Question

a corporate bond has a current vaule of $975 and with a par value of $1000 and a 9% coupon paid annually. what is the bonds yield to maturity and effective annual rate of return.

Answer 1

A) Calculation of effective annual rate :

In the given case, interest = 9% x $1,000 = 90

However, the current value of the bond = $975 (which implies that investment amount is 975 and not 1,000)

Hence, the interest rate earned effectively = 90/975 = 9.23%

Effective rate = 9.23% which is greater than 9% coupon rate, this is because the investor is receiving coupon rate on the par value. However, the bond is trading at a discount.

B) Calculation of YTM

YTM is the rate at which the coupon payments and the redemption value of the bond has to be discounted, such that the sum equals the current market price.

In simple words, when future cashflows from the bond (coupon payments + redemption value at maturity) is discounted at YTM, the sum will be equal to the maket value of the bond

It is the total return expected by the investor until the bonds are held to maturity

MV of the bond = Coupon 1/(1+YTM)^1 +  Coupon 1/(1+YTM)^2.....................Redemption value/(1+YTM)^n

where n is the no of years after which the bond matures

In the given example, no information is given on when the bond is expected to mature. Let's assume, the bond matures in exactly 1 year and interest is also paid after 1 year.

Hence, YTM =

975 = 100/(1 + YTM )^1 + 1000/(1 + YTM )^1

Using the above equation, YTM = 12.82%