Question

Joshua Industries is considering a new project with cash inflows of $478,000 for the indefinite future. Cash costs are 68 percent of the cash inflows. The initial cost of the investment is $685,000. The tax rate is 34 percent and the unlevered cost of equity is 14.2 percent. The firm is financing $200,000 of the project cost with debt. What is the adjusted present value of the project?

A. $102,429.67
B. $98,311.16
C. $32,408.18
D. $93,940.85

Answer 1

D. $93,940.85

Step-by-step explanation:

Cash inflows (Ci) = $478,000

Cash costs (Cc) = 0.68 of Ci

Initial investment (I) = $685,000

Tax rate (r) = 0.34

Unlevered cost of equity (Ue) = 0.142

Amount financed with cost of debt (D) = $200,000

Earnings after taxes (E) are given by:

`E = C_c(1-C_i)(1-r)\\E=\$478,000*(1-0.68)*(1-0.34)\\E=\$100,953.60`

Net present value is given by the earnings adjusted by the unlevered cost of equity minus the initial investment:

`NPV = (E)/(U_e) -I\\NPV = (\$100,953.60)/(0.142) -\$685,000\\NPV=\$25,940.85`

The adjusted present value (APV) is given by the NPV added to the present value of the cost of debt financing:

`APV =NPV+(D*r)\\APV =\$25,940.85 +(\$200,000*0.34)\\APV = \$93,940.85`