculations. Roundup your answer to the nearest whole dollar.)

Explanation / Answer

Adjusted Present Value = Present Value of Cash Flows + Present Value of Tax Savings

Scenario a:

Equity = $3,000,000

Debt = $7,000,000

Interest rate= 7.75%

Tax rate = 34%

Cost of capital = 11.75%

Cash flow after tax = $1,730,000

Present value of cash flows = Cash flow / cost of capital = $1,730,000 / 0.1175 = $14,723,404

Initial Investment = $10,000,000

NPV = PV of cash flows - Initial investment = $14,723,404 - $10,000,000 = $4,723,404

Interest outgo = $7,000,000 * 7.75% = $542,500

Present value of tax savings = ( Interest outgo * Tax rate ) / Rate of interest = ($542,500 * 34%) / 0.0775 = $2,380,000

Therefore, APV = $4,723,404 + $2,380,000 = $7,103,404

Scenario b:

Issue cost = $600,000

NPV = $4,723,404 (as calculated in part a)

Therefore, revised NPV = $4,723,404 - $600,000 = $4,123,404

Present value of tax savings = ( Interest outgo * Tax rate ) / Rate of interest = ($542,500 * 34%) / 0.0775 = $2,380,000

Therefore, APV = $4,123,404 + $2,380,000 = $6,503,404

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