Investment X and Investment Y are both growing perpetuities with initial cash flow of $100. Both investments have the same interest rate (r) and cash flows. 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?

Question

Quizplus · Accepted Answer

CThe present value of a growing perpetuity is calculated using the formula PV = C / (r - g), where PV is the present value, C is the initial cash flow, r is the interest rate, and g is the growth rate. Given that Investment X has a higher present value than Investment Y with the same initial cash flow and interest rate, it implies that Investment X must have a lower growth rate (g) in the denominator, making the fraction larger. However, without knowing the specific interest rate (r), we cannot definitively conclude the relationship between the growth rates beyond the implications of the formula, hence why knowing the interest rate is also necessary for a complete understanding.

Investment X and Investment Y Are Both Growing Perpetuities with Initial