Independent solution

How to solve this Cash-Flow and Risk Matching question

Setup

Setup

Express the liability and first-bond cash flows in thousands at each annual date.

(12,12,12,12,162)−(10,10,10,10,110)=(2,2,2,2,52)(12,12,12,12,162)-(10,10,10,10,110)=(2,2,2,2,52)

Model

Model

Subtracting date by date leaves four coupons of 2 and a final total of 52 for the second bond.

F2=50,c2F2=2⟹c2=0.04F_2=50,\qquad c_2F_2=2\Longrightarrow c_2=0.04

Compute

Compute

Those residuals imply face 50 and coupon rate 4%; discounting at 8% gives price 42.015 thousand.

P2=2a5‾∣ 0.08+50(1.08)−5=42.015P_2=2a_{\overline{5}|\,0.08}+50(1.08)^{-5}=42.015

Answer

Answer

The second bond described in choice A exactly completes the cash-flow match.

4% coupon and price 42015(A)\boxed{\text{4\% coupon and price }42015\quad\text{(A)}}

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; 5 N; 8 I/Y; 2000 PMT; 50000 FV; CPT PVPV = -42014.58END mode; I/Y is annual and all bond receipts are positive, so purchase price is negative.