|
|
|
|
|
|
|
Decision
|
|
|
|
Notes:
|
|
|
Significance
|
5%
|
|
= Significance = 1-confidence
|
|
|
Critical value (z)
|
(1.64)
|
|
|
|
|
|
|
|
|
|
CAPM
|
|
|
|
|
|
|
Riskless rate
|
5.00%
|
|
|
|
|
Equity premium
|
4.00%
|
|
|
|
|
|
|
|
|
|
Firm before project
|
|
|
|
|
|
|
Cash flow (CF)
|
$100.0
|
|
|
|
|
CF volatility
|
$20.0
|
|
|
|
|
CFAR
|
-$32.9
|
|
= CF volatility x critical value
|
|
|
|
|
|
|
|
Additional large project
|
|
|
|
|
|
|
Investment
|
$50.0
|
|
|
|
|
CF volatility
|
$30.0
|
|
|
|
|
Correlation
|
0.5
|
|
between firm CF and large project CF
|
|
|
Project beta w/ respect to market portfolio
|
0.5
|
|
co-movement with market
|
|
|
Payoff (end of single period)
|
$60.0
|
|
|
|
|
COC
|
7.00%
|
|
= riskless rate + (equity premium x beta)
|
|
|
Project NPV
|
$6.1
|
|
= discounted payoff - investment
|
|
|
|
|
|
|
|
Firm plus add'l large project
|
|
|
|
|
|
|
Vol of cash flow, incl. project
|
$43.6
|
|
classic 2-asset portfolio volatility, but with cash flows
|
|
|
CFaR, including project
|
-$71.7
|
|
= volatility x critical value
|
|
|
Cost of CFaR/dollar
|
$0.10
|
|
How much does an additional $1 of CFaR cost the firm?
|
|
|
Project NVP, adjusted for CFaR
|
$2.2
|
|
= project NPV - incremental cost of CFaR (i.e., net benefit - net cost)
|