Download cost of capital

COST OF CAPITAL
Cost of Debt
Suppose a firm issued $1,000 par value bonds at face value that paid an
8% coupon rate of interest. At that time, the before-tax cost of debt was 8% for
those bonds. If the company has a 40% tax rate, then the after-tax cost of debt
would have been 4.8% since the interest payments are tax-deductible.
Before-tax Kd * (1-t) = After-tax Kd
8% * (1-.4) = 4.8%
Suppose interest rates have risen since the bonds were issued, however, to a
current 10% market rate of interest. The price of the bond will have fallen to, say,
$950 in the market. This means that the cost of debt would have risen to 10%
before-tax or 6% after-tax. Why is the cost of debt not still 8%? Because the
opportunity cost of debt funds is based upon the market rate of interest. What is
one alternative use of any money that the company has? It could go out into the
marketplace and buy back its bonds for $950 and thus earn a rate of return of
10%. By not doing so, it is foregoing the opportunity cost of earning 10%.
Notice also that the amount of debt is only $950 and not the $1,000 that is
on the balance sheet. This is because the accounting for the debt is based upon
historical costs and not the economic value. When debt is set at a fixed rate of
interest, who wins when interest rates go up? Think of a mortgage on your
home. If you lock in a 30-year mortgage at 7% and interest rates go up to 8%,
you are a winner because your debt is at a below-market rate of interest. Of
course, the lender is the loser since for every winner there is a loser in the
markets.
So how do you determine the market value cost of debt? Consider the
following bond’s current price and contractual payments:
0
1 ----------------------
N-1
N
$950
(80) - - - - - - - - - - - - - - - - - - - - -
(80)
(1,080)
If these are before-tax cash flows, what is the before-tax cost of debt? Turn the
question around. If you were to buy this bond for $950 today and receive interest
payments of $80 per year for N years and $1,000 at the end of N years, what
rate of return would you be earning? The answer is whatever the Internal Rate of
Return is on the bond. Thus, the cost of the debt is the IRR between the amount
of money you get and the amounts of money that you must pay back. While the
after-tax cost of debt should really be the IRR on the after-tax cash flows, simply
multiplying the before-tax cost by (1-t) is a very close approximation.
Cost of Preferred Stock
We previously determined that the price of a share of preferred stock was
PP / S 
Div
KP
Rearranging to solve for the preferred stockholder’s required rate of return we get
KP 
Div
PP / S
Thus, if a share of preferred stock pays a $10 annual dividend and is selling for
$100 per share in the market, the cost of the preferred stock is 10%. Again, this
is an opportunity cost based upon market prices.
If the company intends to sell new preferred stock using a broker, the
flotation costs result in an increase in the effective cost of preferred stock. For
example, suppose the same company wanted to sell more preferred stock paying
a $10 dividend. The price that it would be offered in the market would be $100 in
order to avoid diluting the market price. Let’s assume that the broker would
charge a 10% commission for selling the stocks. Then the company would only
net $90 per share and the cost of the new preferred stock would be 11.1% as
follows:
K Pnew 

Div
PP / S *(1  F )
$10
$10

 11.1%
$100(1.1) $90
While the purchasers of the preferred stock are still willing to buy it for only a
10% yield, or $10 on the $100 they pay for the stock, the company must earn
11.1% on the $90 that it receives in order to be able to pay the $10 dividend each
year.
Cost of Retained Earnings
From the stockholder’s viewpoint, what is the difference between $1
invested in the purchase of stock from the company, which ends up in the
Common Stock account, and $1 of earnings that the company retains and ends
up listed in the Retained Earnings account? Both represent a $1 investment in
the company, the only difference is how the accountant records the source of the
$1. Thus, we can essentially ascribe a cost to the retained earnings of the
company as being equal to the stockholder’s required rate of return.
KR / E  KS 
D1
g
P0
Just as in the case of Preferred Stock, however, if new common stock is sold we
must take into account the flotation costs incurred from its issuance. Thus,
KNew C/S 
D1
g
P0 (1  F )
In some instances, primarily those where a company pays no dividends, the cost
of equity will have to be estimated using the Capital Asset Pricing Model.
KS  RF  ( RM  RF )
As before, the cost of equity is always based upon current market rates
and prices.
The Average Cost of Capital
In order to calculate the average cost of capital, we need only to take a
weighted average of the costs of the different components of capital.
K Avg  K d (1  t )
Debt
P/S
C/S
 KP
 KS
Debt + P/S + C/S
Debt + P/S + C/S
Debt + P/S + C/S
The values in calculating the weights are all based upon the market values
of the Debt, Preferred Equity (P/S) and Common Equity (C/S) and not based
upon the book values.
We saw how the weighted average cost of capital was used in valuing
individual projects when we looked at Net Present Value. Now let’s look at how
the cost of capital is calculated.
Looking at Handout #12, we are provided with the current balance sheet
of SA Confections and some miscellaneous data. Suppose we were to calculate
the marginal cost of capital for the company. As you may recall from Economics,
the term marginal refers to the next unit. Thus, we are going to calculate the cost
of raising one dollar of additional capital. Of this dollar, we want part of it to be
debt and part of it to be equity in order to maintain the capital structure that we
currently have which we have been informed is considered to be optimal for the
company. So let’s first see what the capital structure is for the firm.
Remember that we want to use market values for the capital and not the
historical book values of accounting convention. Since the coupon rate of
interest of the debt (10%) is the same as the market rate of interest if we were to
privately place more debt, we know that the market value of the debt is equal to
the par value of $500,000. From the common stock account and a par value of
$1 per share, we can determine the total market value of the equity as 20,000
shares * $50/share = $1 million. Thus, the total value of the firm is $1.5 million
with one-third debt and two-thirds equity.
The after-tax cost of debt can be determined as
k d  10%(1  .3)  7%
when a 30% tax rate is applied. The cheapest form of equity is retained earnings
which can be determined by applying the Gordon Growth Model
kr  ks 
D1
g
P0

