The net present value (NPV) is a classic economic method of evaluating investment projects. It is defined as the measure of the difference between the present value of future cash inflows and the present value of cash outflows of a project. The net present value uses a discount rate in its computation. We have already seen that discount rate is the rate of return from an investment, or the opportunity cost of capital. The opportunity cost of capital is the expected rate of return that an investor could earn if the money would have been invested in financial assets of equivalent risk. Hence it’s the return that an investor would expect to earn.
How to Calculate NPV
When calculating the NPV the cashflows are used and this implies that any non-cash item such as depreciation if included in the cashflows should be adjusted for. In computing NPV the following steps should be followed:
Cashflows of the investment should be forecasted based on realistic assumptions. If sufficient information is given one should make the appropriate adjustments for non-cash items
- Identify the appropriate discount rate (It is usually provided)
- Compute the present value of cash flows identified in step 1 using the discount rate in step 2
- The NPV is found by subtracting the present value of cash out flows from present value of cash inflows.
The formula for calculating NPV is:
NPV = PV (inflows) – PV (outflows)
Where:
- ∑ refers to sum or the total of something
- C_{t} = net cash flow at time t
- C_{o} = Cash outflows (initial investment)
- n = period (number of years)
- t = time of the cash flow
- k = discount rate/cost of capital
Sometimes you can find a formula that uses different symbols, but the idea is the same. So the same formula can be given as follows:
NPV_{t} = ∑ X_{t}/(1 + R)^{t} – X_{o}
Where,
- X_{t }= total cash inflow for period t
- X_{o }= net initial investment expenditures
- R = discount rate, finally
- t = total time period count
In either case, the first part of the formula refers to net or total cash inflows for the entire life of the project. It is the projected future values expressed in present value, which means that the present value formula is incorporated in the first section of the NPV formula. The second part of the formula after the minus sign represents the cost of investments in the project. It is the net amount of money used by the investor to pay for the investments. So in simple terms NPV formula just involves subtracting cost of investment from cash inflows received from the investment. Or earnings minus costs. The complication only comes in when the future cash flows are discounted to represent the present value.
Example
Kenya Investment Ltd wants to invest in a project that has an initial cost of $265,000. The project will receive cash inflows for the next five years as follows:
- Year 1 – $60,000
- Year 2 – $70,000
- Year 3 – $80,000
- Year 4 – $90,000
- Year 5 – $100,000
Required: Find the NPV and conclude whether it is a worthy investment, assuming the rate of return is 10%
Solution:
First, calculate present value of future cash flows for each year
Cash inflow | Calculation [C_{t}/(1+k)^{n}] | Present Value | |
Year 1 | 60,000 | 60,000/(1+0.1)^{1} | 54,545.5 |
Year 2 | 70,000 | 70,000/(1+0.1)^{2} | 57,851.2 |
Year 3 | 80,000 | 80,000/(1+0.1)^{3} | 60,105.2 |
Year 4 | 90,000 | 90,000/(1+0.1)^{4} | 61,471.2 |
Year 5 | 100,000 | 100,000/(1+0.1)^{5} | 62,092.1 |
Sum of the Present Value of Cash Inflows | 296,065.2 |
Secondly, subtract initial cost of investment from the cash inflows
NPV = $296,065.2 – $265,000 = $31,065.2
Decision: invest in the project because it has a positive NPV.