Question

1. You own a 20-year, $1000 face value bond paying 8% coupon annually. If market price of the bond is 1000, what should be the Yield to Maturity of the bond?

You also own a 20-year, $1000 face value bond paying 8% coupon annually. What should be the market price of the bond so that its Yield to Maturity is exactly 10%?

Answer 1

1. If Price of bond and Par Value is same YTM and coupon rate are same. YTM =8%

2. Number of Years =20
Coupon =8%*1000 =80
YTM =10%
Par Value of Bond =1000
Price of bond =PV of Coupons +PV of Par Value =80*((1-(1+10%)^-20)/10%)+1000/(1+10%)^20 =829.73

Alternate method: Using excel formula =PV(10%,20,-80,-1000) =829.73

Answer 2

SOLUTION :

For the first bond,

Market price of the bond 

= Face value 

= 1000 ($)

So,

Yield rate = coupon rate = 8% (ANSWER)

For the second bond :

Yield = k = 10% = 0.1

=> (1 + k) = 1.1

n = 20 years

Coupon amount = 1000 *0.08 = 80 ($0 per year.

So,

Market price of the bond

= PV of future cash flows 

= Coupon amount  ( (1+k)^n - 1)/(k(1+k)^n)  + Face Value / (1+k)^n

= 80(1.1^20 - 1)/(0.1*1.1^20) + 1000/1.1^20

= 829.73 ($) (ANSWER).