Transcript Cost of Capital

Risk, Cost of Capital,
and Capital Budgeting
Valuing a Project

When valuing a project you need two things:
1.
2.

Initially you were given both (Unit 1), then
you learned how to find the cash flows (Unit
2), so what are we learning know?
2
Method 1: Matching
Basic Idea: Find another project with the same
systematic risk characteristics, and use that
project’s return as the discount rate
3
Example

Assume you need to find the discount rate for
an apple picking machine, and you find that a
pear picking machine offers a return of 15%.
 Assume
that pears and apples have the same
systematic risk

The appropriate discount rate for the apple
picking machine is _____%.
4
Method 2: CAPM

CAPM: E(ri) = rf + βi (rM - rf)

CAPM gives the expected return for a given
level of systematic risk
 The
expected return is what an investment with
this much risk should earn
5
Project β Example

Think of the project’s β being like the β of a
portfolio, and how did we find the portfolio
β?

The project/firm can be thought of as a
portfolio of its components: Financing,
Assets, Divisions, etc
6
Firm β Example

f represents the systematic risk
associated with the firm assets
If the firm is all equity financed then βf

If the firm is all debt financed then βf

If the firm is financed with both

7
Using βa

Once we have our estimate of βa, we can plug
it into the CAPM and find the appropriate
discount rate
ra = rf + βa (rM - rf)
8
Method 3: Weighted Average Cost
of Capital (WACC)

Here we are going to work with the returns
required by the firms investors (Equity,
Debt, etc) to find the company’s/projects
cost of capital
9
Weighted Average Cost of Capital
(WACC)
If you own all of the debt and equity you own
the whole firm, and the return you receive is
simply the weighted average of the return on
debt (rd) and equity (re)
 ra = WACC =

10
Weights General

Market Value of the Firm = E + D
 E:
Market Value of Equity = Price * # of shares
outstanding

Equals the PV of the cash flows to all equity holders
 D:
Market Value of Debt = Price * # of bonds
outstanding

Equals the PV of the cash flows to all debt holders
11
Weights Examples

What is the firm’s debt and equity weight
 If
debt-to-equity = 0.8
 If
debt-to-value = 0.8
12
Equity and Debt’s Expected Return
We will generally use CAPM to get re
 We will use the YTM to get rd

 Why

do we use the YTM?
If the firm has no debt but it has plans to issue
debt why do we use the coupon rate as rd , Why?
13
Example
Suppose a firm is worth $100m and its equity
is worth $40m. Given that the return on equity
is 20% and the return on debt is 10%, calculate
the firm’s WACC.
 WACC = ra =
 What does WACC represent?

14
Example Continued

What would be the asset beta if we assume that
d = 0.5, and e = 1.5?

What will ra be according to CAPM?
 rf =
5%, rm = 15%
15
Alternative WACC Calculations

Using Returns:
 WACC=

D/V * rd + E/V * re
Using Beta’s (Similar To CAPM):
 Use e
and d to get a, then use CAPM to get
WACC
 a = D/V * d + E/V*e
 WACC = Rf + a * E(Rm - Rf)

Both methods give the same result
16
Alt Formula Proof: Not on Test
WACC = Rf + a*(Rm–Rf)
 WACC=


WACC = D/V*rd + E/V*re
17
What happens to WACC as the Firm’s
Capital Structure Changes

Going back to our WACC example. Investor’s
required a 14% return on the whole firm. If the
firm decides to issue debt and buyback equity,
what will happen to the return required by:
 An
investor owning the entire company
 Equity investors
 Debt investors
18
Why are Equity and Debt Cash
Flows Riskier?

As a firm takes on more debt, it is more likely
that the firm will not be able to meet it debt
obligations, and declare bankruptcy
 This

is known as Default or Financial Risk
As a firm issues more debt what will happen to
default risk?
19
Default Risk and Required Returns

As default risk increases, increasing the required
return for equity and debt, how can the firms
required return remain constant?
20
WACC Graph
23%
Required Return
18%
13%
8%
3%
E/V (5%)
Re
Rd
WACC
21
Changing Leverage: WACC = 13%
E/V
Re
Rd
E/V
Re
Rd
1
0.95
0.90
0.85
13.0%
13.5%
14.0%
14.5 %
3.5 %
4.0%
4.5 %
0.50
0.45
0.40
0.35
18.0%
18.5 %
19.0%
19.5 %
8.0%
8.5 %
9.0%
9.5 %
0.80
0.75
0.70
15.0%
15.5 %
16.0%
5.0%
5.5 %
6.0%
0.30
0.25
0.20
20.0%
20.5 %
21.0%
10.0%
10.5 %
11.0%
0.65
0.60
0.55
16.5 %
17.0%
17.5 %
6.5 %
7.0%
7.5 %
0.15
0.10
0.05
21.5 %
22.0%
22.5 %
11.5 %
12.0%
12.5 %
22
Default Risk and 

What happens to the company’s  as the
company’s capital structure changes?
23
What will happen
Suppose the firm decides to alter its capital
structure by raising $20m in equity and using
the cash to pay down debt.
 What should happen to βd & βe? Explain

24
Boeing Example
 Boeing
is planning to increase its capacity
so that it can cater to increased demand.
 The firm currently has no debt
 What is the appropriate discount rate for its
expansion?
Rf
= 5%, Rm - Rf = 10%, e = 1.5.
25
Levered Boeing

Now, assume Boeing has debt in the capital
structure.



