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Chapter 12 Risk Topics and Real Options in Capital Budgeting and Cash Flow Estimation. Cash Flows as Random Variables. “Risk” in every day usage: the probability that something bad will happen “Risk” in financial theory: Associated with random variables and their probability distributions.
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Chapter 12 Risk Topics and Real Options in Capital Budgeting and Cash Flow Estimation
The Wing Foot Shoe Company is considering a new running shoe. A market study indicates a 60% probability that demand will be good and a 40% chance that it will be poor.
C0 is $5M. Cash inflows are estimated at $3M per year for three years at full manufacturing capacity if demand is good, but just $1.5M per year if it’s poor. Wing Foot’s cost of capital is 10%.
Develop a rough probability distribution for NPV.
A decision tree diagram and NPVs along each path are:
P = .6
P = .4
The expected NPV is:
The decision tree explicitly calls out the fact that a big loss is quite possible, although the expected NPV is positive.
Wing Foot now feels there are two possibilities along the upper branch.
If first year demand is good, there’s a 30% chance it will be excellent in the second and third years, and a $1 million factory expansion will generate cash inflows of $5 million in years 2 and 3.
That means net cash inflows will be $4 million in year 2 and $5 million in year 3.
A decision tree for the project with this additional possibility is on the next slide
The NPV for the new upper path is
The project’s probability distribution expected return are as follows.
The cost of capital (k) plays a key role in both NPV and IRR.
Calculate the risk-adjusted rate for the project:
k = 5% + (10% - 5%)2.0 = 15.0%
Then calculate the project's NPV using the 15% risk-adjusted rate:
NPV = -$10.0M + $3M[PVFA15,5]
= -$10M + $3M[3.3522]
NPV at Orion’s own 8% cost of capital is $2.0M clearly indicating acceptance. Adjusted for risk, however, the project is marginal . This is a crucial insight!
Since the NPV is barely positive, the project is marginal at best.