# finance

Pages: 35 (1707 words) Published: October 28, 2014
Project vs Firm Risk and the
Impact of Leverage

The SML and WACC
§  Consider 100% equity financed firm
§  Beta = 1
E/V = 1!
D/V = 0!
§  WACC =?

E
D
WACC = × RE + × RD × (1 − TC ) = RE
V
V
WACC = Cost of equity from CAPM

[

]

WACC = RE = R f + β × E [RM ] − R f = E [RM ]
Beta =1!

2

SML and WACC
SML

Expected
Return
WACC = E[RM]

Rf

[

R f + β × E [RM ] − R f

]

β=1

Beta
3

Accept Projects Y and/or Z?
Expected
Return
IRRz
WACC = E[RM]
IRRY

SML

Z
Y

Rf

β=1

Beta
4

Accept Projects Y and/or Z?
E[R]

SML

E[RZ]

Z

WACC = E[RM]

Y

E[RY]
Rf

βY

β=1

βZ

Beta
5

Accept Projects Y and/or Z?
E[R]

SML
Incorrect

Z

WACC = E[RM]

acceptance
Incorrect
rejection

Y

Rf

β=1

Beta
6

Project Y
§  IRR of Project Y is lower than WACC
§  Project Y would be rejected based on
WACC
§  BUT: Project Y is less risky than firm as a
whole
§  Its return is higher than the expected
return from CAPM (it is above the SML)
§  Accept Project Y
7

Project Z
§  IRR of Project Z is higher than WACC
§  Project Z would be accepted based on
WACC
§  BUT: Project Z is more risky than firm as a
whole
§  Its return is lower than the expected
return from CAPM (it is below the SML)
§  Reject Project Z
8

Solutions to the problem
§  Pure play (opposite of conglomerate)
§  Use WACC of “pure play” companies in the
same industry (a pure play company operates
in a single industry only: for example,
Blackberry maker Research in Motion is a pure
play in smart phones and related software)

§  Subjective
§  Adjust firm’s WACC to reflect the riskiness of
the project relative to riskiness of the firm
9

Finding Comparable Pure Play
§  Often difficult to find comparable pure play
companies

§  Honda Motors Beta:
§  Embraer

0.96
1.65

10

Systematic vs. Unique Risk
§  Higher discount rates for investments involving
new products and lower rates for ones that
§  Higher discount rate is used to compensate for
higher uncertainty in the case of new products
§  Problem: this is justified only if the betas of the projects differ substantially
§  Incorporate impact of difficulties/uncertainties
during new product launch in expected cash flow
calculation (NOT in discount rate)
11

Leverage and Capital Budgeting

WACC and APV

WACC Method (D/E const.)
T

§  Firm value:
rWACC

PV = ∑
t =1

FCFt

(1 + rWACC )

t

⎛ E ⎞
⎛ D ⎞
= ⎜
× rE + ⎜
× rD × (1 − TC )
⎟
⎟
⎝ D + E ⎠
⎝ D + E ⎠

§  Assumptions

§  Constant (target) debt-equity ratio
§  WACC represents the average return firm needs to pay to its investors on an after-tax basis

13

WACC Method (D/E const.)
§  Unlevered cost of capital (D/E constant ):
⎛ E ⎞
⎛ D ⎞
rU = ⎜
×
r
+
× rD
E
⎟
⎜
⎟
⎝ D + E ⎠
⎝ D + E ⎠

§  rE when debt-to-equity ratio is constant:

⎛ D ⎞
rE = rU + (rU − rD ) × ⎜ ⎟
⎝ E ⎠
14

Project Risk vs Firm Risk
§  Project has same risk and leverage as the firm
ð Can use firm’s WACC (or industry WACC if firm
has the same leverage as the industry)
§  Suppose project risk and leverage is different from that of the firm:
1.  Find comparable firms with same risk as project
2.  Calculate comparable firms’ unlevered cost of capital (or beta)
3.  Re-lever using project leverage
4.  Calculate project-based WACC
15

Alberta Energy Corp (AEC) WACC
§  AEC stock is not publicly traded + WACC estimate based on a single company would be inaccurate ⇒ comparables

§  Average industry WACC (10 firms): rWACC, CE = 7.85% §  Comparables’ average D/V ratio:
D/VCE =...