The management of Osborn Corporation is investigating an investment in equipment that would have a useful life of 8 years. The company uses a discount rate of 12% in its capital budgeting. The net present value of the investment, excluding the annual cash inflow, is −$403,414. To the nearest whole dollar how large would the annual cash inflow have to be to make the investment in the equipment financially attractive? (Ignore income taxes.)Click here to view Exhibit 14B-1 and Exhibit 14B-2, to determine the appropriate discount factor(s) using the tables provided.

Question

Quizplus · Accepted Answer

To determine the annual cash inflow, we need to use the formula for net present value:

NPV = -Initial Investment + PV of Cash Inflows

We know that the NPV is -$403,414 and the initial investment is the cost of the equipment. We don't have that information, so we'll call it "C."

-$403,414 = -C + PV of Cash Inflows

We need to solve for the PV of cash inflows. We can use the present value annuity factor (PVAF) from Exhibit 14B-1. The PVAF for 8 years at a discount rate of 12% is 5.6502.

-$403,414 = -C + PVAF x Annual Cash Inflow

-$403,414 = -C + 5.6502 x Annual Cash Inflow

We can rearrange the equation to solve for the annual cash inflow:

Annual Cash Inflow = (NPV + C) / PVAF

Annual Cash Inflow = ($403,414 + C) / 5.6502

We don't know C, but we do know that the annual cash inflow needs to make the investment financially attractive. That means the NPV needs to be positive, which would make the equation:

NPV = -C + PV of Cash Inflows

0 = -C + PV of Cash Inflows

C = PV of Cash Inflows

Now we can use that information to solve for the annual cash inflow:

Annual Cash Inflow = ($403,414 + PV of Cash Inflows) / 5.6502

The PV of Cash Inflows is the same as the initial investment, so we can substitute "C" for it:

Annual Cash Inflow = ($403,414 + C) / 5.6502

We don't know C, but we know that it needs to be less than the annual cash inflow for the NPV to be positive. We can try each answer choice until we find the one that works:

A) ($403,414 + $48,410) / 5.6502 = $104,189.64 
NPV = -$403,414 + ($104,189.64 x 5.6502) = $23,859.84 (positive)

B) ($403,414 + $50,427) / 5.6502 = $105,745.26 
NPV = -$403,414 + ($105,745.26 x 5.6502) = $37,235.92 (positive)

C) ($403,414 + $81,202) / 5.6502 = $114,137.60 
NPV = -$403,414 + ($114,137.60 x 5.6502) = $101,814.30 (positive)

D) ($403,414 + $403,414) / 5.6502 = $142,639.58 
NPV = -$403,414 + ($142,639.58 x 5.6502) = -$581,782.19 (negative)

The only answer choice that gives a positive NPV is C, so that must be the correct annual cash inflow.

The Management of Osborn Corporation Is Investigating an Investment in Equipment