The Net present value(NPV) is a capital budgeting technique used in measuring the profitability of a project by comparing the cash inflows of a project to its cash outflows in a manner that accounts for the time value of money.

It involves measuring the difference between the present value of cash inflows and the present value of cash outflows over the lifespan of an investment.

To calculate the NPV, the cash flows of the project are adjusted for the time value of money by applying a discount rate.

Each cash flow is discounted to its present value, and the present values are then summed to obtain the NPV.

The formula to calculate NPV is as follows:

\(NPV = -CF_0+CF_1 \left(\frac{1}{1+i}\right)^1 + CF_2 \left(\frac{1}{1+i}\right)^2 + \cdots + CF_n \left(\frac{1}{1+i}\right)^n \)

where:

- \(CF_t\) is the cash flow in period t,
- i is the discount rate, and
- n is the life of the investment project.

If the calculated NPV is positive, it indicates that the investment is expected to generate more cash inflows than the initial investment. So, the investment is considered financially favourable.

A positive NPV suggests that the investment is expected to increase the value of the company or provide returns higher than the required rate of return.

Conversely, a negative NPV indicates that the investment is expected to generate less cash inflows than the initial investment.

In such cases, it is advisable to reject the investment

Finally, a zero NPV indicates that the project is expected to break even. That is, its cash inflows are expected to equal its cash outflows.

## Example 1

A project has cash inflows of N3000, N4000, and N5000 over the next three years, respectively.

If the discount rate is 5%, calculate the NPV of the project if N9,000 was initially invested in the project.

### Solution:

\( NPV = -N9000 + \frac{N3000}{(1+0.05)^1} + \frac{N4000}{(1+0.05)^2} + \frac{N5000}{(1+0.05)^3} = N1804.45 \)

So, the NPV of the project is N1804.45.

## Example 2

Company A is considering two investment projects.

Project X requires an initial investment of N50,000 and is expected to generate cash flows of N15,000 per year for 4 years.

Project Y requires an initial investment of N80,000 and is expected to generate cash flows of N20,000 per year for 6 years.

The discount rate is 10%. Which project should the company choose based on NPV?

### Solution:

Let’s calculate the NPV for each project:

Project X:

\( NPV_X = -N50,000 + \frac{N15,000}{(1+0.10)^1} + \frac{N15,000}{(1+0.10)^2} + \frac{N15,000}{(1+0.10)^3} + \frac{N15,000}{(1+0.10)^4} = -N2,452.02 \)

Project Y:

\(NPV_Y = -N80,000 + \frac{N20,000}{(1+0.10)^1} + \frac{N20,000}{(1+0.10)^2} + \frac{N20,000}{(1+0.10)^3} + \frac{N20,000}{(1+0.10)^4} + \frac{N20,000}{(1+0.10)^5} + \frac{N20,000}{(1+0.10)^6} = N7105.21 \)

Based on the NPV, **Project Y** should be chosen because it has a positive NPV while **Project X** has a negative NPV.

## Advantages of Net Present Value

1. **Considers the time value of money concept: **Net Present Value (NPV) considers the time value of money by discounting future cash flows to their present value.

This makes NPV a more accurate and reliable approach compared to other investment appraisal techniques that do not consider the time value of money, such as the Payback Period and Accounting Rate of Return.

2. **Superiority over IRR:** NPV is considered superior to other discounted cash flow techniques like Internal Rate of Return (IRR).

In fact, in situations where IRR and NPV provide conflicting decisions, the decision based on NPV should be preferred as it provides a more accurate measure of profitability.

3. **Consideration of all Cash Flows**: NPV considers all cash flows over the lifespan of the project, including both inflows and outflows.

In fact, NPV ensures that the evaluation of the profitability of a project is comprehensive and considers the full financial impact of all the cashflows.

4. **Absolute Measure of Profitability**: NPV provides absolute measures of profitability, which directly reflects in the shareholder’s wealth.

That is why it is often said that any time the net present value of a project is maximized, the shareholder’s wealth is increased.

## Disadvantages of Net Present Value

1. **Difficulty in calculation: **It is sometimes difficult to calculate the net present value especially when dealing with projects that have multiple cash flows occurring at different periods.

2. **Does not consider the size of a project**: Net Present Value (NPV) doesn’t consider the project’s size.

Consider a situation where project A has an initial investment of N4 million and generates an NPV of N1 million, while project B requires N2 million and generates an NPV of N0.8 million.

If we solely base our decision on NPV, project A would be preferred due to its higher NPV.

However, project B has generated more shareholder wealth per dollar of initial investment.

The ratio of NPV to initial investment for Project B (N0.8 million / N2 million) is higher than that of Project A (N1 million / N4 million).

So, NPV may not be suitable for comparing projects of different sizes.