Assume that the price of a $1,000 zero-coupon bond with five years to maturity is $567 when the required rate of return is 12 percent. If the required rate of return suddenly changes to 15 percent, what is the price elasticity of the bond?

Question

Quizplus · Accepted Answer

We can use the price elasticity of demand formula: 
Price Elasticity = (% Change in Quantity Demanded)/(% Change in Price)

In this case, the quantity demanded is fixed (since it's a bond with a set maturity and face value). So we just need to calculate the percentage change in price when the required rate of return changes from 12% to 15%.

Initial price: $567 
New required rate of return: 15% 
New price: ?
Using the bond pricing equation: 
New price = $1,000/(1+0.15)^5 = $497.18

% Change in price = [(New price - Initial price)/Initial price] x 100% 
% Change in price = [($497.18 - $567)/$567] x 100% = -11.94%

% Change in required rate of return = [(New required rate - Initial required rate)/Initial required rate] x 100% 
% Change in required rate of return = [(15% - 12%)/12%] x 100% = 25%

Price Elasticity = (-11.94%)/(25%) = -0.4788 ≈ -0.494.

Therefore, the price elasticity of the bond is -0.494, which is approximately -0.49. 
The answer choice is C.

Assume That the Price of a $1,000 Zero-Coupon Bond with Five