Question

Your R&D division has just synthesized a material that will superconduct electricity at room temperature. You are about to give the go ahead to consider producing this material commercially. It will take five years to find out whether the material is commercially viable, and you estimate that the risk neutral probability of success is 25%. Development will cost $10 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 $1 billion to put in place and will generate risk-free profits of $100 million at the end of every year in perpetuity. No Excel. Done by Hand. Step-by-Step.

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 either 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?

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%	-10	-10	-10	-10	-10	-1000	100 per year
75%	-10	-10	-10	-10	-10

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

= 100 / 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%	100 / 0.12 = 833.3	833.3 / 1.1 = 757.545	757.545 - 1000 = -252.455
10%	100 /0.1 = 1000	1000 / 1.1 = 909.091	909.091 - 1000 = -90.909
8%	100 / 0.08 = 1250	1250 / 1.1 = 1136.364	1136.364 - 1000 = 136.364
5%	100 / 0.05 = 2000	2000 / 1.1 = 1818.182	1818.182 - 1000 = 818.182