Yield to Maturity of a bond

I'm having trouble understanding how to calculate the yield of maturity of a bond.

Here is an excerpt from my textbook.

Quote:

Suppose that the current term structure has the following yields on zero coupon bonds

Term ___________ Zero Coupon Bond Rate

1/2 Year______________8%

1 Year________________9%

1 1/2 Year____________10%

2 Year________________11%

Find the price per $100 face amount and yield to maturity of each of the following 2-year bonds (with semi-annual coupons):

(i) zero coupon bond

(ii) 5% annual coupon rate

(iii) 10% annual coupon rate

Then it has them solutions listed below

Quote:

(i) Price is 100(1+.055)^-4= 80.72 and yield to maturity is (nominal) 11%

(ii) Price is 2.5[(1.04)^-1+(1.045)^-2+(1.05)^-3]+102.5(1.055)^-4= 89.59

Yield to maturity is (nominal) 10.9354%

(iii) Price is 5[(1.04)^-1+(1.045)^-2+(1.05)^-3]+105(1.055)^-4= 98.46

Yield to maturity is (nominal) 10.8775%

I understand how they calculated the price, but I have look throughout my whole notes and the book and it never explains how they calculated the yield to maturity.

If anyone knows how, i would highly appreciate it, final exam is tomorrow!

Bond Price Calculation for Non Zero Coupon Bonds

Quote:

Originally Posted by

**fenderic** I understand how they calculated the price, but I have look throughout my whole notes and the book and it never explains how they calculated the yield to maturity.

I do understand how the author may have computed the YTM, but I am unable to understand the way the author is calculating the bond prices for 5% 2 yr and 10% 2 year $100 bonds (Sleepy)

The table you show on top gives yields for Zero Coupon bonds maturing in 6 months, 1 year, 1 and half year and 2 years

Why is the author using these yields to solve for Bond prices of ii) and iii)

The formula for Bond Price discounts each interest payment at period t and adds it to the discounted terminal value of the bond

The formula he is using is right but I am unable to understand why the author is using semi annual yields from the table to discount each of the interest payments.

Price of the Non Zero Coupon Bond Formula (Semi Annual Compounding)

P = INT x PVIFA(YTM%/2, 2N) + Par Value x PVIF(YTM%, 2N)

which is equivalent to what the author has it

P = SIGMA T=1->2N-1 [ INT/(1+YTM%/2)^T ] + (INT+Par Value)/(1+YTM%/2)^2N