$3.50 * (1.06)
 .06
$50

$3.71
 .06
$50
 13.42%
Taking a weighted average of the debt and equity,
kd = 7% *.33
= 2.31
kr = 13.42% *.67 = 8.99
Marginal Cost of Capital = 11.30%
This is for the first dollar that we raise. What about the second dollar? Since the
second dollar that we raise will require an additional 33 cents of debt costing 7%
after-tax, this cost does not change. In addition, the 67 cents of additional equity
will only bring our total equity requirements for the first two dollars up to $1.34 so
we can still use the anticipated $100,000 of retained earnings from this year’s
operations to finance the equity portion of the second marginal dollar. The
marginal cost of capital will remain 11.3% for each dollar until we run out of a
cheap form of a financing component, in this case the retained earnings, and
have to use a more expensive form (issuing new equity). We need to determine
at what point we run out of retained earnings:
X*(2/3)
X
= $100,000
= $150,000
If we go over $150,000 in total financing, we will need more than $100,000 of
equity which will require that we issue new common stock. The cost of new
common stock is
k NewC / S 

D1
g
P0 * (1  F )
$3.71
 .06
$50 * (.9)
 14.24%
This changes the marginal cost of capital on the $150,001st dollar to
kd = 7% *.33
= 2.31
kNew C/S = 14.24% *.67 = 9.54
Marginal Cost of Capital = 11.85%
At this point, we assume that we can sell all of the debt that we want at a beforetax yield of 10% and we can sell all of the common stock that we want at $50 per
share and net $45 per share after flotation costs. When we plot the marginal
cost of capital on a graph, it appears as the blue line on the following page’s
graph:
15%
14%
13%
12%
11%
10%
9%
100
200
300
$1,000s
Having determined the marginal cost of capital at all different levels, we now
want to look at our investment opportunities. Starting with our best project (A),
we want to compare the expected rate of return of the project with the marginal
cost of capital. Thus,
15%
A
14%
13%
12%
11%
10%
9%
100
200
300
$1,000s
Since the expected return exceeds the marginal cost of capital, we want to
accept Project A.
Having decided to take Project A, we next want to consider Project B.
Since we have already determined that Project A is acceptable, Project B’s
$80,000 cost would be added on top of the $100,000 we will have to pay for
Project A.
15%
A
14%
13%
B
12%
11%
10%
9%
100
200
300
$1,000s
Again, since the expected rate of return on Project B exceeds the cost of
financing it, we want to accept this project. We continue in this manner with all of
the projects under consideration:
15%
A
14%
13%
B
12%
MCC
C
11%
D
10%
9%
100
200
300
$1,000s
Since the marginal returns for Projects C and D are less than the cost of
financing these projects, they should not be accepted. Thus, the capital budget
for the coming year should be for $180,000 for Projects A and B. Of this amount,
we want one-third (or $60,000) to be debt ($180,000*1/3 = $60,000) and the
other $120,000 to be common equity ($180,000*2/3=$120,000). Of the $120,000
of equity, only $20,000 of new common stock needs to be sold since we will have
$100,000 available in the form of retained earnings.
These amounts really represent targets. In practice, it wouldn’t make
sense to incur the fixed costs of selling new common stock if you only needed
$20,000 so you would probably just issue additional debt. At some point in the
future, you will adjust back the other way as you issue more equity and less debt.
For now, though, we are just engaged in another planning function to see how
we would like for things to be.
Suppose you were informed that Project C was risk-free. In that case, we
would be rejecting a project with a positive Net Present Value. How can we
know that the NPV would be positive? Because the risk-free rate of interest must
be less than 10% which is the cost of the company’s debt which is risky. Or is it?
Is the weighted average marginal cost of capital of the company risk-adjusted?
Do lenders consider the risk of the firm when they decide what rate of interest to
charge? Do stockholders look at the risk of the company when they decide how
much they’re willing to pay for the stock? Yes, the cost of capital is risk-adjusted.
Thus, since Project C has an expected rate of return (11%) that is greater than
the required rate of return (the risk-free rate) it must have a positive NPV. How
can we reconcile these two approaches?
Based upon NPV, we would accept Project C. But if Project C were riskfree, then by accepting it, we would reduce the risk of the company overall. If the
risk of the company is reduced, then the company’s cost of capital should fall.
Thus, while it looks like we would be losing money by accepting Project C, we
would be more than making it up through the lower cost of capital on all of the
other projects of the firm.
The point here is that we should not be comparing Project C with the
company’s average cost of capital. The average cost of capital is risk-adjusted
for the average risk of the firm. If a project is not average risk, then the required
rate of return should be adjusted accordingly and not just utilize the average cost
of capital blindly. The bigger danger would be accepting a high-risk project
because it has a high expected rate of return that is greater than the average
cost of capital. This would increase the average risk of the company and raise
the average cost of capital, which would require future projects to have a higher
rate of return (and probably higher risk) to exceed the cost of capital.
Now let’s suppose that instead of anticipating $100,000 of retained
earnings it is $200,000. Then, if we only need $120,000 of equity we will have a
surplus of $80,000. What should be done with this surplus? We should pay it
out in dividends. This is referred to as the residual theory of dividends.
Dividends are a residual after considering our financing needs. If we can
reinvest profits to earn the stockholders’ required rate of return (or hopefully
more) then we should not pay any dividends. Only if we do not have investment
opportunities that will earn the required rate of return on earnings should we pay
out a dividend.