How does the interest rate and growth rate affect the present value of a perpetuity payment with growth?

The present value of a perpetuity payment with growth is affected by both the interest rate and the growth rate.

The interest rate, also known as the discount rate or the required rate of return, represents the opportunity cost of investing in a particular asset. It reflects the rate of return that an investor expects to earn on their investment. As the interest rate increases, the present value of a perpetuity payment with growth decreases. This is because a higher interest rate implies a higher discount rate, which reduces the value of future cash flows. Therefore, the higher the interest rate, the lower the present value of the perpetuity payment.

On the other hand, the growth rate represents the rate at which the perpetuity payment is expected to increase over time. A higher growth rate leads to a higher present value of the perpetuity payment. This is because a higher growth rate implies that the future cash flows will be larger, and therefore, more valuable in present terms. Consequently, the higher the growth rate, the higher the present value of the perpetuity payment.

It is important to note that the relationship between the interest rate and the growth rate is also crucial in determining the present value of a perpetuity payment with growth. If the growth rate is higher than the interest rate, the present value of the perpetuity payment will be positive. This is because the growth rate compensates for the discounting effect of the interest rate, resulting in a higher present value. However, if the growth rate is lower than the interest rate, the present value of the perpetuity payment will be negative, indicating that the perpetuity is not valuable.

In summary, the interest rate and growth rate have opposite effects on the present value of a perpetuity payment with growth. The interest rate decreases the present value, while the growth rate increases it. The relationship between these two factors is crucial in determining the overall value of the perpetuity payment.