Independent solution

How to solve this Callable Bond Valuation question

Setup

Setup

Recover the shared coupon amount from the non-callable bond's price.

2300=Ca20‾∣ 0.07+2000v20⟹C=168.322300=Ca_{\overline{20}|\,0.07}+2000v^{20}\Longrightarrow C=168.32

Model

Model

The coupon rate exceeds the required yield, so an earlier return of par removes valuable above-market coupons.

C/2000>0.07⟹nworst=18C/2000>0.07\Longrightarrow n_{\mathrm{worst}}=18

Compute

Compute

Price the callable cash-flow stream to its earliest permitted redemption at the guaranteed 7% yield.

Pmax⁡=168.32a18‾∣ 0.07+2000v18=2284.85P_{\max}=168.32a_{\overline{18}|\,0.07}+2000v^{18}=2284.85

Answer

Answer

The maximum protected purchase price is approximately 2,285, corresponding to choice C.

Pmax⁡≈2285(C)\boxed{P_{\max}\approx2285\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 20 N; 7 I/Y; 2300 +/- PV; 2000 FV; CPT PMTPMT = 168.32
  2. 18 N; 7 I/Y; 168.32 PMT; 2000 FV; CPT PVPV = -2284.85Use the earliest allowed call for this premium bond.