Question

24-

An enterprise issue a bond which will mature in 22 years and have a coupon rate of 6.80% with a face value of $1000. Yield to maturity for similar bond is 7%. The enterprise expect to raise $35 million so how many bonds should they sell to raise the debt?

Answer 1

coupon value , C = coupon rate*par value = 0.0680*1000 = 68

price of bond = present value of coupons + present value of maturity amount

Present value of coupons = C*PVIFA( 7% , 22 years)

PVIFA( 7% , 22 years) = present value interest rate factor of annuity

= [((1+YTM)ⁿ - 1)/((1+YTM)ⁿ*YTM)] = [((1.07)²² - 1)/((1.07)²²*0.07)] = 11.06124050

Present value(PV) of coupons = C*PVIFA( 7% , 22 years) = 68*11.06124050 = 752.16435383

PV of maturity amount = par value/(1+YTM)ⁿ = 1000/(1.07)²² = 225.71316518

Price of bond when YTM is 7% = 752.16435383 + 225.71316518 = $977.87751

let the no. of bonds they should sell = n

n*price of bond = money that needs to be raised

n*977.87751 = 35 million = 35,000,000

n = 35,000,000/977.87751 = 35,791.803 or 35,792 ( rounding off tonearest integer value)