This Exam FM sample reference tests Bond Valuation. Writing both five-year bond prices at 4% and using the 20% price ratio gives P = 10,445.20 and coupon rate r = 6.85%, choice B.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A is inconsistent with the coupled five-year coupon-and-redemption price equations; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the coupled five-year coupon-and-redemption price equations; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the coupled five-year coupon-and-redemption price equations; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the coupled five-year coupon-and-redemption price equations; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: coupon rate from a discounted heritage bond
A five-year heritage bond has face 1,000, redemption 950, annual coupons at rate r on face, and annual effective yield 4%. Its price is 920. Determine r.
A 2.50%
B 2.80%
C 3.13%
D 3.50%
E 4.00%
Variant answer in brief
Removing the discounted redemption from price and dividing by the coupon annuity factor gives r = 3.13%, choice C.
Setup
Setup
Separate the unknown coupon annuity from the known discounted redemption.
920=1000ra5∣0.04+950(1.04)−5
Model
Model
The residual price after removing redemption is the present value of five level coupons of 1,000r.
1000ra5∣=920−950(1.04)−5
Compute
Compute
Dividing by the five-year annuity factor and face amount gives rate 0.0312612.
r=0.0312612
Answer
Answer
The annual coupon rate is approximately 3.13%, choice C.
r=3.13%(C)
Calculator reproduction
BA II Plus keystrokes
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 5 N; 4 I/Y; 920 +/- PV; 0 PMT; 950 FV; CPT PMTPMT = 31.2612END mode; I/Y is annual. Divide the positive coupon by face 1,000 for the coupon rate.
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