A company needs $8 million in new capital for expanded composites manufacturing. It is offering small-denomination corporate bonds at a deep discount price of $800 for a 4% $1000 face value bond that matures in 20 years and pays the dividend semiannually. Find the nominal and effective annual rates, compounded semiannually, that this company is paying per investor

nominal interest rate = 4% annual

effective interest rate = 5.56% annual

Explanation:

the bond's nominal rate is basically the coupon rate

to calculate the bond's effective interest rate we must calculate its yield to maturity:

YTM = [coupon + [ (face value - present value) / n]} / [ (face value + present value) / 2]

coupon = $1,000 x 4% x 1/2 = $20 FV = $1,000 PV = $800 n = 40

YTM = [20 + [ (1,000 - 800) / 40]} / [ (1,000 + 800) / 2]

YTM = 25 / 900 = 2.777 semiannual ⇒ 5.56% annual