Question

. Joe Avery recently graduated from college and has an idea for a juice shop using only organic and locally-sourced ingredients. He has saved just enough money to cover the initial investment required to open the shop, $40,000. Using his corporate finance training, he estimates that the free cash flow from the shop will be $4,000 per year, forever. Consider a rate of return of 15%.

a. What is the NPV of the project?

b. In fact, the annual cash flow of $4,000 is an expected value: there is a 50% chance that annual cash flow will be $10,000 and a 50% chance that it will be -$2,000. Because of a very restrictive leasing contract, he cannot close down the shop even if there is no demand. What is the expected NPV of the project?

c. Fortunately, Joe's relatives are willing to provide him with enough capital to open another 10 shops after the first year if there is a lot of demand. What is the true NPV of the project?

d. What is the value of the option to expand?

Answer 1

a) NPV of the project is calculated by computing the difference between the present value of Inflows and present value of Outflows.

PV of Outflow is given as 40000

PV of Inflow : 4000/.15 = 26667 (rounded off)

So NPV = 26667-40000 = -13333

b) There are 50% chances of 10000 and 50% changes of -2000 but since there is no option to close the shop the excepted cash inflow are calculated as : (50%*10000) + (50%*-2000) = 4000

Hence NPV will be same as calculated above i,e - 13333

c) There's a option to open 10 more shops if there is a lot of demand. Therefore Joe will open the shops if the demand will be more and otherwise he wont open the shops.

Scenario 1 : Demand is more and expected cash flow 10000. So Joe will open 10 more shops after year 1

So Expected Inflow will be (10000/.15) + 10*[(10000/.15)/1.15] = 66667+ 579710 = 646377

Expected Outflow will be : 40000 + (10*40000)/1.15 = 387826

NPV in scenario 1 = 646377-387826 = 258551

Scenario 2 : Demand is less and expected cash flow is -2000. So Joe will not open any more shops and he cannot close the current shop.

Expected Inflow : (-2000/.15) = -13333

Expected Outflow : 40000

NPV = -13333-40000 = -53333

NPV given the option to open 10 more shops will be : (Probability of Scenario 1 * NPV of Scenario 1) + (Probability of Scenario 2 * NPV of Scenario 2)

=(50%*258551)+ (50%*-53333)

=102609

d) Value of the option will be NPV with the option - NPV without the option

=102609-(-13333)

=115942