At current prices and a 13% cost of capital,a project's NPV is $100,000.By what minimum amount must the initial cost of the project decrease (revenues will be unchanged)before you would wait 2 years to invest?
A) $21,685
B) $26,000
C) $27,690
D) $29,380

Question

Quizplus · Accepted Answer

To calculate the minimum initial cost reduction needed to wait for 2 years, we need to use the following formula:

PV of Costs = PV of Benefits
where PV is the present value of cash flows

Given, NPV = $100,000, which means that the present value of benefits is $100,000 more than the present value of costs. Let's assume that the initial cost of the project is X.

So, NPV = PV of Benefits - PV of Costs
=> $100,000 = PV of Benefits - X

Also, the present value of benefits is the same as the initial cost (X), since revenues will be unchanged. Therefore,

PV of Benefits = X

Substituting this in the above equation, we get:

$100,000 = X - X/(1+13%)^2
=> $100,000 = X(1 - 1/1.169)^2
=> X = $100,000/(1 - 1/1.169)^2
=> X = $127,690

Thus, the initial cost of the project should be reduced by at least ($127,690 - X) = $27,690 to wait 2 years to invest.

Hence, the best choice is C.

At Current Prices and a 13% Cost of Capital,a Project's