Independent solution

How to solve this Bond Valuation question

Setup

Setup

At the lower yield the coupon exceeds yield, so the earliest permitted call determines the guaranteed price.

P=40a10‾∣ 0.034+1000(1.034)−10=1050.15P=40a_{\overline{10}|\,0.034}+1000(1.034)^{-10}=1050.15

Model

Model

The given price difference fixes the higher-yield price at 926.79.

Q=P−123.36=926.79Q=P-123.36=926.79

Compute

Compute

At the higher yield the bond is at a discount, making the latest redemption date limiting; solving that semiannual price equation gives 38 periods.

926.79=40a2n‾∣ 0.044+1000(1.044)−2n926.79=40a_{\overline{2n}|\,0.044}+1000(1.044)^{-2n}

Answer

Answer

Thus the bond term is 19 years, which is choice C.

2n=38⟹n=19(C)\boxed{2n=38\Longrightarrow n=19\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 10 N; 3.4 I/Y; 40 PMT; 1000 FV; CPT PVPV = -1050.15END mode; I/Y is the half-year effective yield for the first bond.
  2. 2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 4.4 I/Y; 926.79 +/- PV; 40 PMT; 1000 FV; CPT NN = 38.00 half-yearsEND mode; I/Y is the second bond's half-year yield, so 38 periods equal 19 years.