An investment of $1.5 million is expected to generate cash flows of $600 000 p.a. ,at constant prices,over the next three years.Given that the nominal required rate of return is 12% p.a.and that prices are expected to increase at the rate of 5% p.a. ,the project's net present value is:
A)($58 901)
B)$84 229
C)(187 031)
D)$13 154

Question

Quizplus · Accepted Answer

To calculate the net present value (NPV) of the project, we first need to adjust the nominal required rate of return to reflect the real rate of return, considering the inflation rate. This can be done using the Fisher equation, which is (1 + nominal rate) = (1 + real rate) * (1 + inflation rate). Rearranging to solve for the real rate gives us the real rate of return. Given:- Nominal rate = 12% or 0.12- Inflation rate = 5% or 0.05Real rate = (1 + nominal rate) / (1 + inflation rate) - 1           = (1 + 0.12) / (1 + 0.05) - 1           = 1.12 / 1.05 - 1           = 0.0667 or 6.67%Now, we use the real rate to discount the cash flows:Year 1: 600,000 / (1 + 0.0667)^1 = $562,814Year 2: 600,000 / (1 + 0.0667)^2 = $527,907Year 3: 600,000 / (1 + 0.0667)^3 = $495,008Total present value of cash flows = $562,814 + $527,907 + $495,008 = $1,585,729NPV = Total present value of cash flows - Initial investment     = $1,585,729 - $1,500,000     = $85,729The closest option to our calculation is B) $84,229, acknowledging a slight discrepancy due to rounding or calculation differences in the exact method of applying the real rate of return.

An Investment of $1