Question

Kidder Corporation's balance sheet shows an historical book value for long-term debt (bonds, at par) of $23, 500,000. The bonds have an 6.4% coupon rate, payable semiannually, and a par value of $1,000. They mature exactly 10 years from today. The yield to maturity is 9.20%, so the bonds now sell below par.

Answer 1

Price of the bond = Sum of present values of all coupons + Present value of redemption value

For calculating sum of present values of coupons we can use formula for present value of annuity

PVA = C * (1- 1/(1+r)^n ) / r

C = coupon = 1000 * (6.4% / 2) = 32

r = yeild = 9.2% / 2 = 4.6%

n = Number of years = 10*2 = 20

PVA = 32 * (1- 1/(1+0.046)^20 ) / 0.046 = 412.67

Present value of redemption value = 1000 / (1 + r)^n

r = 9.2%

n = 10 years

PV = 1000 / (1 + 0.092)^10 = 414.73

Price = 412.67 + 414.73 = 827.24

Bond is selling below par value of 1000