Content
1. Abstract
We all have a consciousness that today’s
money won’t equal tomorrow’s which means that it always contains future value
when dealing with the pending cashing flow. So as for the bonds issue problem,
this essay will start with the basic finance theory of coupon rate, effective
rate, amortization and the calculation formula for them. Then it will give us an
example of non-biased testifies based on the assumption according to the given
case in this report. In terms of the assumption, it will list all of the five situations
that may occur and try to analyze them respectively. In the analysis part, it
will not only give us a general idea of whether it is reasonable to lower the
coupon rate in order to reduce company’s cost , but also illustrate the
drawbacks and limitation of the assumption in this case. In the end, the whole
group reaches the consensus that it is not wise of the subordinate to lower the
coupon rate to cut down cost because he missed the amortized cost.
2. Introduction
Without loans,
most of us wouldn't be able to afford things like a car, a home or education.
And, just as people borrow money to help them succeed, so do businesses.
Businesses often need loans to fund operations, move into new markets, innovate
and grow in general. But the amount they need often surpasses what a bank can provide.
So another useful way for corporations to raise the necessary funds is to issue bonds to whoever wants to buy them.
But that's all a bond is a loan. When you buy a bond,
you're lending money to the organization that issues it. The company, in
return, promises to pay interest payments to you for the length of the loan. How much and
how often you get paid interest depends on the terms of the bond. The interest
rate, also called the coupon, is typically higher with long-term bonds. These interest
payments are usually doled out semi-annually, but they can also be sent out
annually, quarterly or even monthly. When the bond reaches the date of maturity, the issuer repays the principle, or original amount of the loan.
2.1 Scope of the problem
Here our scope
is to compare the different coupon rates vs the market rate and check whether
lowering the coupon rate would lead to an increase in profits for the company. “Assume
that you are the CFO of the company that intends to issue bonds to finance a
new manufacturing facility. A subordinate suggests lowering the coupon rate on
the bond to lower interest expense and to increase the profitability of your
company. Is the rationale for this suggestion a good one?”
2.2 Concept
In order to analyze the above mentioned problem we need to
understand some key definitions as follows:
Coupon rate
A coupon payment on a bond is a periodic interest payment that the bondholder receives
during the time between when the bond is issued and when it matures.
Coupons are normally described in terms of the coupon rate, which is calculated by adding the total amount
of coupons paid per year and dividing by the bond's face value. For example, if
a bond has a face value of $1,000 and a coupon rate of 5%, then it pays total
coupons of $50 per year. For the typical bond, this will consist of semi-annual
payments of $25 each.
Significance of Coupon Rate
The term coupon rate used
to have a much more literal meaning than it does today. To receive interest
payments in the past, bondholders would have to clip a coupon from their physical certificate of bond ownership and take it to the bank to obtain the cash. Today, your broker is more likely to deposit the payments straight into your account.
Some bonds, known as zero-coupon bonds, do not pay coupons, and instead are
sold at a price less than par value.
Effective rate
Effective rate is the interest rate on a loan or
financial product restated from the nominal interest rate as
an interest rate with annual compound interest payable in arrears. It is used to compare the annual
interest between loans with different compounding terms (daily, monthly,
annually, or other). The effective interest rate differs in two important
respects from the annual percentage rate:
1. The effective interest
rate generally does not incorporate one-time charges such as front-end fees;
2. The effective interest
rate is (generally) not defined by legal or regulatory authorities.
The effective interest rate is calculated
as if compounded annually. The effective rate is calculated in the following
way, where r is the
effective annual rate, i the
nominal rate, and n the
number of compounding periods per year (for example, 12 for monthly
compounding):
Par Value Bond
Par Value is the nominal
value or dollar value of a security stated by the issuer. For stocks, it is the
original cost of the stock shown on the certificate. For bonds, it is the
amount paid to the holder at maturity (generally $1,000).
Discount Bond
Discount bond is a type of
bond that is issued for less than its par (or face) value, or a bond currently
trading for less than its par value in the secondary market.
The "discount" in a discount bond doesn't necessarily mean that investors get a better yield than the market is offering, just a price below par. Depending on the length of time until maturity, zero-coupon bonds can be issued at very large discounts to par, sometimes 50% or more.
