Net Present Value (NPV) Calculation: Step-by-Step Guide with Example

Net Present Value (NPV) Calculation: Step-by-Step Guide with Example

Net Present Value (NPV) Calculation

An initial investment of $400,000 is made in an IT project, which is expected to generate the following cash inflows over the next five years:

Year	Cash Inflows
1	$70,000
2	$120,000
3	$140,000
4	$140,000
5	$40,000

If the opportunity cost of capital is 8% per annum, determine whether the project should be accepted or rejected using the Net Present Value (NPV) method.

Solution Approach:

1. Calculate the Present Value (PV) of cash inflows for each year using the discount rate of 8%.
2. Sum up the present values of all future cash inflows.
3. Compute the NPV using the formula:

   $$NPV = \text{Total Present Value of Cash Inflows} - \text{Initial Investment}$$

4. Decision Rule:
   • If NPV > 0, accept the project.
   • If NPV < 0, reject the project.

Should the project be accepted based on the NPV calculation?

 

Explanation of Net Present Value (NPV) Calculation

Net Present Value (NPV) is a method used in capital budgeting to evaluate the profitability of an investment. It calculates the present value of future cash inflows and compares it to the initial investment (cash outflow). The formula for NPV is:

$$NPV = \sum \frac{C_t}{(1 + r)^t} - C_0$$

Where:

• $C_t$ = Cash inflow in year $t$
• $r$ = Discount rate (opportunity cost of capital)
• $t$ = Year number
• $C_0$ = Initial investment

Steps in the Given Example

1. Identify the cash flows:
   • Initial investment = $400,000
   • Yearly inflows: $70,000, $120,000, $140,000, $140,000, $40,000
   • Discount rate = 8% (0.08)
2. Calculate the Present Value (PV) of each year's cash inflow using the formula:

   $$PV = \frac{\text{Future Cash Flow}}{(1 + r)^t}$$

   Year	Calculation	Result
   1	$70000 / 1.08$	$64814.81$
   2	$70000 / 1.08$	$102880.7$
   3	$70000 / 1.08$	$111136.5$
   4	$70000 / 1.08$	$102904.2$
   5	$70000 / 1.08$	$27223.33$

3. Sum up all Present Values of Cash Inflows:

   $64814.81 + $102880.7 + $111136.5 + $102904.2 + $27223.33 =

   $408959.5

   Total present value of cash inflows = $408,959

4. Calculate NPV:

   $$NPV = PV_{\text{cash inflows}} - PV_{\text{cash outflows}}$$

   $$NPV = 408959 - 400000 = 8959$$

Decision Rule

• If NPV > 0 → Accept the project (Profitable).
• If NPV < 0 → Reject the project (Not Profitable).

 

Conclusion: Since the NPV is $8,959 (positive), the project should be accepted because it adds value to the company.