Independent solution

How to solve this Bond Valuation question

Setup

Setup

First obtain the observable bond price from the term structure by discounting each date separately.

P=1001.03+1001.0352+11001.043=1168.33P=\frac{100}{1.03}+\frac{100}{1.035^2}+\frac{1100}{1.04^3}=1168.33

Model

Model

Yield to maturity is the one constant annual rate that reproduces that market price.

1168.33=100a3‾∣ y+1000(1+y)−31168.33=100a_{\overline{3}|\,y}+1000(1+y)^{-3}

Compute

Compute

Solving the three-year bond equation gives 0.0394.

y=0.0394y=0.0394

Answer

Answer

The bond's annual effective yield to maturity is 3.94%, corresponding to choice D.

y=3.94%(D)\boxed{y=3.94\%\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

Check END/BGN, period, sign, TVM, and cash-flow setup

  1. CF; 2nd CLR WORK; CF0=-1168.33; C01=100; F01=1; C02=100; F02=1; C03=1100; F03=1; IRR; CPTIRR = 3.94First compute 1,168.33 from the spot curve.