Use Expected NPV and PVR analysis for a minimum rate of return of 20.0%to evaluate the economic potential of buying and developing the rights to a new process with the following estimated costs, revenues, and success probabilities
Use Expected NPV and PVR analysis for a minimum rate of return of 20.0%to evaluate the economic potential of buying and developing the rights to a new process with the following estimated costs, revenues, and success probabilities
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
- Use Expected
NPV and PVR analysis for a minimumrate of return of 20.0%to evaluate the economic potential of buying and developing the rights to a new process with the following estimated costs, revenues, and success probabilities. The process rights would cost $100,000 at time zero, and it is considered 100% certain that an experimental development pilot plan work will be done one year later for a cost of $500,000. There is a 60.0% probability that the experimental development results will look good enough to take the project to production for a $400,000 capital cost at year one. If the experimental development results are unsatisfactory, a pilot plan abandonment cost of $40,000 will be incurred at year 1. If the project is taken to production, it is estimated there will be a 50.0% probability of generating production that will give $450,000 peryear net positive cash flow for years 2 through 10, a 35.0% probability of generating $300,000 per year net positive cash flow for years 2 through 10, with a 15.0% probability of the project development being unsuccessful due to unforeseen technical difficulties giving a year 2 salvage value of $250,000 for production equipment. (Hint: use expected NPV and expected MCE for PVR calculation.)
Expert Solution
Step 1
ENPV is the net current worth of risky cash flows that are expected to occur in the future.
Here we have a set of possibilities from the initiation of the project.
The probability that the experimental development pilot plan will be undertaken is 100%, so we can definitely move to the next stage.
This has two possibilities:
- Experimental development results are good - 60%
- Pilot plan abandonment - 40%
If the project is taken to production;
- Situation 1: Successful development that yields an income of $450,000 per year
- Situation 2: Successful development that yields an income of $300,000 per year
- Situation 3: Failure that yields a salvage value of $250,000 at the end of year 2
- Situation 4: Failure that yields an abandonment costs of $40,000 at the end of year 1
We can show all this in Excel and formulate the expected ENPV discounted at 20%.
Step 2
| Years | |||||||||||||
| situation | probability | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ENPV |
| 1 | 30.0% | -100000 | -900000 | 450000 | 450,000 | 450,000 | 450,000 | 450,000 | 450,000 | 450,000 | 450,000 | 450,000 | 198483.73 |
| 2 | 21.00% | -100000 | -900000 | 300,000 | 300,000 | 300,000 | 300,000 | 300,000 | 300,000 | 300,000 | 300,000 | 300,000 | 33125.74 |
| 3 | 9.00% | -100000 | -900000 | 250,000 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -60875.00 |
| 4 | 40% | -100000 | -540000 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -220000.00 |
| NPV | -49265.53 | ||||||||||||
Working in Excel
| Years | |||||||||||||
| situation | probability | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ENPV |
| 1 | =50%*60% | -100000 | =-(500000+400000) | 450000 | 450,000 | 450,000 | 450,000 | 450,000 | 450,000 | 450,000 | 450,000 | 450,000 | =((D4/(1+20%))+(E4*(1-(1+20%)^-9)/20%)/(1+20%)+C4)*B4 |
| 2 | =35%*60% | -100000 | =-(500000+400000) | 300000 | 300,000 | 300,000 | 300,000 | 300,000 | 300,000 | 300,000 | 300,000 | 300,000 | =((D5/(1+20%))+(E5*(1-(1+20%)^-9)/20%)/(1+20%)+C5)*B5 |
| 3 | =15%*60% | -100000 | =-(500000+400000) | 250000 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | =((D6/(1+20%))+(E6/(1+20%)^2)+C6)*B6 |
| 4 | 0.4 | -100000 | =-(500000+40000) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | =((D7/(1+20%))+C7)*B7 |
| NPV | =SUM(N4:N7) | ||||||||||||
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