e. The project has an expected NPV of over $9M, which is a likely value for a point-estimated NPV, and would strongly imply accepting the project. The detailed probability distribution shows that there’s a significant chance (12%) of a substantial loss ($6M) associated with the project. If management is risk averse, they’re likely to reject a project with that big a loss potential even though the expected NPV is very positive. 14. If Spitfire elects to do the project, what is an abandonment option at the end of year 1 worth if Spitfire can recover $8M of the initial investment into other uses at that time? If the recovery is $13M? 46 .50 .40 .30 .20 .10 - $6.0 - $0.6 0 $7.5 $21.0 Probabilities NPV (in $M)
For the new third path ($M): Path 3 NPV = - 15 + 12[PVF 12,1 ] = - 15 + 12(.8929) = - 15 + 10.7 = - 4.3 Probability = .4 Expected NPV calculations Path NPV Probability Product 1 $21.0M .42 $8.82M 2 7.5 .18 1.35M 3 - 4.3 .40 - 1.72M 1.00 $8.45M = Exp Value Hence the abandonment option is worth nothing since it reduces expected NPV. If the recovery is $13M we have: Additional NPV along path 3 $5 Contribution to expected NPV $5 × .4 × .8929 = $1.8 New expected NPV $8.45 + $1.8 = $10.25 Problem 6 expected NPV $9.28 Increase in expected NPV $10.25 - $9.28 = $0.97 Hence the abandonment option is worth just under $1M. 15. The New England Brewing Company produces a super premium beer using a recipe that’s been in the owner’s family since colonial times. Surprisingly, the firm doesn’t own its own brewing facilities, but rents time on the equipment of large brewers who have excess capacity. Other small brewers have been doing the same thing lately, so capacity has become difficult to find, and must be contracted for several years in advance. New England’s sales have been increasing steadily, and marketing consultants think there’s a possibility that demand will really take off soon. Last year’s sales generated net cash flows after all costs and taxes of $5M. The consultants predict that sales will probably be at a level that will produce 47
Chapter 12 net cash flows of $6M per year for the next three years, but they also see a 20% probability that sales could be high enough to generate net cash inflows of $8M per year. Meeting such an increase in demand presents a problem because of the advance contracting requirements for brewing capacity. Unless New England arranges for extra facilities now, there’s a 70% chance that brewing capacity won’t be available if the increased demand materializes. An option arrangement is available with one of the large brewers under which it will hold capacity for New England until the last minute for an immediate, nonrefundable payment of $1M. New England’s cost of capital is 9%. a. Draw a decision tree reflecting New England’s cash flows for the next three years without the option and calculate the expected NPV of operating cash flows. (Note that there’s no need to include an initial outlay because we’re dealing with ongoing operations.) b. Redraw the decision tree to include the capacity option as a real option in your calculations.
- Fall '13
- Net Present Value