Question

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.

Answer 1

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 = $\sum$(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 = $\sum$(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.