Assume that e remains the same even though
we know this is not true.
It’s target debt-equity ratio is 30%, and it’s
debt has a beta of 0.2.
Now, what is the appropriate discount rate?
26
Lubbock Brewing Example

Lubbock Brewing’s common stock has a
market value of $40m, and its debt has a
market value of $10m. Assume these values
reflect the target D/E ratio.
 The
beta of the stock is 1.2 and the expected risk
premium on the market is 10%.
 The current T-bill rate is 5%.
 Assume debt is risk free.
27
Calculate




The required return on Lubbock Brewery equity
and debt
 re =
 rd =
Asset beta
 a =
WACC using both methods
 WACC =
 WACC =
Discount rate for an expansion project
28
Apparel Expansion

Lubbock Brewery is considering diversifying
into the apparel business. There are two
apparel companies that are similar to the
project being considered. These firms are not
involved in any other business.

Fashion Clothing, which has no debt in the
capital structure, with an equity beta of 0.9.
 Tempe Trends has a debt-value ratio of 0.1,
an equity beta of 0.9 and a debt beta of 0.1.

What is the appropriate discount rate?
29
Lingo Example


Lingo Co. is currently involved in the manufacture
of steel. It has a modernization plan which is
expected to save $10m in cash flows each year
over the next 3 years. The investment required is
$20m. Should it take up the project?
The following details are available: Firm's current
equity beta and debt beta are 1.2 and 0.3
respectively. Risk free rate is 4%. Expected
market risk premium is 10%. Firm's target debtequity ratio is 0.5.
30
Lingo Computer Expansion

Lingo Co is planning to diversify further into
computers. It has identified two competitors
Compaq
Toshiba


e
1.2
D/V
0.3
Coupon
8%
YTM
6%
1.5
0.4
9%
7%
While Compaq manufactures only computers, Toshiba
manufactures other products as well.
What is the discount rate for this diversification
project?
31
Discounting Projects with WACC


The WACC is the discount rate for the entire
company
True/False:
 Since we now have the company’s WACC, are we
able to value all of the firm’s potential investments
32
So why all this work to find
WACC
A firm’s WACC is a benchmark
 Determining how risky a project is can be
difficult
 Determining how risky a project is compared
to what you currently do is easy

 We
can adjust the firm’s WACC to account for the
riskiness of the new project
33
Relative Discount Rates

Project with same risk as firm
 Discount

Project with more risk than firm
 Discount

rate will ________ firm’s WACC
rate will ________ firm’s WACC
Project with less risk than firm
 Discount
rate will ________ firm’s WACC
34
What about TAXES



Without taxes all of a firm’s cash goes to investors,
equity or debt holders
With taxes the firm also needs to payoff the
government
As some of the firm’s cash flows are needed to payoff
non-investors (Uncle Sam) what will happen to firm
value compared to the no tax world
35
Who is paid first?

In a world with taxes the firm needs to payoff,
equity, debt and Uncle Sam. What is the order
of payments?
1.
2.
3.

What does this order of payments imply?
36
WACC with TAXES

No Taxes: WACC= E/V * re + D/V * rd

With taxes WACC =
37
Using WACC with Taxes

To find the value of a firm using WACC we
either:
Use pre-tax cash flows and tax adjusted WACC
2. Use after-tax cash flows and WACC without tax
adjustments
1.

We cannot use after-tax cash flows and
adjusted WACC → Double counting tax
effects
38
Summary
The company’s cost of capital is not the
expected return on it’s stock or debt
 The company cost of capital is a weighted
average of the returns that investors expect
from the debt and equity issued by the firm.
 The company cost of capital is related to the
firm’s asset beta, not to the beta of the
common stock.

39
Summary Continued
The asset beta can be calculated as a weighted
average of the betas of the various securities.
 When the firm changes its financial leverage,
the risk and expected returns of the individual
securities change. The asset beta and the
company cost of capital do NOT change.

40
Quick Quiz
How do we determine the cost of equity
capital?
 How can we estimate a firm or project beta?
 How does leverage affect beta?
 How do we determine the cost of capital with
debt?

41
Why We Care

Refinement of the time value of money,
learning how to get the proper discount rate
42