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 $10,000 per year, forever. Investments with similar risk deliver a rate of return of 12%. The NPV of the project would be $43,333. In fact, the annual cash flow of $10,000 is an expected value: there is a 50% chance that annual cash flow will be $25,000 and a 50% chance that it will be -$5,000. Because of a very restrictive leasing contract, he cannot close down the shop even if there is no demand. The expected NPV of this project would be $43,333, it does not change.

Fortunately, Joe's rich relatives are willing to provide him with enough capital to open another 8 shops after the first year if there is a lot of demand.

What is the true NPV of the project?

What is the value of the option to expand?

Answer 1

(a) What is the true NPV of the project ?

Ans: NPV of the project is the difference between the Present Value of Cash flow and Present Value to Outflow. (Present Value of Inflow - Present Value of Outflow)

Calculation: In the question Present Value of outflow has been given as $40000.

Further Cash inflow has also been given as $10000.

Cost of Capital is 12%

Years : Infnte

So Present Value of Inflow would be Annual Cash flow / Cost of capital

10000 / .12 = 83333.33

Hence NPV would be $83333.33 - $40000 = $43333.33

Alternatively we can also compute the annual cash flow through following method:

Cash flow x Probabability = Expected Cash flow

Thus,

$25000 x 0.50 = $12500

& $-5000 x 0.50 = $-2500

Hence AnnualCash outflow would be $12500 + $-2500 = $ 10000.

(B) What is the Value of option to expand?

Answer: Initial Investment required to open the shop is $40000

Calculation of Initial investment afrer one year:

Future value = Present Value (1+r)^n

Future value = 40000(1+.12)^1

= $44800

Hence future value after one year for one shop is $44800

for 8 shops it would be $44800 x 8 = $358400.

Thus the value of option to expand after one year is $358400.

Answer (A) $43333

Answer (B) $358400