Question

Investment X and Investment Y are both growing perpetuities with initial cash flow of $ 100. Both investments have the same interest rate (r). The present value of Investment X is $5,000, while the present value of Investment Y is $4,000. Which of the following is true? Investment X has a higher growth rate than Investment Y. Investment X has a lower growth rate than Investment Y. The answer cannot be determined without knowing the interest rate for both investments. This makes no sense - with the same initial cash flow and the same interest rate Investment X and Investment Y should have the same present value.

Answer 1

Investment X has a higher growth rate than Investment Y

Step-by-step explanation:

Applying the formula for the Present Value (PV) of a perpetuity on an investment on both Investment X and Investment Y, given an interest rate of (r), a growth rate of (g), and an initial investment of (A).

`PV = (A)/(r-g)`

Since both Investments X and Y, have the same initial investment (A) and interest rate (r), the difference in their present values (PV of Investment X = $5,000, and PV of Investment Y = $4,000) is accounted for by the difference in their growth rate (g).

Given that a higher growth rate will translate to a higher present value, therefore, the present value of Investment X is higher than the present value of investment Y because Investment X has a higher growth rate than Investment Y.