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?

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, it implies that Investment X must have a lower growth rate in the denominator, making the fraction larger. However, the correct interpretation is that Investment X must have a higher growth rate than Investment Y to result in a higher present value, indicating a misunderstanding in the explanation. The correct explanation is that with the same initial cash flow and interest rate, for Investment X to have a higher present value, it would typically indicate a difference in another variable, such as the growth rate. However, the formula and explanation provided were incorrectly applied, leading to a contradictory statement. The correct reasoning should be based on understanding that the present value difference indicates a variation in parameters not specified (e.g., growth rate), but the initial explanation was flawed in its application of the formula and logic.

Investment X and Investment Y Are Both Growing Perpetuities with Initial