Question

Crane Company is about to issue $261,200 of 10-year bonds paying an 8% interest rate, with interest payable semiannually. The discount rate for such securities is 8%. How much can Crane expect to receive for the sale of these bonds?

Answer 1

There is a search for price of the bond (V).

Face value (F) = 261,200

Semiannual coupon interest (C) = F × Coupon rate = 261,200 × 8% × (1/2) = 10,448

Number of coupon payment in a year = m = 2

Number of year = n = 10

Rate of discount = r = 0.08

By the formula,

V = {C/(r/m)} × [1 – {1/(1 + r/m)^(n × m)}] + [F/(1 + r/m)^(n × m)]

    = {10,448/(0.08/2)} × [1 – {1/(1 + 0.08/2)^(10 × 2)}] + [261,200 / (1 + 0.08/2)^(10 × 2)]

    = 261,200 × [1 – {1/1.04^20}] + [261,200 / 1.04^20]

    = 261,200 × [1 – 1/2.191123] + (261,200 / 2.191123)

    = 261,200 × (1 – 0.45638) + 119,208.28

    = 261,200 × 0.54362 + 119,208.28

    = 141,993.54 + 119,208.28

    = 261,201 (Answer)