Suppose
your company needs to raise $36.2 million and you want to issue 22-year
bonds for this purpose. Assume the required return on your bond issue
will be 8.7 percent, and you’re evaluating two issue alternatives: a 8.7
percent semiannual coupon bond and a zero coupon bond. Your company’s
tax rate is 35 percent.
| Requirement 1: |
| (a) |
How many of the coupon bonds would you need to issue to raise the $36.2 million? (Do not round intermediate calculations. Enter the whole number for your answer, not millions (e.g., 1,234,567).)
|
| Number of coupon bonds |
| (b) |
How many of the zeroes would you need to issue? (Do
not round intermediate calculations. Enter the whole number for your
answer, not millions (e.g., 1,234,567). Round your answer to 2 decimal
places (e.g., 32.16).)
|
| Number of zero coupon bonds |
| Requirement 2: |
| (a) |
In 22 years, what will your company’s repayment be if you issue the coupon bonds? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567).)
|
| Coupon bonds repayment | $ |
| (b) |
What if you issue the zeroes? (Do
not round intermediate calculations. Enter your answer in dollars, not
millions of dollars (e.g., 1,234,567). Round your answer to the nearest
whole dollar amount (e.g., 32).)
|
| Zero coupon bonds repayment | $ |
| Requirement 3: | |
| Assume that the IRS amortization rules apply for the zero coupon bonds. | |
|
Calculate the firm’s aftertax cash outflows for the first year under the two different scenarios. (Do
not round intermediate calculations. Input a cash outflow as a negative
value and a cash inflow as a positive value. Enter your answers in
dollars, not millions of dollars (e.g., 1,234,567). Round your answers
to 2 decimal places (e.g., 32.16).)
|
| Coupon bond cash flow | $ |
| Zero coupon bond cash flow | $ |
| | |
Explanation:
| 1: |
| (a) |
|
The
coupon bonds have a 8.7 percent coupon which matches the 8.7 percent
required return, so they will sell at par. The number of bonds that must
be sold is the amount needed divided by the bond price, so:
|
| Number of coupon bonds to sell = $36,200,000 / $1,000 = 36,200 |
| (b) |
| The number of zero coupon bonds to sell would be: |
| Price of zero coupon bonds = $1,000/1.043544 = $153.58 |
| Number of zero coupon bonds to sell = $36,200,000 / $153.58 = 235,709.19 |
| 2: |
| (a) |
|
The repayment of the coupon bond will be the par value plus the last coupon payment times the number of bonds issued. So:
|
| Coupon bonds repayment = 36,200($1,000) + 36,200($1,000)(.087/2) = $37,774,700 |
| (b) |
| The repayment of the zero coupon bond will be the par value times the number of bonds issued, so: |
| Zeroes repayment = 235,709.19($1,000) = $235,709,193 |
| 3: |
|
The
total coupon payment for the coupon bonds will be the number bonds
times the coupon payment. For the cash flow of the coupon bonds, we need
to account for the tax deductibility of the interest payments. To do
this, we will multiply the total coupon payment times one minus the tax
rate. So:
|
| Coupon bonds: (36,200)($87)(1 – .35) = $2,047,110 cash outflow |
| Note that this is cash outflow since the company is making the interest payment. |
|
For
the zero coupon bonds, the first year interest payment is the
difference in the price of the zero at the end of the year and the
beginning of the year. The price of the zeroes in one year will be:
|
| P1 = $1,000/1.043542 = $167.23 |
|
The Year 1 interest deduction per bond will be this price minus the price at the beginning of the year, which we found in part b, so:
|
| Year 1 interest deduction per bond = $167.23 – 153.58 = $13.65 |
|
The
total cash flow for the zeroes will be the interest deduction for the
year times the number of zeroes sold, times the tax rate. The cash flow
for the zeroes in year 1 will be:
|
| Cash flows for zeroes in Year 1 = (235,709.19)($13.65)(.35) = $1,126,264.81 |
|
Notice
the cash flow for the zeroes is a cash inflow. This is because of the
tax deductibility of the imputed interest expense. That is, the company
gets to write off the interest expense for the year, even though the
company did not have a cash flow for the interest expense. This reduces
the company’s tax liability, which is a cash inflow.
|
|
During
the life of the bond, the zero generates cash inflows to the firm in
the form of the interest tax shield of debt. We should note an important
point here: If you find the PV of the cash flows from the coupon bond
and the zero coupon bond, they will be the same. This is because of the
much larger repayment amount for the zeroes.
|
| Calculator Solution: |
|
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.
|
| (a) | The coupon bonds have a 8.7% coupon which matches the 8.7% required return, so they will sell at par. For the zeroes, the price is: |
| Enter |
22 × 2
|
8.7% / 2
| | |
±$1,000
| ||||||||||
| | |
N
| | |
I/Y
| | |
PV
| | |
PMT
| | |
FV
| |
| Solve for | | |
$153.58
| | | ||||||||||
| (c) | The price of the zeroes in one year will be: |
| Enter |
21 × 2
|
8.7% / 2
| | |
±$1,000
| ||||||||||
| | |
N
| | |
I/Y
| | |
PV
| | |
PMT
| | |
FV
| |
| Solve for | | |
$167.23
| | | ||||||||||
