Question

A 10-year U.S. Treasury bond with a par value of $ 1000 is currently selling for $ 1025.

The bond carries a 7.5% p.a. coupon payable annually. If purchased today and held to maturity, what is its expected yield to maturity?

Does your answer change if the coupon payments of 7.5% p.a. are made half-yearly (i.e. 3.75% every half -year)? How & why?

Could you please show me step by step calculations so I can understand? thank you.

Answer 1

The Approximate Yield to Maturity Formula =[Coupon + ( Face Value - Market Price) / Number of years to maturity] / [( Face Value + Market Price)/2 ] *100

= [$ 75+ ( $ 1,000- $ 1025) /10] /[( $ 1,000+ $ 1025)/2] *100

= 72.5/1012.5*100

= 7.16%

Note : Coupon = Rate * Face Value

= 7.5% * $ 1,000

= $ 75

Since this formula gives an approximate value, the financial calculators can be used alternatively.

where,

Par Value = $ 1,000

Market Price = $ 1025

Annual rate = 7.5% and

Maturity in Years = 10 Years

Hence the yield to maturity = 7.14%

Answer = 7.14%

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The Approximate Yield to Maturity Formula =[Coupon + ( Face Value - Market Price) / Number of years to maturity] / [( Face Value + Market Price)/2 ] *100

= [$37.50+ ( $ 1,000- $ 1025) /20] /[( $ 1,000+ $ 1025)/2] *100

= 36.25/1012.50*100

=3.58%

Annual YTM =3.58% * 2

= 7.16%

Note :Semi Annual Coupon = Rate * Face Value

= 7.5% /2* $ 1,000

= $ 75/2

= $ 37.50

Since this formula gives an approximate value, the financial calculators can be used alternatively.

where,

Par Value = $ 1,000

Market Price = $ 1025

Coupon rate = 3.75% and

Maturity in Years = 20 Years

Hence the yield to maturity =1.79%

Answer = 3.58%*2

= 7.16%

The reason the yield of maturity is different because there are two periods of compounding and when the periods of compounding increases the effective annual rate also increases.