Norris Co. has developed an improved version of its most popular product. To get this improvement to the market will cost $48 million but the project will return an additional $13.5 million for 5 years in net cash flows. The firm's debt-equity ratio is .25, the cost of equity is 13 percent, the pretax cost of debt is 9 percent, and the tax rate is 21 percent. All interest is tax deductible. What is the net present value of this proposed project

$0.88 million

Explanation:

For computing the net present value first we have to determine the after cost of debt, cost of capital which is shown below:

After tax cost of debt is

= 9% × (1 - 0.21)

= 7.11%

As we know that

Cost of capital = (Weight of debt × after tax cost of debt) + (Weight of equity × cost of equity)

= (0.25 ÷ 1.25 × 7.11%) + (1 ÷ 1.25 × 13%)

= 1.422% + 10.4%

= 11.82%

Now the net present value is

YearCash flowsDiscount rate 11.82%PV of cash inflows  (in millions)

0        -$48million                 1                         -$48.00  (B)

1         $13.5 million0.8942944017          $12.07

2         $13.5 million0.7997624769          $10.80

3         $13.5 million0.7152231058          $9.66

4         $13.5 million0.6396200195          $8.63

5         $13.5 million0.5720086027          $7.72

Total present value                              $48.88  (A)

Net present value                                                   $0.88 million (A - B)

The discount rate is computed by  

= 1 ÷ (1 + interest rate)^years

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