Coupon Rate

Are you sure you do mean the coupon rate, because although it could be asked for, usually you are told the coupon rate (the interest rate on nominal) because the bonds will usually be referred to in the question as 6% bonds (are whatever)?

Assuming you do mean the coupon rate, then for redeemable bonds, the market value is the present value of the future receipts.

So, best by example.

Suppose the market value is $120, the nominal (par) value is $100, and they will be redeemed in 5 years time at a premium of 10%. Investors required return is 13%.
Let the coupon rate be X%

The future receipts will be:

1 – 5 X p.a.
5 110

To get the present value, you will discount the 110 for 5 years at 13% – no problem.
The present value of the interest will be X x 5 years annuity factor at 13%.

The total present value will equal the market value which is $120.

So the present value of the interest of X p.a. will be 120 – (PV of the 110).

So to get X, divide the present value by the 5 year annuity factor.

Once you know X (the interest p.a.) then the coupon rate is simply X / par value (obviously as a percentage).

Note that company tax is irrelevant in the above, because it is the shareholders that determine the market value using their required return and the receipts that they expect. We always ignore income (personal) tax, and so they will receive the full interest.

Hope that helps 🙂

(Incidentally, you said ‘expected return for the bond’ – in fact what matters is the return that investors require! 🙂 )

That’s correct 🙂