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n NPV = Σ t=1 FCFt
t
(1 + k)  IO How can we adjust this model to
take risk into account?
take
n NPV = Σ t=1 FCFt
t
(1 + k)  IO Adjust the Aftertax Cash Flows (ACFs),
Adjust
or
or Adjust the discount rate (k). Certainty Equivalent Approach: consider this;
Certainty Play a roulette game for free
Play
(black and red).
red If you win, you get $1,000. But if you
If
lose you get 0 (chance 50/50).
lose So the expected value (risky CF) is
So
((0.5x$1,000)+(0.5x$0)) = $500.
((0.5x$1,000)+(0.5x$0)) Certainty equivalent = the amount
Certainty
you would demand to make you
indifferent with regard to playing and
not playing the game = $300
not Certainty Equivalent Approach
Certainty Adjusts the risky aftertax cash flows
Adjusts
risky
to certain cash flows.
certain The idea:
The Certainty Equivalent Approach
Certainty Adjusts the risky aftertax cash flows
Adjusts
risky
to certain cash flows.
certain The idea: (remove the risk from risky CFs by CE)
(remove
The
Risky
Cash
Cash
Flow X Certainty
Equivalent
Equivalent
Factor (αt) Certain
=
Cash
Flow Certainty Equivalent Approach
Certainty
Risky
Cash X
Cash
Flow
Risky
$500 Certainty
Equivalent
Equivalent
Factor (α )
t .60 = Certain
Cash
Flow
“safe”
$300 The greater the risk associated
The greater
with a particular cash flow,
the smaller the CE factor.
smaller Certainty Equivalent Method
Certainty
n NPV = Σ
t=1 FCFt
 IO
t
(1 + krf)
t Riskfree discount rate Certainty Equivalent Approach
Certainty Steps:
1) Adjust all aftertax cash flows by
1)
certainty equivalent factors to get
certain cash flows.
certain
2) Discount the certain cash flows by
2)
the riskfree rate of interest.
riskfree Example Not given
Project A:
(A)
Expected
Year (Expected
Cash Flow 0
1
2
3
4 $1,000,000
500,000
700,000
600,000
500,000 NPVA = $ 726,380 (B) (A x B) (TVM Table) (NPV) αt Factor
Cash Flow) x (αt) Present Value
at
Present
5% (Rf)
Value 1.00
.95
.90
.80
.70 $1,000,000
475,000
630,000
480,000
350,000 1.000
.952
.907
.864
.823 $1,000,000
452,2...
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This document was uploaded on 02/03/2014.
 Spring '14

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