Question

HMK Enterprises would like to raise $14 million to invest in capital expenditures. The company plans to issue​ five-year bonds with a face value of $1,000 and a coupon rate of 12.3%

​(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​ (%)	11.8	12.0	12.3	12.6	13.1

a. Assuming the bonds will be rated​ AA, what will the price of the​ AA-rated bonds​ be?

b. How much total principal amount of these bonds must HMK issue to raise $14 million​ today, assuming the bonds are AA​ rated? (Because HMK cannot issue a fraction of a​ bond, assume all fractions are rounded to the nearest whole​ number.)

c. What must the rating of the bonds be for them to sell at​ par?

d. Suppose that when the bonds are​ issued, the price of each bond is $971.93.What is the likely rating of the​ bonds? Are they junk​ bonds?

Note​: Assume annual compounding.

Answer 1

a]

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond at issue is calculated using PV function in Excel :

rate = 12% (YTM of bonds of AA rating)

nper = 5 (Years remaining until maturity with 1 annual coupon payment each year)

pmt = 1000 * 12.3% (annual coupon payment = face value * coupon rate)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $1,010.81

b]

Number of bonds to issue = amount to raise / price per bond

Number of bonds to issue = $14,000,000 / $1,010.81

Number of bonds to issue = 13,850.22

This is rounded off to 13,850.

Total principal amount = Number of bonds to issue * face value per bond

Total principal amount = 13,850 * $1000 = $13,850,000.

c]

If a bond sells at par, its coupon rate equals its YTM.

The coupon rate is 12.3%.

The yield of A-rated bonds is 12.3%.

The rating of the bonds should be A

d]

YTM is calculated using RATE function in Excel with these inputs :

nper = 5 (Years remaining until maturity with 1 annual coupon payment each year)

pmt = 1000 * 12.3% (annual coupon payment = face value * coupon rate)

pv = -971.93 (Issue price of bond. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

RATE is calculated to be 13.10%

The yield of BB rated bonds is 13.1%.

The likely rating of these bonds is BB.

A bond with a rating of BB or below is considered a junk bond.