**Unformatted text preview: **take
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 After-tax 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 after-tax cash flows
Adjusts
risky
to certain cash flows.
certain The idea:
The Certainty Equivalent Approach
Certainty Adjusts the risky after-tax 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 Risk-free discount rate Certainty Equivalent Approach
Certainty Steps:
1) Adjust all after-tax cash flows by
1)
certainty equivalent factors to get
certain cash flows.
certain
2) Discount the certain cash flows by
2)
the risk-free rate of interest.
risk-free 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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