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 3.5% ​(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​ (%)	3.03.0	3.13.1	3.53.5	3.93.9	4.34.3

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 $964.68. What is the likely rating of the​ bonds? Are they junk​ bonds?

Note​: Assume annual compounding.

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 3.5% (annual payments). The following table summarizes the yield to maturity for five-year (annual-pay) coupon corporate bonds of various ratings. AA BBB BB Rating YTM (%) AAA 3.0 A 3.5 3.1 3.9 4.3 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 $964.68. What is the likely rating of the bonds? Are they junk bonds? Note: Assume annual compounding.

Answer 1

First, we model the cash flows arising out of the bonds issue in an Excel sheet
We include proceeds received from the issue, annual coupon payment and principal repayment.
Here we don't know at what price the bonds are isued, hence we don't know what are the proceeds arising out of the issue. We assume any value and we'll later solve for this value using Excel function. For the time being, this can be any arbitrary value.
We sum cash flows in each year to arrive at net cash flows in that year
IRR of this cash flow is going to be the yield of the bonds.

Year	0	1	2	3	4	5
Issue proceeds	$                      980
Coupon payments		$        (35)	$        (35)	$        (35)	$        (35)	$        (35)
Principal repayment						$ (1,000)
Net cash flow	$                      980	$        (35)	$        (35)	$        (35)	$        (35)	$ (1,035)
Yield	3.9%

At this stage, we have done the groundwork to solve all the subparts of the bond

a.

If the bonds are rated AA, the yield will be 3.1%

We go to our Excel model, go to Data tab -> What If analysis -> Goal Seek function

In the analysis, we set the value of yield cell to 3.1% by changing value of issue proceeds, and click Ok. Excel will solve it for us and we'll get the calculations done. Issue proceeds will be the price of the bonds

Year	0	1	2	3	4	5
Issue proceeds	$                   1,018
Coupon payments		$        (35)	$        (35)	$        (35)	$        (35)	$        (35)
Principal repayment						$ (1,000)
Net cash flow	$                   1,018	$        (35)	$        (35)	$        (35)	$        (35)	$ (1,035)
Yield	3.1%

Hence, if the bonds are AA rated, the price of the bonds will be $1.018

b.

We first find out the number of bonds issues.

Issue size = Bond price x number of bonds

Number of bonds = Issue size / bond price
Number of bonds = 14,000,000 / 1,018
Number of bonds = 13,758

Total principal amount = Number of bonds x Face value
Total principal amount = 13,758 x 1,000
Total principal amount = $13,758,000

Hence the total principal amount is $ $13,758,000

c.

We go back to our Excel model, and simply change the value of issue proceeds to $1,000

The IRR we get for these cash flows is the yield of the bonds

Year	0	1	2	3	4	5
Issue proceeds	$                   1,000
Coupon payments		$        (35)	$        (35)	$        (35)	$        (35)	$        (35)
Principal repayment						$ (1,000)
Net cash flow	$                   1,000	$        (35)	$        (35)	$        (35)	$        (35)	$ (1,035)
Yield	3.5%

We see that the yield is 3.5%

For the yield to be 3.5%, the bonds must be rated A, as per the table given in the question.

Hence the rating of the bonds must be A for them to sell at par

d.

Again, we go back to our model and change the value of the issue proceeds to 964.68

Year	0	1	2	3	4	5
Issue proceeds	$                964.68
Coupon payments		$        (35)	$        (35)	$        (35)	$        (35)	$        (35)
Principal repayment						$ (1,000)
Net cash flow	$                      965	$        (35)	$        (35)	$        (35)	$        (35)	$ (1,035)
Yield	4.3%

We see the yield of the bonds is 4.3%

Hence the bonds must be rated BB

Bonds with a rating lower than BBB are considered to be junk bonds
Hence these bonds would be junk bonds