Corporate Finance Assignment Decision Tree
AZ Corporation’s R&D division has just synthesized a carbon nanotube material that will superconduct electricity at room temperature; you have given the go-ahead to try to produce this material commercially. It will take five years to find out whether the material is commercially viable, and you estimate that the probability of success is 25%. Development will cost $1 million per year, paid at the beginning of each year. If development is successful and you decide to produce the material, the factory will be built immediately. It will cost $100 million to put in place, and will generate profits of $10 million at the end of every year in perpetuity. Assume that the current five-year risk-free interest rate is 10% per year, and the yield on a perpetual risk-free bond will be 12%, 10%, 8%, or 5% in five years. Assume that the risk-neutral probability of each possible rate is the same. What is the value today of this project?
1. Draw a decision tree of the decisions faced.
2. Calculate the NPV5 of producing the material using 12%, 10%, 8%, and 5% as the discount rate
3. Calculate the EV of successful development.
4. Calculate the NPV0 of the development opportunity.
5. Decide whether to pursue the opportunity for commercial development of the material and support your decision.
All values are in $ millions.
Decision tree:
Probability | Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 to perpetuity | |
25% | -1 | -1 | -1 | -1 | -1 | -100 | 10 per year | |
75% | -1 | -1 | -1 | -1 | -1 |
NPV at Year 5
NPV5 = PV of inflows - Outflow at year 5
NPV5 = PV of inflows - 100
PV of inflows (in case of perpetuity) = Inflow per year / Perpetual risk free bond rate
= 10 / Perpetual risk free bond rate
Perpetual risk free bond rate |
PV of inflows at Year 6 |
PV of inflows at Year 5 (at 10% risk free rate) |
NPV5 |
12% |
10 / 0.12 = 83.33 |
83.33 / 1.1 = 75.7545 |
75.7545 - 100 = -25.2455 |
10% |
10 /10.1 = 100 |
100 / 1.1 = 90.9091 |
90.9091 - 100 = -9.0909 |
8% |
10 / 0.08 = 125 |
125 / 1.1 = 113.6364 |
113.6364 - 100 = 13.6364 |
5% |
10 / 0.05 = 200 |
200 / 1.1 = 181.8182 |
181.8182 - 100 = 81.8182 |
EV of successful Development
EV5 = (risk-neutral probability of each rate * PV of inflows at each rate)
Since risk-neutral probability at each rate is equal, therefore, risk neutral probability = 1/4 = 0.25 = 25%
EV5 = (0.25 * 75.7545) + (0.25 * 90.9091) + (0.25 * 113.6364) + (0.25 * 181.8182)
= 18.9386 + 22.7273 + 28.4091 + 45.4546
= 115.5296
NPV at Year 0 at risk free rate of 10%
NPV0 = (probability * (PV of Inflows - PV of Outflows))
PV of Inflows = (EV5 / 1.15)
= 115.5296 / 1.15
= 115.5296 / 1.6105
= 71.7348
PV of Outflows = 1 + 1/1.11 + 1/1.12 + 1/1.13 + 1/1.14 + 100/1.15
= 1 + 1/1.1 + 1/1.21 + 1/1.331 + 1/1.4641 + 100/1.6105
= 1 + 0.9091 + 0.8264 + 0.7513 + 0.683 + 62.0925
= 66.2623
NPV0 = (0.25 * (71.7348 - 66.2623)) + (0.75 * (0 - 4.1698))
*Note: 75% probability of unsuccessful development with no inflows or factory
NPV0 = (0.25 * 5.4725) + (0.75 * -4.1698)
= 1.3681 + (-3.1274)
= -1.7593
Since, NPV0 of the pursuit of the development opportunity is negative, it should not be undertaken.
Corporate Finance Assignment Decision Tree AZ Corporation’s R&D division has just synthesized a carbon nanotube material...
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