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**Unformatted text preview: **Risk, Cost of Capital and Capital Budgeting
Chapter 12 Cost of Debt
Cost of Preferred Stock
Cost of Retained Earnings
Cost of Newly Issued Equity
Weighted Average Cost of Capital (WACC)
Factors that Affects WACC
Adjusting the Cost of Capital for Risk
Marginal Cost of Capital
The cost of capital is an important issue for financial managers because:
In order to maximize the value of the firm the financial manager must minimize all costs
In order to make capital budgeting decisions, the financial manager must discount the cash flows
of the project by a certain rate (the cost of capital), and
Other investment decisions such as short term financing, bond refunding, etc., require the
estimation of the cost of capital.
Cost of Capital
Are the rates of return expected by those individuals or firms who contribute to the financial
structure: preferred and common shareholders.
Now, as we know, when it comes to financing a project, for example, a firm can finance it in many
different ways. Some may choose to finance their projects through debt, others by issuing preferred
stocks and others may use their retained earnings or any combination of them. Nevertheless,
depending on their financing decision, the firm will have to discount the projects cash flows
accordingly. For those who chose debt financing, they will have to use the cost of debt to discount
their cash flows. For those who used preferred stocks will need to use the cost of preferred stocks.
And for those who used a combination will have to use what is known as the Weighted Average of
Capital.
Let us look at the different cost of capitals in more detail. Cost of Retained Earning, rs
Cost of Retained Earnings - is the rate of return required by investors who own common
stock. r s = rRF + (rM - rRF )bi
Input Variables
1. Risk free rate – the rate on long term treasury bonds since treasury bills tend
to be more volatile
2. Market Risk Premium (rM - rRF ) - can be estimated using
a. Historical risk premiums – calculated as the difference between
historical realized return and rates on T-bonds. Available form
Ibbotson Associates
b. Forward Looking data – uses the discounted cash flow approach to
estimate the market risk premium.
⎤
⎡D
rM = ⎢ 0 (1 + g )⎥ + g
⎦
⎣ P0
where g is the historical growth rate.
c. Beta for a Corporation
Can be calculated as:
slope coefficient in a regression, with the company’s stock returns
on the y axis and the market return on the x axis.
or β= σ i ,m
2
σm Cost of Debt, Rd
Cost of Debt - is used to calculate WACC
- it is the cost required to raise new debt (either short or long term).
Rd = interest rate on the firm's new debt Now, since interest is tax deductible, the after tax cost of debt is found by using the equation
rd(1-T) = after-tax component cost of debt; T= firm's marginal tax rate.
If rd is not given to us, how can we estimate it? Well, if you recall the chapter on bond
valuation you may recall that one way we estimated the cost of debt Kd was by using the
YTM formula. Therefore we could say that: Copyright © 2006 by M.E. de Boyrie – Ehrhardt & Brigham 2 ⎛ M − Vb ⎞
INT + ⎜
⎟
⎝N⎠
Rd = YTM =
⎛ M + 2VB ⎞
⎜
⎟
3
⎝
⎠ Debt and Cost of Capital Companies generally use financing mix comprising debt and equity.
The cost of capital for a company will reflect the mix of financing used.
The following relationships have to be kept in mind when using the cost of capital is to value a
company's assets.
Company Cost of Capital = r assets = r portfolio = equity
debt
* r equity
* r debt +
debt + equity
debt + equity The company cost of capital is the expected return on a portfolio of the debt and equity of the
firm.
This reflects the average cost for the funds used by the firm and is often referred to as the
weighted average cost of capital (W ACC).
Example: Mitsubishi Inc. is a levered firm with a debt-to-equity ratio of 0.25. The beta of the
common stock is 1.15, while the beta of debt is 0.3. The market risk premium is 10% and
the risk free rate is 6%. The corporate tax rate is 35%. If a new project of the company
has the same risk as the overall firm, what is the weighted average cost of capital on the
project?
