Question

Initial investment required for a project is estimated $65,000. There is 40% probability of success and 60% probability of failure. In case of success, initial investment at present time yields the annual income of $22000 for six years, from first to sixth year with zero salvage value. In case of failure, there will be salvage value of $50,000 at the end of first year without any annual income. Considering minimum ROR 10%, calculate the expected NPV and explain if this investment is satisfactory. Explain your work in detail including all the required equations and calculations.

Answer 1

NPV is is the difference between the present value of cash inflows and the present value of cash outflows over a period of time.

For Case 1 - Success: Probability of 40%

NPV = PV (Cash inflows) - Initial Investment

Cash inflows is an annuity of $22,000 for 6 years with 10% required return.

PV of an annuity can be mathematically calculated using the mathematical approach:

PV = $95,814.74

NPV = 95,814.74 - 65,000 = $30,814.74

For Case 2 - Failure: Probability of 60%

NPV = PV (Cash inflows) - Initial Investment

In this case, there is only one cash flow at the end of year 6.

PV = 50000/(1 + 10%)⁶ = $28,223.70

NPV = $28,223.70 - $65,000 = - $36,776.30

Expected NPV = Probability weighted NPV of scenarios.

Expected NPV = (40% * $30,814.74) + (60% * - $36,776.30) = $12,326.29 - $22,065.78 = - $9,739.49. Answer