Question

What is the bond price elasticity for a Southwest Airlines zero-coupon bond with 25 years to maturity, a par value of $1,000, and an interest rate change from 3% to 8%?

Answer 1

bond price elasticity = % change in bond price/% change in interest rate or yield or required return

first we need to calculate bond price with interest rate of 3% and 8%.

Price of zero-coupon bond = Par value/(1+interest rate)years to maturity

Price of zero-coupon bond at 3% interest rate = $1,000/(1+0.03)25 = $1,000/1.0325 = $1,000/2.0937779296542147631485938409019‬ = $477.61

Price of zero-coupon bond at 8% interest rate = $1,000/(1+0.08)25 = $1,000/1.0825 = $1,000/6.8484751962193159337240787632855‬ = $146.02

% change in bond price = (Price at 8%/Price at 3%) - 1 = ($146.02/$477.61) - 1 = 0.3057306170306317 - 1 = -0.6943 or -69.43%

% change in interest rate = (0.08/0.03) - 1 = 2.666666666666667‬ - 1 = 1.6667 or 166.67%

bond price elasticity = -0.6943/1.6667 = -0.42