The initial investment is $1,500. NPC has the opportunity to invest in a project

Question

The initial investment is $1,500. NPC has the opportunity to invest in a project that has a 75% chance of generating $500 per year for 7-years under good conditions or a 25% chance of generating $25 per year for 7-years. Assuming that all cash flows are discounted at 10%, calculate the effect of waiting on the project’s risk, using the same data. By how much will delaying reduce the project's coefficient of variation? (Hint: use the expected NPV.)

Please help to explain this problem, please note that this is NOT liek the other similar problems on Chegg.

Thank you!

Explanation / Answer

Initial Investment = $ 1500

Expected cash flow in good conditions = $ 500

Period = 7 years

Discount rate = 10% or 0.10

NPV under good conditions = -1500 + 500 * [(1-(1/(1.10)^7))/0.10]

                                                  = -1500 + 500 * [(1-(1/1.9487171))/0.10]

                                                  = -1500 + 500 * [(1-0.5135812)/0.10]

                                                  = -1500 + 500 * (0.48684188/0.10)

                                                  = -1500 + 500 * 4.8684188

                                                  = -1500 + 2434.2094

                                                  = 934.2094

Expected cash flow in bad conditions = $ 25

Period = 7 years

Discount rate   = 10% or 0.10

NPV under bad conditions = -1500 + 25 * 4.8684188

                                                  = -1500 + 121.71047

                                                  = -1378.2895

Probability associated with NPV under good conditions = 0.75

Probability associated with NPV under bad conditions = 0.25

Expected NPV = 0.75 * 934.2094 + 0.25 * -1378.2895

                           = 700.6571 – 344.5724

                           = 356.0847

Variance of NPV = 0.75 * (NPV in good conditions – Expected NPV)^2 + 0.25 * (NPV under bad conditions –Expected NPV)^2        

Variance of NPV = 0.75* (934.2094-356.0847)^2 + 0.25 * (-1378.2895-356.0847)^2

                               = 0.75 * 578.1247^2 + 0.25 * -1734.3742^2

                               = 0.75 * 334,228.1688 + 0.25 * 3008053.8656

                               = 250,671.1266 + 752,013.4664

                               = 1,002,684.593

Standard Deviation of NPV = Square root of (Variance) = (1002684.593)^0.5

                                                  = 1001.34139 or 1001.3414

Coefficient of Variation = (Standard Deviation of NPV /Mean of NPV)

                                            = (1001.3414/356.0847)      

                                            = 2.812 or 281.20%

Coefficient of variation denotes the extent of variation of NPV with reference to Mean.

That is if the bad conditions prevail in the economy, then waiting till the end of bad period increases the cash flows by 281.2% from the expected NPV.

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