Question

You are considering a project that offers up the following possible payout with an opportunity cost of 20%.

Time 0 1 2

Base Case -$60,000 10,000 10,000

At the end of year two you know there is a 10% possiblity you will buy out your competitor which has the potential to create opportunities that are worth $1,028,231 at that time. How much potential value is created or lost by taking on this project (i.e. what is the NPV)?

Answer 1

Computation of the net present value (NPV) is:

Net present value (NPV) = Initial cash flow + Present value of cash flow for year 1 + Present value of cash flow for year 3

= -$60,000 + $8,333.33 + $78,349.36

= $26,682.69

Hence, the net present value (NPV) is $26,682.69

Working Notes:

Opportunity cost of project (r) = 20%

1.

Computation of the present value of cash flow for year 1 is:

Present value of cash flow for year 1 = Base cash flow for year 1 / (1 + r)^n

= $10,000 / (1 + 0.20)^1

= $10,000 / (1.20)^1

= $10,000 / 1.20

= $8,333.33

Hence, the present value of cash flow for year 1 is $8,333.33

2.

Computation of the cash flow for year 2 is:

Cash flow for year 2 = Base cash flow for year 2 + (Opportunity value * Percentage of possibility)

= $10,000 + ($1,028,231 * 0.10)

= $10,000 + $102,823.10

= $112,823.10

Hence, the cash flow for year 2 is $112,823.10

3.

Computation of the present value of cash flow for year 2 is:

Present value of cash flow for year 2 = Cash flow for year 2 / (1 + r)^n

= $112,823.10 / (1 + 0.20)^2

= $12,823.10 / (1.20)^2

= $112,823.10 / 1.44

= $78,349.36

Hence, the present value of cash flow for year 2 is $78,349.36