Question

(Bootstrapping) The bond prices of six-month and one-year zero-coupon bonds are 94.0 and 89.0. A 1.5-year bond that provides a coupon of 8% per annum semiannually currently sells for $94.84. A two-year bond that provides a coupon of 10% per annum semiannually currently sells for $97.12. Calculate the six-month, one-year, 1.5-year, and two-year zero rates

Answer 1

We assume that the Par Value = $ 100

A) Six month bond price = $ 94

Par Value = $ 100

Difference in par value and price will be the yield which is = 100 - 94

= $ 6

Rate = 6 / 94

= 0.06383 or 6.38% semi annually or 12.77% annually

B) 1 Year bond price = $ 89

Par Value = $ 100

Difference in par value and price will be the yield which is = 100 - 89

= $ 11

Rate = 11 / 89

= 12.36% annually

C) 1.5 Year bond price = $ 94.84

Par Value = $ 100

Coupon = 8% annually or 4% semi annually which is $ 4

Using the Rate function in excel, we can calculate the required result as follows:

= RATE(nper,pmt,-pv,fv)

= RATE(3, 4, -94.84, 100)

= 11.85% anually

D) 2 Year bond price = $ 97.12

Par Value = $ 100

Coupon = 10% annually or 5% semi annually which is $ 5

Using the Rate function in excel, we can calculate the required result as follows:

= RATE(nper,pmt,-pv,fv)

= RATE(4, 5, -97.12, 100)

= 11.30% anually