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Please review the adjoined file
below then go on to apply the results to valuing a firm both unlevered (no
debt) and levered (debt). The levered firm is shown to be more valuable. Two
identical firms (see the supplemental materials) and the firm with debt is more
highly valued. Does this make sense? Why or Why not? Why not use 100 percent
debt financing if debt increases value?
Details
A project
(or firm) will be financed through a combination of equity and debt.
Q: What is
equity?
Q: What is
debt?
The value
of a firm or project can be thought of as:
V = B + S
(eq. 1)
Where,
V = value,
B = market value of debt, S = market value of equity
(recall if firms obtain debt financing in the financial markets, they
issue bonds…hence the B for
debt, you could also have loans etc.)
Example:
You start a
project. You and your classmates invest $1,000,000 ($1M) of your own funds
into the
project and you obtain $9,000,000 ($9M) of debt financing (this mix of debt and
equity is the
capital
structure.).
Q: What is
the value of the project?
V= $1M +$
9M =$ 10M
Assume a
nearly identical project across the street from yours sells for $15M the day
after you arrange
the
financing above. (this is a gross simplification for illustrative purposes)
Q: What is
the value of debt? Equity? And total value?
If the
project is nearly identical than it appears the market is pricing the
project at
$15M, so V = $15M
Value of
debt (B) is what?
Debt
holders are the ones who have a claim against your project via interest paid on
the loan. The
bond/debt
holders are the ones who can force you into bankruptcy and hold a higher
priority of
claim (they
get paid first). Debt holders do not partake in the increase in the value of
equity so the value.
Therefore,
the value of B is: $ 9 m
Who gets
the increase in value, the equity holders. You and your classmates now have
equity of $6M.
MBAA 518 - Managerial Finance
May 2015 1
Does
financing all have to come from external sources?
No, can use
retained earnings.
The use of
the capital is not free, there is a cost (cost of capital). Do you go to the
market to purchase
groceries?
Do people go to the financial markets to purchase capital? Is there a cost when
you buy
groceries?
Do you think there is also a cost of capital? The answer is yes.
Determining
(estimating) the cost of capital is important in the evaluation of projects.
The cost of
capital is
the “r” we have been using in our analysis. Another term for “r” is the
weighted average cost
of capital
(WACC), to estimate the cost of capital the estimate must:
Consider
all sources of capital*
Be computed
on an after tax basis
Use nominal
rates of return
(*For this course we will assume there is equity (S) and debt (B)
only. There can be other financial
instruments used to finance a firm.)
Formula for
estimating WACC
Recall
equation 1 form above:
V = B + S
If you
divided both sides of the equation by V the result is:
1 = B/V +
S/V (eq. 2)
Note, that
B/V and S/V represent the weights of each component of the firm’s financing.
The total
value is V,
B divided by V and S divided by V would give the percentage of each type of
financing of the
capital
structure.
After taxes
also needs to be considered. Recall EBIT. The I is for interest which is an
expense that
reduces
taxable income. Therefore, debt actually costs is less than the stated interest
rate.
For
example:
Company XYZ
has a corporate tax rate (Tc) of 39 percent with expected earnings
before
interest and taxes (EBIT) of $2 million dollars each year. All earnings are
paid out as
dividends.
MBAA 518 - Managerial Finance
May 2015 2
Two
alternative capital structures are under consideration. For Plan I, XYZ will
have
no debt and
under Plan II, XYZ would have $8,000,000(B) in debt and the cost of
the debt is
10 percent (rb). What would the cash flows for XYZ look like under the
two plans?
Plan I Plan
II
EBIT
2,000,000 2,000,000
Interest on
debt 0 800,000
EBT
2,000,000 1,200,000
Taxes
780,000 468,000
Earnings
After Tax 1,220,000 732,000
Total Cash
Flows to Investors1 1,220,000 1,532,000
(1: interest + earnings, interest is paid out to investors who
provided debt and in this example all earnings
are paid out as dividends to shareholders)
What is of
most interest to us?
Total cash
flows to investors which includes interest paid to debt holders and earnings
paid to
shareholders. The difference in the two plan is:
1,532,000 –
1,220,000 = 312,000
This
difference is due to the change in the amount of taxes paid:
780,000 –
468,000 = 312,000
Interest
escapes corporate taxation while earnings do not.
This
reduction in taxes is equal to:
Tc x rb x B (eq. 3)
= 0.39 x
0.10 x 8,000,000 = $312,000
The real
cost of the debt (interest paid less the decrease in taxes) =
(800,000‐312,000)/8,000,000
= 0.061
Or an after
tax cost of debt of 6.1 percent
Another way
of calculating the cost of debt is:
(1 ‐ Tc)(rb) (eq. 4)
(1‐0.39)(0.10)
= 0.061 (or 6.1 pct)
MBAA 518 - Managerial Finance
May 2015 3
The
financing arrangements are referred to as capital structure. (Just like you may
have a structure (i.e.
your house)
framed from wood, you can have a project built in all equity, all debt (may be
unlikely) or a
combination
of debt and equity).
We still
are missing the cost of equity financing which is the opportunity cost of
equity financing. This is
a complex
question which requires a discussion of risk, return, some statistical
properties of stock
market
returns relative to the return of a given stock and the derivation of models to
estimate the cost
of capital.
Numbers that are required are the risk free rate, market risk premium and beta.
(you have
studied
this in the previous modules). The cost of equity should be the market cost of
equity for a
similar
project/firm. For this example, we will use a cost of equity of 10 percent.
We now have
the components to calculate the weighted average cost of capital (WACC)
WACC = rb (1‐Tc)(B/V) + rs(S/V) (eq.
5)
Where:
WACC =
weighted average cost of capital
rb = pretax
market expected yield to maturity
Tc = corporate
tax rate
B = market
value of debt
S = market
value of equity
Here is
something to think about (and discuss…see activity 5)
In the
example above, assume Plan I and Plan II refer to firms I and II. We saw above
the levered
project
(now firm) will play less in taxes and the reduction in taxes was calculated
using equation 3. This
amount,
$312,000, if often called the tax shield from debt similar to a tax shield from
depreciation.
Assuming
the firm remains in a positive tax bracket and the savings from debt is
perpetual the present
value of
the tax shield is:
Tc x rb x B / rb = Tc B (eq. 6)
If the firm
is unlevered, there would be no tax shield. Firm I represents the unlevered
firm and the
Value of
the unlevered firm Vu would be equal to the discounted after tax cash flows. Assuming the
cash flows
occur perpetually the value of the unlevered firm would be:
Vu = EBIT x (1
– Tc)/ ru (eq. 7)
MBAA 518 - Managerial Finance
May 2015 4
Where ru =
cost of capital for unlevered firm
Vu =
2,000,000 (1 – 0.39) / 0.10 = $13,800,000
The value
of the levered firm (Firm II) would have to incorporate the present value (PV)
of the debt tax
shield
(recall comment above about the cost of equity). Combining equations 5 and 6
results in the
value of
the levered firm.
Vl = EBIT x (1
– Tc)/ ru + Tc x rb x B / rb (eq. 8)
Resulting
in:
Vl = 2,000,000
x (1 – 0.39)/ 0.10 + 0.39 x 8,000,000 = $14,112,000
The value
of the levered firm is higher than the unlevered firm due to the savings in
taxes.
