Question

Pro & Gamble has outstanding an issue of $1,000 face value, 12 5/8% coupon bonds that mature in 14 years. Calculate the bond’s yield-to-maturity if its current market price is: Excel

a. $ 875

b. $ 950

c. $1,000

d. $1,080

Answer 1

Price of the bond is calculated using the formula: P= C/(1+r)+C/(1+r)^2+....C/(1+r)^n+P/(1+r)^n; where C is the coupon payment per period, P is the face value of the bond, r is the yield to maturity and n is the number of years to maturity.

For the coupons part, we can use the formula of present value of annuity which is C*(1-(1+r)^-n)/r; where C is the annual cashflow, r is the discount rate and n is the number of years.

Coupon Payments= 12.625%*1000= $126.25, Face value is $1000 and n= 14 years.

a). For the current Market Price of $875,

875= 126.25*(1-(1+r)^-14)/r

(1-(1+r)^-14)/r= 6.93069

r= 14.787%

b). For the current Market Price of $950,

950= 126.25*(1-(1+r)^-14)/r

(1-(1+r)^-14)/r= 7.52475

r= 13.436%

c). For the current Market Price of $1000,

1000= 126.25*(1-(1+r)^-14)/r

(1-(1+r)^-14)/r= 7.92079

r= 12.625%

d). For the current Market Price of $1080,

1080= 126.25*(1-(1+r)^-14)/r

(1-(1+r)^-14)/r= 8.55445

r= 11.452%