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8/4/2019 Risk Budgeting
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CH 11Capital Budgeting and Risk Analysis
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Three Measures of a Projects Risk
Project Standing
Alone Risk Riskdiversified away
within firm as thisproject is combined
with firms other
projects and assets.
Risk
diversified away
by shareholders as
securities are combined
to form diversified
portfolio.
Projects
Contribution-to-Firm Risk
Systematic Risk
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Incorporating Risk into Capital
Budgeting
Certainty Equivalent Approach
Adjust free cash flows (FCF)
Use risk-free rate to discount
CFs
Risk-Adjusted DiscountRate Adjust discounting rate
Two Approaches
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Certainty Equivalent Approach
Adjusts the risky after-tax cash flowsto certain cash flows.
The idea:
Risky Certainty Certain
Cash X Equivalent = CashFlow Factor (a) Flow
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Certainty Equivalent Approach
Risky Certainty Certain
Cash X Equivalent = Cash
Flow Factor (a) FlowRisky safe
$1000 .70 $700
Risky safe
$1000 .95 $950
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The greater the risk associated
with a particular cash flow,
the smaller the CE factor.
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Certainty Equivalent Method
tNPV = - IOt FCFt(1 + krf)
n
t=1S
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Certainty Equivalent Approach
Steps:
1) Adjust all after-tax cash flows by
certainty equivalent factors to getcertain cash flows.
2) Discount the certain cash flows by
the risk-free rate of interest.
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Incorporating Risk into
Capital Budgeting
Risk-Adjusted Discount Rate
Approach
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Risk-Adjusted Discount Rate
Simply adjust the discount rate (k)
to reflect higher risk.
Riskier projects will use higherrisk-adjusted discount rates.
Calculate NPV using the new risk-
adjusted discount rate.
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Risk-Adjusted Discount Rate
NPV = - IOFCFt
(1 + k*)t
n
t=1S
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Risk-Adjusted Discount Rates
How do we determine the
appropriate risk-adjusted discount
rate (k*) to use? Many firms set up risk classes to
categorize different types of
projects.
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Risk Classes
Risk RADRClass (k*) Project Type
1 12% Replace equipment,
Expand current business
2 14% Related new products
3 16% Unrelated new products
4 24% Research & Development
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Yr FCF(t) Alpha PV at 0.06 PV of FCF(t)
0-
800000 1.0000
-800000
1 100000 0.92 0
.9434 86957
2 100000 0.85 0
.8900 75614
3 100000 0.78 0
.8396 65752
4 100000 0.72 0.7921 57175
5 100000 0.67 0
.7473 49718
6 100000 0.61 0
.7050 43233
7 100000 0.57 0
.6651 37594
8 100000 0.52 0
.6274 32690
9 100000 0.48 0
.5919 28426
10 100000 0.44 0
.5584 24718
NPV ( , . )
CE Approach (with alpha)
RAA approach impliesthat risk becomesgreater as cash flows
are further away.Reducing alphaindicates that risk isgreater.(Alpha = 1 = Sure
thing!
Yr FCF(t) PV at 0.15 PV of FCF(t) Yr FCF(t) PV at 0.06 PV of FCF(t)
0-
800000 1.0000
-800000 0
-800000 1
.0000
-800000
1 100000 0.8696 86957 1 100000 0
.9434 94340
2 100000 0.7561 75614 2 100000 0
.8900 89000
3 100000 0
.6575 65752 3 100000 0
.8396 83962
4 100000 0.5718 57175 4 100000 0
.7921 79209
5 100000 0.4972 49718 5 100000 0
.7473 74726
6 100000 0.4323 43233 6 100000 0
.7050 70496
7 100000 0.3759 37594 7 100000 0
.6651 66506
8 100000 0.3269 32690 8 100000 0
.6274 62741
9 100000 0.2843 28426 9 100000 0
.5919 59190
10 100000 0.2472 24718 10 100000 0
.5584 55839
NPV ( , . ) NPV ( , . )
Risk Adjusted Approach CE Approach (w/o alpha)