How to solve Bonds — approximate yield rate and callable-bond price-to-worst questions on Exam FM?

Question

A bond with face amount $5,000$, redeemable at par, pays $8.19\%$ coupons per period for $n = 15$ periods and is priced at $8,230.67$. Using the standard approximation $i \approx (Fr + (C-P)/n)/((C+P)/2)$, estimate the yield per period.

Accepted Answer

Formula
For an approximate bond yield, $i\approx\dfrac{Fr+(C-P)/n}{(P+C)/2}$; for an exact yield, solve $P=Fr\,a_{\overline n|i}+Cv^n$. For several possible call dates, the price-to-worst at the target yield is the minimum of their cash-flow present values.

Why this formula applies
A yield is the rate that equates price with the present value of promised cash flows. For a callable bond, repeat that equation for each possible call date and use the yield relevant to the issuer's exercise choice.

Substitution and calculation
$i \approx \dfrac{Fr + (C-P)/n}{(C+P)/2} = \dfrac{194.1220}{6615.3350} = 0.0293$. Requested value: $0.0293$.

Answer
The answer is 0.0293, option (C).

How to Solve Bonds — approximate yield rate and callable-bond price-to-worst Questions on Exam FM

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