Question

HMK Enterprises would like to raise $10 million to invest in capital expenditures. The company plans to issue five-year bonds with a face value of $1000 and a coupon rate of 6.5% (annual payments). The following table summarizes the yield to maturity for five-year (annual-pay) coupon corporate bonds of various ratings:

Rating	AAA	AA	A	BBB	BB
YTM	6.20%	6.30%	6.50%	6.90%	7.50%

1. a. Assuming the bonds will be rated AA, what will the price of the bonds be?
2. b. How much of the total principal amount of these bonds must HMK issue to raise $10 million today, assuming the bonds are AA rated? (Because HMK cannot issue a fraction of a bond, assume that all fractions are rounded to the nearest whole number.)
3. c. What must the rating of the bonds be for them to sell at par?
4. d. Suppose that when the bonds are issued, the price of each bond is $959.54. What is the likely rating of the bonds? Are they junk bonds?

Answer 1

(a) Bond Rating: AA, Corresponding Bond Yield to Maturity(YTM) = 6.3 %, Face Value = $ 1000, Coupon Rate = 6.5 % with annual payments, Bond Tenure = 5 years

Bond Coupon = 0.065 x 1000 = $ 65

Bond Price = Total Present Value of All Coupons + Face Value redeemed at maturity = 65 x (1/0.063) x [1-{1/(1.063)^(5)}] + 1000/(1.063)^(5) = $ 1008.36

(b) Target Fund = $ 10000000 and Price per Bond = $ 1008.36

Number of Bonds to be Issued = 10000000 / 1008.36 = 9917.093 ~ 9917

(c) If bond sells at par then YTM should equal the bond's annual coupon of 6,5 %. Bond YTM = 6,5 % corresponds to a rating of A

(d) Let the bond YTM be R and Bond Price = $ 959.54

Therefore, 959.54 = 65 x (1/R) x [1-{1/(1+R)^(5)}] + 1000 / (1+R)^(5)

Using hit and trial method/EXCEL's Goal Seek Function to solve the above equation, we get:

R = 0.075 or 7.5 %

A YTM of 7.5 % corresponds to a rating of BB