Transcript Real Options

Flow-to-Equity Approach
Calculate Free Cash Flow to Equity
Compute their NPV using rE as a discount
rate.
Expected Free Cash Flows to Equity from Avco’s RFX
Project (continuing last lecture example))
Alternative way to compute FCFE:
9.98 9.76 9.52 9.27
NPV ( FCFE)  2.62 
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 $33.25 mln
2
3
4
1.10 1.10 1.10 1.10
The same NPV as with WACC and APV!
Project-Based Cost of Capital
What if the project changes either the
leverage of the firm or its risk or both?
Taking into account the project’s risk
We need to compute
Assume rD is known. Then we need to compute rE
But how to compute rU?
“Pure-play technique”. Find firms in the market
(comparables) whose whole business is similar to
your project, and take their rU
These firms may be levered, then you
have to find their rU first
Example:
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Comparable 1: rE=12%, rD=6%, D/(E+D)=40%
 rU=9.6%
Comparable 2: rE=10.7%, rD=5.5%,
D/(E+D)=25%  rU=9.4%
Average rU=9.5%
Assume the leverage of the firm before the project was
1, and its cost of debt was = 6% (see last lecture). If we
assume that both things stay the same, we obtain
D
rE  rU  ( rU  rD )  9.5%  1  (9.5%  6%)  13.0%
E
rwacc
E
D
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rE 
rD (1   c )  0.5  13%  0.5  6%(1  0.4)  8.3%
ED
ED
Instead we could directly use
(from the two formulas above)
where d is D/(E+D) – the project’s debt-to-value ratio
Note: sometimes you don’t know rE and rD of the
comparable firms, but know (or can estimate) their βE
and βD. Then you simply use CAPM to find rE and rD, or
you can directly compute
E
D
U 
E 
D
ED
ED
And then use CAPM to determine rU.
In general, your project may have D/(E+D) different from
the rest of your firm. Then in the formulas in the previous
slide you need to use the project’s D/(E+D). See
example (next two slides)
Example: Computing Divisional
Costs of Capital
Determining a project’s D/(D+E)
(incremental leverage of a project)
Let dp=Dp/(Dp+Ep) is the debt-to-value ratio you want for
your project
Compute the project’s PV using WACC (assuming you
know the project’s risk, i.e. rU, and rD, you can always
find its rE)
Then Ep = PVp – Dp, and dp=Dp/PVp you can find Dp such
that you achieve your desired dp
If you need to achieve certain target D/(D+E) for your
firm, then you need to solve simultaneously:
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(Dold+Dp)/(Dold+Dp+Eold+Ep) = D/(D+E)
Dp+Ep ≡ PVp = dicounted FCF using WACC
WACC is determined by dp=Dp/(Dp+Ep)
Real Options Approach to Capital
Budgeting
Managers are always faced with various options
(start a project or not, expand the business or
not, terminate or not, etc…) the costs and
benefits of which may change in time depending
on the realization of some uncertainty
Thus managers should not stick to a certain
strategy once and for all. Rather they should
change it according to the circumstances
How to account for this flexibility?
Failure of traditional capital
budgeting
Option to defer investment:
The manager has an option to defer building a plant for a
year.
If he chooses to defer, after a year he either may or may
not find it profitable to build a plant
What is the value of this flexibility?
Setup
At t = 0 investment outlay (required inv-t) I0 = 104
At t = 1:
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If the market moves up (prob. q) the plant generates V+ = 180
If the market moves down (prob. 1-q) the plant generates V– = 60
The manager has a choice:
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To invest at t = 0 and get 180 with prob. q and 60 with prob 1-q,
or
To wait until t = 1 and build a plant only in the “good” state of
nature (i.e. if the market has moved up). But then the required
investment is I1 = 112.32. Thus, then he gets
E+ = 180 – I1 = 67.68 in the good state
E+ = 0 in the bad state.
Setup (cont-d)
Assume q = 1/2
Risk free rate: r = 8%
There exist a risky security (“twin” security),
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which payoffs are perfectly correlated with the payoffs
of the project: S+ = 0.2*V+ = 36, S– = 0.2*V– = 12
which price S = 20
 rate of return k = (½* S+ + ½* S–)/S = 20%
How much a manager would pay for this
investment opportunity (what is the NPV of the
project)?
q=0.5
V=100, S=20
I0=104
0.5
V+=180, E+=67.68
S+=36
V-=60, E-=0
S-=12
I1=112.32
No flexibility case:
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Assume there’s no option to defer
The traditional DCF technique yields:
V0 = (qV+ + (1-q)V-)/(1+k) = (0.5*180 + 0.5*160)/(1+
0.2) = 100
NPVpassive = V0 - I0 = 100 – 104 = - 4
Reject the project!
Now let’s account for flexibility
Using probabilities q and the rate of return on
the “twin” security k = 20% we can discount cash
flows, assuming we wait until t=1:
E0 = (qE+ + (1-q)E-)/(1+k) = 28.20 > 0
Apparently we should wait instead of rejecting
the project right away. This strategy yields NPV
> 0!
But is this a correct estimation? In the riskneutral world, where k would be the risk-neutral
rate – yes. Otherwise – no!
Correct Way to Value This Opportunity
The opportunity to delay is a “call option”
on the plant with an exercise price I1
So we can use the same technique as with
financial options to value it: replicating
portfolio (risk neutral valuation)
Consider a strategy: Buying N shares of the twin security
S, partly financed by borrowing of amount B at the
riskless rate r = 8%
We can always pick such N and B that:
E+ = NS+ - (1+r)B
E- = NS- - (1+r)B
Thus, we can replicate the payoffs from the project with
this portfolio  the arbitrage argument tells us that the
project value must be the same as the price of the
portfolio: E0 = NS - B
N = (E+ - E-)/(S+ - S-)
B = (NS- – E-)/(1+r)
We obtain the “risk-neutral” valuation:
E0 = NS – B = (pE+ + (1-p)E-)/(1+r)
where p = ((1 + r)S – S-)/(S+ - S-)= (1 + r – d)/(u - d)
Notice: q does not enter the expression for E0 Why?
Because q is already incorporated in the price of the
“twin” security S.
pE+ + (1-p)E- can be viewed as Certainty Equivalent of
the random payoff at t = 1.
For our project:
p = 0.4, E0 = 25.07
The value of the option to delay investment:
E0 – NPVpassive = 25.07 – (-4) = 29.07
If you consider that without flexibility you would not
actually invest then the value of the option would be E0 =
25.07 – this is how much you would agree pay to have
the flexibility
Notice that when we used the actual probabilities q and
the rate of return on the “twin” security k = 20% to
discount cash flows we got
E0 = (qE+ + (1-q)E-)/(1+k) = 28.20 > 25.07 – it was an
overestimation