The "discount" in a discount bond doesn't necessarily mean that investors get a better yield than the market is offering, just a price below par. Depending on the length of time until maturity, zero-coupon bonds can be issued at very large discounts to par, sometimes 50% or more.
Premium Bond
Premium bond is a bond that is trading above its par value. A
bond will trade at a premium when it offers a coupon rate that is higher than
prevailing interest rates. This is because investors want a higher yield, and
will pay more for it.
A specific type of bond issued in nations such as the United Kingdom and Canada. In the U.K., premium bonds are referred to as a lottery bond issued by the British government's National Savings & Investment scheme. In Canada, the Canada Premium Bond, first introduced in 1998, offers a higher interest rate at the time of issue than a comparable Canada Savings Bond.
A specific type of bond issued in nations such as the United Kingdom and Canada. In the U.K., premium bonds are referred to as a lottery bond issued by the British government's National Savings & Investment scheme. In Canada, the Canada Premium Bond, first introduced in 1998, offers a higher interest rate at the time of issue than a comparable Canada Savings Bond.
3. Assumption and analysis
In order to analysis whether this company can increase
its profitability by decreasing the coupon rate of the issued bonds, we need to
compare the cost of decreasing the coupon rate to the cost before this strategy
has been applied. First of all, we need to assume some numbers. We illustrate
that this company issued the bonds with face value of $100,000, paying interest
semiannually for 5 years. The effective (market) rate is 10%（i）,
and we assume that it remains unchanged. Then, we need to consider three
different situations.
Situation 1:
a. Issue at par: the
coupon rate is 10% (r). P = {1-[1 / (1+
i) ^t]}/i, t represents the interest payment period.
P = {1-[1 / (1+ 5%) ^10]}/
5% = 7.72137
Interest payment every
period = 100,000 * (10% / 2) = 5,000
The present value of
total interest payment = 5,000 * 7.72137 = 38,609
When the bonds are issued at par, the cost of the
company is only the interest payment which is $38,609.
b. The company decreases
the coupon rate from 10% to 8%, the bonds issued at discount.
Interest payment every
period = 100,000 * (8% / 2) = 4,000
The present value of
total interest payment = 4,000 *7.72137 = 30,885.48
Present value (issue
price) of bonds = 100,000 / (1+5%) ^10 + 30,885.48= 92,276.81
Discount balance =
100,000 – 92,276.81 = 7,723.19
The total cost = total
interest payment + discount balance
= 30,855.48 +
7,723.19 = 38,609
Bond face value
|
Effective value
|
Coupon rate 10%
|
Interest payment
pv=38,609
|
Cost
38,609
|
100,000
|
10%
|
Coupon rare 8%
|
Interest payment
pv=30,886
Issued bond
pv=92,277
Discount balance=7,723
|
Cost
38,609
|
When the company decreases the coupon rate, issue of
the bonds change from par to discount, the cost of the company includes the
total interest payment and the part of discount, which are 38,609.
a.
issued at discount: the coupon rate is 8%.
The total cost = 38,609
(the calculation is the same as situation (1) b)
b.
The company decreases the coupon rate from 8% to 6%, the bonds issued still at
discount.
Interest payment every
period = 100,000 * (6% / 2) = 3,000
The present value of
total interest payment = 3,000 *7.72137 = 23,165
Present value (issue
price) of bonds = 100,000 / (1+5%) ^10 + 23,165= 84556
Discount balance =
100,000 – 84,556 = 15,444
The total cost = total
interest payment + discount balance
= 23,165+
15,444 = 38,609
Bond face value
|
Effective value
|
Coupon rate 8%
|
Present Value of
Interest payment =38,609
|
Cost
38,609
|
100,000
|
10%
|
Coupon rare 6%
|
Present Value of
Interest payment =23,165
Present Value of Issued
bond =84,556
Discount balance =15,444
|
Cost
38,609
|
When the company lower the coupon rate, issue of the
bonds still remain discount, the cost of the company includes the total
interest payment and the part of discount, which is 38,609.
Situation 3:
a.
