Question

DO LOPJOJ DIO U 1) You are considering buying a 10 year $1000 bond with a coupon rate of 6% paid annually. If the discount rate is 6%, what is the maximum that you are willing to pay for this bond? How about with discount rate at 12%? And at 3%? When is the bond selling at par? And when it is selling at a premium?

Answer 1

1)

price of coupon = Coupon payment per period * [1-(1+i)^-n]/i + par value/(1+i)^n

i = interest rate per period

n = number of periods

a)

at coupon rate equal to yield to maturity, bond sells at par

hence

price at 6% = 1000

b)

Price at 12% = 60 * [1-(1+12%)^-10]/12% + 1000/(1+12%)^10

= 660.99

c)

Price at 3% = 60 * [1-(1+3%)^-10]/3%  + 1000/(1+3%)^10

= 1255.91

d)

at 6% selling at par

e)

at 3% selling at premium