Question

1.   Zen international chemical company has a 15% annual coupon interest rate on a $1,000 par value bond with 20 years left to maturity. Bonds of same maturity now sell to yield 11% return.

(a) How much would you be willing to pay for Zen’s bonds today? Will you buy it? Why?   

(b) If the bond is selling for $ 1,141 what is the yield to maturity?

(C) Explain why some bonds sell at a premium over par value while other bonds sell at a discount. What do you know about the relationship between the coupon rate and the YTM for premium bonds? What about for discount bonds? For bonds selling at par value?

Answer 1

Solution:-

a) Calculation of the fair price of the bond

Annual interest = $1000*15%= $150

Number of years= 20

Required return( RR)= 11%

Calculation of the fair price of the bond

            =Annual interest *PVIFA(RR, years)+Redeemable value*PVIF(RR,years)

            =150*PVIFA(11%,20)+1000*PVIF(11%.20)

            =150*7.963328+1000*0.124034

            =1194.50+124.034

            =$1318.53

No, I will not buy the bond because it is trading at premium .

b) Calculation of YTM if it is selling at $1141

            We will use hit and trail method to calculate the YTM .

First we take discount rate 12% as discount rate ,

            Price of bond = 150*PVIFA(12%,20)+1000*PVIF(12%,20)

                                    = 150*7.469444+1000*0.103667

                                    =$1224.083

This price is less than the requires $1141 hence we have to increase the discount rate

Now we will assume discount rate to be 13%.

Price of bond = 150*PVIFA(13%,20)+1000*PVIF(13%,20)

                                    = 150*7.024752+1000*0.086782

                                    = $1140.495

Now YTM of bond can be calculated as follows

YTM=Lower DR+Difference b/w DRs{[PV of lower DR-PV]/Absolute difference B/w DRs}

Where, DR stands for discount rate

            PV stands for present value

            B/W stands for between.

Now substituting the value

YTM = 12%+1%*(1224.083-1141)/83.588

            =12%+0.99%

            =12.99%

Hence the YTM = 12.99%

c)

i) When the coupon rate is greater than YTM the bond will be selling at           premium .

ii)When the coupon rate is less than YTM the bond will sell at discount.

iii)For premium bonds, coupon rate >YTM

iv) For discount bond, Coupon rate<YTM

v) For bond selling at par , Coupon rate = YTM

Please feel free to ask if you have any query in the comment section