A $1000 face value bond with a 20-year maturity and 9% semiannual coupon rate is callable in 10 years at a call price of $1,050

We can calculate the price of bond by using the following formula in excel:-

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

Here,

PV = Price of bond

Rate = 8%/2 = 4% (semiannual)

Nper = 20*2 = 40 periods (semiannual)

Pmt = Coupon payment = $1,000*9%/2 = $45

FV = $1,000

Substituting the values in formula:

= -pv(4%,40,45,1000)

= $1,098.96

We can calculate the yield to call by using the following formula in excel:-

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

Here,

Rate = Yield to call (semiannual)

Nper = 10*2 = 20 periods (semiannual)

Pmt = Coupon payment = $1,000*9%/2 = $45

PV = $1,098.96

FV = Call price = $1,050

Substituting the values in formula:

= rate(20,45,-1098.96,1050)

= 3.94%

Yield to call = Rate * 2

= 3.94% * 2

= 7.89%