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?
A)Investment X has a higher growth rate than Investment Y.
B)Investment X has a lower growth rate than Investment Y.
C)The answer cannot be determined without knowing the interest rate for both investments.
D)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.

Question

Quizplus · Accepted Answer

The present value of a growing perpetuity is calculated as PV = C / (r - g), where C is the initial cash flow, r is the interest rate, and g is the growth rate. Since Investment X has a higher present value than Investment Y with the same initial cash flow and interest rate, Investment X must have a higher growth rate than Investment Y.

Investment X and Investment Y Are Both Growing Perpetuities with Initial