Independent solution

How to solve this Callable Bond Guaranteed Price question

Setup

Setup

Evaluate the bond under each permitted redemption date at the required 3% half-year yield. The cash flows differ in both number of coupons and redemption amount.

Pcall15=40a30‾∣ 0.03+1200v30=1278.40P_{\text{call15}}=40a_{\overline{30}|\,0.03}+1200v^{30}=1278.40

Model

Model

The call-at-15 value is 1,278.40; the maturity-at-20 value is 1,261.80. To guarantee the required yield regardless of the issuer’s choice, the purchase price cannot exceed the smaller value.

Pmat20=40a40‾∣ 0.03+1100v40=1261.80P_{\text{mat20}}=40a_{\overline{40}|\,0.03}+1100v^{40}=1261.80

Compute

Compute

The guaranteed price is therefore 1,261.80, which rounds to 1,262.

Pmax⁡=min⁡(1278.40,1261.80)=1261.80P_{\max}=\min(1278.40,1261.80)=1261.80

Answer

Answer

The calculation gives 1262 for callable bond guaranteed price, matching published choice B.

P=1262(B)\boxed{P=1262\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 30 N; 3 I/Y; 40 PMT; 1200 FV; CPT PV−1278.40First permitted redemption outcome.
  2. 2nd CLR TVM; 40 N; 3 I/Y; 40 PMT; 1100 FV; CPT PV−1261.80Maturity outcome; select the smaller absolute present value.