Answer:
r debt = r f + (r m − r f )beta debt
r debt = .06 + (.10 )(0.3)
r debt = .063 or 6.3%
r equity = r f + (r m − r f )beta equity
r equity = .06 + (.10 )(1.15 )
r equity = .175 or 17.5%
Copyright © 2007 by M.E. de Boyrie – Ross, Westerfield, and Jordan – 6th Edition 3 debt
equity
* r debt * (1 − τ ) +
* r equity
debt + equity
debt + equity
1
4
=
* (.063 ) * (1 − .35) +
* (.175)
1+ 4
1+ 4
= 0.1482 or 14.82% r assets =
r assets
r assets sin ce
debt / equity = .25 = 1 / 4 After Tax Weighted Average Cost of Capital The cost of capital used to reflect the tax deduction allowed for interest payments is
After tax WACC = R D (1 − Tc ) B
S
+ RE
B+S
B+S Optimal Capital Structure The percentage of debt, preferred stock and common equity that will maximize the price of the
stock.
Now, managers will select an optimal Capital structure that will maximize the price of the stocks and
minimize the firm's weighted average cost of Capital (WACC). Why? Because the
Weighted Average Cost of Capital (WACC) - is the overall required rate of return which a
firm must impose in its projects, and if this
rate of return can be reduced then the price of
the stock will go up. Since WACC is a combination of debt and equity we have that
After tax WACC = RD (1 − Tc ) Example: B
S
+ RE
B+S
B+S Arnold's Corporation market value of debt is $4,925,000 and its market value of
equity is $12,000,000. Arnold Corp. can issue bonds at a price of 985, with a face
value of $1,000, a coupon rate of 10 percent and maturity of 10 years. The firm's
marginal tax rate is 34%. If the firm has a beta of 1.2, the risk free rate of 7% and
the market rate of return is 14%, what is Arnold Corp.'s WACC?
Copyright © 2007 by M.E. de Boyrie – Ross, Westerfield, and Jordan – 6th Edition 4 Let us start by looking at the WACC equation
After tax WACC = RD (1 − Tc ) B
S
+ RE
B+S
B+S However, in this example we only work with the market value of debt and equity. Therefore,
we have that,
Market Value of Debt
Market Value of Equity = 4,925,000
= 12,000,000
16,925,000 Since we need to find Ks, we use the SML
r s = rRF + (r m - r RF )b
= 7 + (14 - 7)1.2
= 7 + 8.4
= 15.4%
To find our cost of debt, Kd, we use the YTM formula
⎛ M − Vb ⎞
INT + ⎜
⎟
⎝N⎠
r d = YTM =
⎛ M + 2V B ⎞
⎜
⎟
3
⎝
⎠
⎛ 1,000 − 985 ⎞
100 + ⎜
⎟
10
⎝
⎠
r d = YTM =
⎛ 1,000 + 2(985) ⎞
⎜
⎟
3
⎝
⎠
r d = YTM = 10.25% Therefore
B
S
+ RE
B+S
B+S
4,925,000
12,000,000
After tax WACC = (.1025)(1 − .34)
+ (.1540)
4,925,000 + 12,000,000
4,925,000 + 12,000,000
After tax WACC = 12.89% After tax WACC = R D (1 − Tc ) Copyright © 2007 by M.E. de Boyrie – Ross, Westerfield, and Jordan – 6th Edition 5 Factors that affect the Weighted Average Cost of Capital (WACC) 1. Factors the firm cannot control
a. Interest rates
If interest rates ↑ → cost of debt, cost of preferred stock and cost of retained
earnings ↑
b. Tax rate
If tax rate ↓ → cost of retained earnings and WACC ↓
2. Factors a firm can control
a. Changing capital structure (the weight assigned to debt and equity)
Wd ↑ → WACC ↓
b. Changing dividend policy
Dividend payout ratio ↑ → rs and WACC ↑
c. Altering capital budgeting decision rule
If company invests in an entirely new and risky line of business,
WACC ↑ given that rd and rs ↑ Adjusting the Cost of Capital for Risk Companies that raise capital to finance risky projects will have higher cost of capital than hose
that are investing in safer projects.
Since different projects have different risks, each project should have a cost of capital that
reflects the project’s risk rather than the composite WACC that includes the firm’s overall risk.
This point will be further discussed in chapter 12. Copyright © 2007 by M.E. de Boyrie – Ross, Westerfield, and Jordan – 6th Edition 6 ...

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