Question

Your firm has an opportunity to invest in a project that costs $800 and you expect it to return two payments of 500 per year. The interest rate of the project is 10%. The current NPV of project is $67.77.

You also have the option to wait one year to invest the $800. If you wait you will know more and can revise your expectations such that you either expect to return two payments of $750 with a probability of 0.8 or alternatively two payments of $300 (the probability of this is equal to 1 minus the probability of the first result). The interest rate of the project is still 10%.

What is the current present value of the NPV if they choose to wait?

Answer 1

We need to calcualate the current present values of the cash outflow (investment) as well as the cash inflows.

1.Current Present Value of the Cash Outflow:

Since we need to invest after one year, the current PV of the Cash Outflow, PV_0, will be

PV₀ = PV₁/(1+r)ⁿ

PV₀ = $800/(1.1)¹

PV₀ = $727.27273

2. Determining Expected Cash Flows in years 2 and 3.

Cash Flow -1 Probability -2 Expected Cash Flows = 1 * 2 $750 0.8 750 * 0.8 = 600 $300 1-0.8 = 0.2 300 * 0.2 = 60 Total 1 660 Expected cash flows in years 2 and 3 is $660

3. Dertermining the current present values of cash inflows in years 2 and 3.

PV of Cash flows in year 2

PV₀ = PV₂/(1+r)²

PV₀ = 660/(1.1)² = 660/1.21 = $545.4545

PV of Cash flows in year 3

PV₀ = PV₃/(1+r)³

PV₀ = 660/(1.1)³ = 660/1.331 = $495.867769

The sum of the current present values of cash inflows is: $545.4545 + $495.867769 = $1041.322314.

4. The Current present value of NPV is:

(Sum of current present value of cash inflows) - Current Present Value of Cash Outflows  

Current Present NPV = $1041.322314 -$727.27273 = $314.049587.

The firm's current present NPV if they choose to wait is $314.05.