An entrepreneur is considering a 5-year project requiring a $500,000 investment. He believes there is a 65% chance the project will be successful, in which case it will generate annual cash flows of $200,000. However, he also thinks there is a 35% chance that annual cash flows will be only $25,000. The entrepreneur will be able to observe whether the project will be successful immediately after its launching. If it is successful, then he will expand the scale of the project by a factor of 10. What is the value of the option to expand assuming a discount rate of 15%?
A) $962,132.98
B) $927.244.50
C) $997,021.46
D) $851,205.39
E) $885,567.12
The option is closer to B.($927.244.50).
Considering the probability of the project, we can calculate the expected cash flow in a year by multiplying each scenario’s cash flow by its probability and then make summation over each year:
Hence the projected/expected cash flow may be calculated as :
(Probability*Cash flow in positive scenario)+ (Probability * Cash flow in negative scenario)
= (0.65*2,00,000)+(0.35*25,000) = $138750
Probability | Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
Success rate = 65% | ($5,00,000) | 200000 | 200000 | 200000 | 200000 | 200000 |
Failure rate = 35% | ($5,00,000) | 25000 | 25000 | 25000 | 25000 | 25000 |
Expected Cash Flow | ($5,00,000) | 138750 | 138750 | 138750 | 138750 | 138750 |
We can calculate the absolute value of the expansion option as follows:
Absolute Value(Expansion Option) | ||||||
Discount Rate (r) | 15% | |||||
Number of Periods (Year) (n) | 1 | 2 | 3 | 4 | 5 | |
Expected Cash Flows (C_{i}) | $138,750 | $138,750 | $138,750 | $138,750 | $138,750 | |
Present Value of Expected Cash Flow is calculated using the formula given below | ||||||
PV of expected Cash Flow = C_{i} / (1 + r)^{i} | ||||||
PV of Free Cash Flow | $120,652.17 | $104,914.93 | $91,230.38 | $79,330.76 | $68,983.27 | |
Terminal Value is calculated using the formula given below | ||||||
TV = C_{n} / r | ||||||
Terminal Value | $925,000 | |||||
PV of Terminal Value: | ||||||
PV of TV = TV / (1 + r)^{n} | ||||||
PV of Terminal Value | $459,888 | |||||
Absolute Value is calculated using the formula given below. | ||||||
Absolute Value = ∑ [(C_{i} / (1 + r)^{i}) + (TV / (1 + r)^{n})] | ||||||
Absolute Value | $925,000 | |||||
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