Question

7. A bond matures in 15 years and pays an 8 percent annual coupon. The bond has a face value of $1,000 and currently sells for $985. What is the bond’s current yield and yield to maturity? $

Answer 1

Current Yield:

This is equal to annual coupon divided by current bond price. It tells us what return will the bond give if any investor buys it today and holds it for a year.

Current Yield = Annual Cash flows / Current price of the bond

Current Yield = (8% of 1000) / 985

Current Yield = 8.122%

Yield to maturity:

YTM is the total return if the investor holds the bond till maturity.

Approximate YTM is given by

YTM = { C + [ (FV - PV)/t] } / [ (FV + PV) / 2]

Where

C = Coupon payment

FV = Face/Par value of the bond

PV = present value

t - time to maturity

Putting values

YTM = { (8% of 1000) + [ (1000 - 985) / 15 ] } / [ (1000 + 985) / 2 ]

YTM = ( 80 + 1) / 992.5

YTM = 8.161% (approximate)

In order to calculate actual YTM, we should use below formula and then use excel solver

Bond Price = [ Coupon1 / (1 + YTM)^1 ] + [ Coupon2 / (1 + YTM)^2 ] + .... + [ Coupon15 / (1 + YTM)^15 ] + [ Par Value / (1 + YTM)^15 ]  

Putting values

985 = [ 80 / (1 + YTM)^1] + [ 80 / (1 + YTM)^2] + [ 80 / (1 + YTM)^3] + ....+ [ 80 / (1 + YTM)^15] + [ 1000 / (1 + YTM)^15]

Solve this to get

YTM = 8.177% (Actual YTM)