Question

A business has two investment choices.

a. requires an immediate outlay of $4,000 and offers a return of $25,000 in eight years.
b. requires an immediate outlay of $3,500 in return for which $950 will be received at the end of every six months for the next eight years.
c. the required rate of return on investment is 12% p.a., compounded semi-annually.

Compute the net present value and internal rate of return of each alternative and determine which investment should be accepted or rejected according to the net present value criterion

Answer 1

To determine which investment option to choose based on the net present value criterion, we calculate the NPV and IRR for each option. Option A has a NPV of $7,264.71 and an IRR of approximately 33.02% p.a. Option B has a NPV of $5,013.14 and an IRR of approximately 20.49% p.a. Based on the higher NPV, Option A should be accepted.

Step-by-step explanation:

To calculate the net present value (NPV), we need to discount the cash flows of each investment option at the required rate of return of 12% p.a. compounded semiannually. For Option A, the cash inflow of $25,000 after eight years is discounted to its present value using the formula PV = FV / (1 + r/n)^(n*t), where r is the interest rate, n is the number of compounding periods per year, and t is the number of years. For Option B, we discount each semiannual cash inflow of $950 using the same formula. The NPV is calculated by subtracting the initial outlay from the sum of the discounted cash flows.

For Option A, the NPV is calculated as:

NPV = -$4,000 + $25,000 / (1 + 0.12/2)^(2*8) = $7,264.71

For Option B, we need to discount the semiannual cash inflows for eight years, so t = 16. The NPV is calculated as:

NPV = -$3,500 + ($950 / (1 + 0.12/2)^(2*0.5)) + ($950 / (1 + 0.12/2)^(2*1)) + ... + ($950 / (1 + 0.12/2)^(2*16)) = $5,013.14

The internal rate of return (IRR) is the interest rate that makes the NPV equal to zero. We can calculate it by trial and error or by using financial functions in software like Excel. For Option A, the IRR is approximately 33.02% p.a., and for Option B, the IRR is approximately 20.49% p.a.

Based on the net present value criterion, Option A should be accepted because it has a higher NPV than Option B.