Question

A 10 percent coupon bond was issued 2 years ago and sold at par value. Now, the required return on the same bond is 8 percent. What is the coupon rate today?

Answer 1

The yield to maturity is the required rate of return on a bond expressed as a nominal annual interest rate. For noncallable bonds, the yield to maturity and required rate of return are interchangeable terms. Unlike YTM and required return, the coupon rate is not a return used as the interest rate in bond cash flow valuation, but is a fixed percentage of par over the life of the bond used to set the coupon payment amount.

So in the given problem, the coupon rate on the bond is still 10 percent, and the YTM is 8 percent.

For Example, Say a bond with a par value of $100 issued at par with 5 years of maturity and has 10% Coupon rate and YTM is 8% i.e the bond is redeemed at discounted price which is $90. Example has been created to refer the problem.

Particulars	Amount
Bond Purchased	$ (100.00)
Year 1 Coupon @10%	$      10.00
Year 2 Coupon @10%	$      10.00
Year 3 Coupon @10%	$      10.00
Year 4 Coupon @10%	$      10.00
Year 5 Coupon @10% and Redemption	$   100.00
YTM is i.e. IRR	8%

Suppose, if we decided to sell the bond in outside market in year 3.

Price of the bond in market is calculated by dicounting Future Cash Flows at YTM = $10/1.08+$100/(1.08^2) = $94.99

Particulars	Amount
Bond Purchased	$ (100.00)
Year 1 Coupon @10%	$      10.00
Year 2 Coupon @10%	$      10.00
Year 3 Coupon @10% and Redemption	$   104.99
YTM is i.e. IRR	8%