Question

Assume coupons are paid annually. Here are the prices of three bonds with 10-year maturities:

Bond Coupon (%)	Price (%)
7	89.50
9	108.50
10	139.50

a. What is the yield to maturity of each bond? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Bond Coupon (%)	YTM
7	%
9	%
10	%

b. What is the duration of each bond? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Bond Coupon (%)	Duration
7	years
9	years
10	years

Answer 1

a.

YTM can be calculated using the RATE function in excel:

Bond face value is assumed to be $1000, hence current price of each of bonds is:

7%   $895

9%   $1085

10% $1395

7% Bond =RATE(10,70,-895,1000,,) = 8.61%

9% Bond =RATE(10,90,-1085,1000,,) = 7.75%

10% Bond =RATE(10,100,-1395,1000,,) = 4.91%

b.

Calculation of duration of bond is done using the duration function,

1-4-2017 and 31-3-2017 are taken to make the number of years equal to 10 years, also no intermediate calculation rounded off has not been done, ytm in the below formulas are written just for reference, i have taken the value of ytm upto maximum decimal place possible in actual calculation.

7% Bond =DURATION(1-4-2017,31-3-2027,7%,8.61%,1,) =7.25%

9% Bond =DURATION(1-4-2017,31-3-2027,9%,7.75%,1,)=7.18%

10% Bond =DURATION(1-4-2017,31-3-2027,10%,4.91%,1,)=7.68%