Question

What is the price of a perpetuity that has a coupon of $70 per year and a yield to maturity of 1.5%? If the yield to maturity doubles, what will happen to the perpetuity’s price?

Short answer

The price of perpetuity will be $2333.3

Step-by-step solution

Step 1. Introduction

A perpetuity is a financial instrument that pays for an indefinite period of time. Perpetuity is a never-ending sequence of identical cash flows in finance. The term "perpetuity" is employed in a number of financial theories, including the dividend discount model (DDM).

Step 2. Explanation

$$\begin{gathered} PriceofPerpetuityiscalculatedas: \\ PV=\frac{P}{i} \\ =\frac{70}{1.5\%} \\ =\$4666.67 \\ Iftheyieldgetdoubled,thenthePViscutinhalf: \\ PV=\frac{70}{3\%} \\ =\$2333.3 \end{gathered}$$