A company issues a callable (at par)20-year, 5% coupon bond with annual coupon payments. The bond can be called at par in one year after release or any time after that on a coupon payment date. On release, it has a price of $102 per $100 of face value. What is the yield to maturity of this bond when it is released?

Question

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To calculate the yield to maturity (YTM) of the bond when it is released, we need to find the rate that makes the present value of all future cash flows equal to the current price of the bond.

At issuance, the bond is priced at $102 per $100 of face value, which implies a present value (PV) of $1020 for the bond. The annual coupon payment is 5% of $100, or $5.

If the bond is not called, the bondholder will receive 19 coupon payments of $5 each and the face value of $100 at maturity. We can calculate the present value of these cash flows using the YTM. Let's assume the YTM is y%. Then:

PV = (C / (1+y)^1) + (C / (1+y)^2) + ... + (C / (1+y)^19) + (F / (1+y)^20)

where C is the coupon payment, F is the face value, and PV is the present value.

Using a financial calculator or spreadsheet, we can solve for y by setting PV equal to $1020 and solving for y. The YTM turns out to be 4.84%.

Note that the callable feature of the bond does not affect the YTM calculation, since it only gives the issuer the option to call the bond at a certain price. The YTM represents the return an investor would earn if the bond is held to maturity.

A Company Issues a Callable (At Par)20-Year, 5% Coupon Bond