Question

Mercy Corporation's bonds have 15 years to maturity, an 8.75% coupon paid semiannually, and a $1,000 par value. The bond has a 6.50% nominal yield to maturity, but it can be called in 6 years at a price of $1,050. What is the bond's nominal yield to call?

Please show all work

Answer 1

For the purpose of calculaion of Yield to call we need to first estimate current market price

Using Financial Calculator

=PV(rate,nper,pmt,fv)

rate is the yield to maturity i.e 6.50%/2 = 3.25% (as coupons are paid semiannually)

where nper is Number of years to maturity i.e 15 * 2 = 30 (As coupons are paid semiannually)

pmt is Interest payment i.e 1000 * 8.75% = 87.5 / 2 = 43.75 (Divided by 2 As coupons are paid semiannually)

fv is face value

= - 1000

=PV(3.25%,30,-43.75,-1000)

therefore ,Current Market Price is 1213.55

Calculation of Yield to call:

Using Financial Calculator

=RATE(nper,pmt,pv,fv)

where nper is Number of years of call i.e 6 * 2 = 12 (As coupons are paid semiannually)

pmt is Interest payment i.e 1000 * 8.75% = 87.5 / 2 = 43.75 (Divided by 2 As coupons are paid semiannually)

pv is Current Market Price

= 1213.55 (calculated above)

Note : pv should be taken as negative.

fv is call price i.e 1050

=RATE(12,43.75,-1213.55,1050)

therefore ,Yield to call is 2.31628%(Semiannual)

Yield to call is 4.63257%(Annual)