Question

(Bond valuation​) Bellingham bonds have an annual coupon rate of 8 percent and a par value of $ 1 comma 000 and will mature in 20 years. If you require a return of 15 ​percent, what price would you be willing to pay for the​ bond? What happens if you pay more for the​ bond? What happens if you pay less for the​ bond?

Answer 1

Formula for bond price is:

Bond price = C x 1 – (1+r)-n/r + F/(1+r) n

F = Face value = $ 1,000

C = Periodic coupon payment = Face value x Coupon rate/Annual coupon frequency

= $ 1,000 x 0.08 = $ 80

r = Rate of return = 0.15

n = Number periods to maturity = 20

Bond price = $ 80 x [1 – (1+0.15)-20]/0.15 + $ 1,000/ (1+0.15) 20

                   = $ 80 x [1 – (1.15)-20]/0.15 + $ 1,000 x (1.15) -20

                   = $ 80 x [(1 – 0.0611002789405532)/0.15] + $ 1,000 x 0.0611002789405532

                   = $ 80 x (0.9388997210594468/0.15) + $ 61.1002789405532

                   = $ 80 x 6.25933147372965 + $ 61.1002789405532

                   = $ 500.746517898372 + $ 61.1002789405532

                   = $ 561.846796838925 or $ 561.85

Bond can be purchased for $ 561.85

If we pay more than $ 561.85 for the bond, we will incur a loss and paying less than this is profitable.