A two-year project costs $100,000. There is a 70% chance that demand will be hig

Question

A two-year project costs $100,000. There is a 70% chance that demand will be high in the first year in which case the net cash flow (NCF) will be $100,000 and a 30% chance it will be low in which case the NCF will only be $40,000. If demand is high in the first year there is a 60% chance it will stay high in the second year with NCF of $100,000 and a 40% chance it will be low with NCF of $40,000. If demand is low in the first year, there is a 60% chance it will stay low with NCF 40,000 and a 40% chance it will be high in the second year with NCF $100,000. Assume the opportunity cost of capital is 12%.

Explanation / Answer

Initial Cost = $100,000

Year 1:

Demand is High : 70% and NCF = $100,000

Demand is Low : 30% and NCF = $40,000

Expected Profit = 70% chance that we get $100,000 and 30% chance that we get $40,000

Expected Profit = 0.70*100,000 + 0.30*40,000 = $82,000

PV of Year 1 Expected Profit = Expected NCF / (1+r) = 82,000 / (1+0.12) = $73214

Year 2:

Demand is High : 0.7*0.6 + 0.3*0.4 = 54%

NCF = $100,000

Demand is Low : 0.7*0.4 + 0.3*0.6 = 46%

NCF = $40,000

Expected Profit = 54% chance that we get $100,000 and 46% chance that we get $40,000

Expected Profit = 0.54*100,000 + 0.46*40,000 = $72,400

PV of Year 2 Expected Profit = Expected NCF / (1+r) = 72,400 / (1+0.12)2 = $57716

Expected NPV = 73214 + 57716 = $130,930

Chance of Negative NPV:

Both Years Low NCF, as otherwise PV of future cashflows is greater than $100,000.

= Probability of Low in year 1 * Probability of Low in year 2

= 0.30*0.46 = 0.138 = 13.8%

Expected cashflow of year 2 = $72,400.

Value of expected cashflow of year at the end of first year = 72400 / (1+0.12) = $64,642

As it is being offered $70,000 which is more than the value of 2nd year time cashflow of $64,642.

So it should abandon the project and accept $70,000

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