As a third illustration, assume that investors demand a 5% semiannual return
for the 6% semiannual coupon rate, while all other details remain the same. The
bond now sells for $107,721, computed as follows:
Interest payment=100,000*6%=6,000
Present value of interest
payment=6,000*7.72173=46,330
Present value of bond
principle value=107,722
Premium
balance=107,722-100,000=7,722
Cost=46,330-7,722=38,609
b.
As the subordinate suggests, we lower the coupon rate to 5.5% semiannual paid,
while all other details remain the same. In this situation, the bond still
sells at premium with a price of $103,861, computed as follows:
Interest
payment=100,000*5.5%=5,500
Present value of interest
payment=5,500*7.72173=42,470
Present value of bond
principle value=103,861
Premium
balance=103,861-100,000=3,861
Cost=42,470-3,861=30,609
c.
If we lower the coupon rate to 5% semiannual paid, while all other details
remain the same. In this situation, the bond sells at par. The cost of bond
issue then comes to the present value of interest payment only.
Cost
=100,000*5%*7.72173=38608.65
d.
If we lower the coupon rate to 4% semiannual paid, while all other details
remain the same. In this situation, the bond sells at discount with a price of
$92,278, computed as follows:
Interest payment=100,000
4%=4,000
Present value of interest
payment=4,000*7.72173=30,885
Present value of bond
principle value=92,278
Discount
balance=100,000-92,278=7,722
Cost =30,885+7,722=38,607
Bond
Face
Value
|
Effective
Rate
|
Coupon rate 12%
|
Present
Value of Interest payment=46,330
Present
Value of Issued bond =107,722
Premium balance=7,722
|
Cost
38,609
|
Coupon rate 11%
|
Present
Value of Interest payment=42,470
Present
Value of Issued bond=103,861
Premium
balance=3,861
|
Cost
38,609
|
||
100,000
|
10%
|
Coupon rate 10%
|
Present Value of
Interest payment=38,608.65
|
Cost
38,608.65
|
Coupon rate 8%
|
Present Value of
Interest payment =30,885
Present Value of Issued
bond =92,278
Premium balance=7,722
|
Cost
38,607
|
As we can see from the calculation, lower
the coupon rate makes no difference to the cost of bond issue, which means that
the profitability will not increase by lowering coupon rate.
4. Drawbacks
Though the assumption seems flawless, it
still remains disputes and limitations in applying which should be taken into
consideration. Due to condition that market rate is fixed, we can only
confidently estimate the scenario which is smooth and stable. In other words,
the market is dynamic so that credit rating and redundancy to risk taking is
also key factor in determining the coupon rate. To some extreme cases, like
company breakdown, economic crisis or violation will cause a devastating
downturn in the coupon market. Apart from the risk, we still underestimate the
human factor in deciding the coupon rate. We do not consider the creditor’s
indications of interest and their purchase intention which is another omission.
5. Conclusion
To determine whether the company can
increase profit with lowering the coupon rate, the purpose of this work is to
verify what the impact of the lowering offer is on the
profitability referring to the lower interest expense.
What the subordinate suggested is
to lower the coupon rate of the bonds to lower the interest cost, however
through our analysis lower coupon rate makes no difference on the profit of
company. Specifically, we find the changes are generated both on interest
expenses and the differences between basic value and face value at the same
time. The reason is that the cost we spend is the combination of the bond
premium or discount and the interest expense. With a lower coupon rate, not
only the more the differences between principal and the paid value but also the
less interest. Therefore, the total expenses have small changes actually. For
instance, in our case if we accept the subordinate advice to lower the coupon
rate no matter the original situation is premium, discount or at par, the
coupon rate at discount will be lower than the market rate. Based on our calculation,
the profit remains the same. In other case, if the bond is at premium
originally there will be no effect on the profit of the company if we lower the
coupon rate to premium or at par. As we can see from the
calculation, lower the coupon rate makes no difference to the cost of bond
issue, which means that the profitability will not increase by lowering coupon
rate.
6. Suggestion
We should be aware that making changes
about the bond rate does not work. Therefore, according to the formula: profit
= revenue – cost, we would like to suggest increasing the sales by advertising
or adding up price when the company keeps strong competitiveness in the market.
Besides, controlling the material supplies or maintaining the machine operating
well will also be effective ways to decrease the cost.
