There are various methods of investment appraisal, or investment appraisal techniques. Some of the most commonly used performance appraisal techniques include:

*Non-Discounted Cash Flow Methods*

- Payback Period
- Accounting Rate of Return (ARR)

*Discounted Cash Flows*

- Net Present Value (NPV)
- Internal Rate of Return (IRR)
- Profitability Index Method (PI)

**1) Payback Period**

The payback period (PBP) is one of the most popular and widely recognized traditional methods of evaluating investment proposals. It is based on the assumption that the degree of risk associated with the fixed asset is the length of time required to recover the investment from the firm’s cash flow. Payback period refers to the number of periods or years that a project will take to recover the initial cash outlay invested in a project. This technique applies cash flows and not accounting profits. If the project generates constant annual cash inflows, the payback period can be computed by dividing cash outlay by the annual cash inflow. That is:

*Example 7.1: Calculating Payback Period with Constant Cash Flows*

Assume that a project requires an outlay of $200,000 and yields annual cash inflow of $40,000 for 9 years. The payback period for the project is:

PB = $200,000/40,000 = ** 5 years**.

2) **Accounting Rate of Return (ARR)**

The accounting rate of return (ARR) is an investment appraisal technique which is used to measure the percentage rate of return expected from an investment or asset compared to the initial cost of the investment. This capital budgeting technique can be calculated by dividing the average net income that an asset is expected to generate by the average cost of capital. ARR uses a formula that compares the net income of an asset with the initial cost of acquiring that asset. It is the only capital budgeting technique that uses profits rather than cash flows to evaluate the viability of a project. ARR takes into consideration various expenses that are incurred by the asset every year, including depreciation.

Accounting Rate of Return is important for businesses because it can be used to compare several projects or investments to determine the expected rate of return for each profit and decide on the best project. Usually, the project with the highest rate of return is chosen because it gives the company more profits and helps them to grow. The formula for calculating ARR is shown below:

ARR = (Average Annual Profit after Tax ÷ Average Cost of Investment) × 100

Where:

*Average Investment = (Book Value at 1st year + Book Value at End of Useful Life)/2**Average Annual Profit = Total profit over Investment Period / Number of Years*

The outcome of dividing annual profit by cost of capital is multiplied by 100 to get the percentage rate of return.

**3) Net Present Value (NPV)**

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.

**4) Internal Rate of Return (IRR)**

The internal rate of return (IRR) is an appraisal technique that utilizes discounted cash flows – taking into account the timing and magnitude of cash flows. It is a rate that the present value of the expected future cash flows with the cost of the investment. In other words, it is the discounting rate that equates NPV to zero. The internal rate of return is also described as the yield on investment, marginal efficiency of capital, time-adjusted rate of internal return, or the rate of return over cost.

**How to Calculate IRR**

The IRR concept is easy to understand if it deals with one project in one period. As an example, consider an investment whose initial cost is $10,000. Assume that the investment will be worth $10,800 after 1 year. The true rate of return for this one-period investment will be given as:

Rate of Return = (10,800-10,000)/10,000 = 0.08 or 8%.

This means that the return on your investment is $10,800 – $10,000 = $800. The rate of return is 800/10,000*100% = *8%.*

So, at the end of 1 year you get your initial investment of $10,000 plus the return of $800. This could be an investment on bonds, shares, property, land, or even fixed deposit in a bank. If your rate of return is negative, then the investment is not worth investing. For instance, if your investment of $10,000 comes to $9,800 after 1 year, the return will be $9,800-10,000 = -200 and the rate of return will be -200/10,000 = *-2%.*

The rate of return of 8% and the rate of return of -2% make the discounted (present) value of the future cash inflows to be equal to the initial investment of $10,000. Thus, 8% makes the future cash inflows of $10,800 to be equal to the initial cost of $10,000. This is the basic idea of internal rate of return.

The formula for the internal rate of return (r) on an investment C_{0} that generates a single cash flow after period (C_{1}) is given as follows:

r = (C_{1}-C_{0})/C_{0} = (C_{1}/C_{0}) – 1………………………………………………………………… (1)

This equation can be rewritten as:

C_{0}/C_{1} = 1 + r

This is also the same as:

C_{0} = C_{1}/(1+r)………………………………………………………………………………… (2)

Equation 2 shows that the rate of return (r) depends solely on the cash flows of the project, and not any other factor. This is why it is known as the internal rate of return. The internal rate of return (IRR) is the rate that equates the investment outlay with the present value of cash inflow received after one period. This also implies that the rate of return is the discount rate which makes NPV = 0. There is no satisfactory way of defining the true rate of return of a long-term asset. IRR is the best available concept.

Based on the equation involving r and C above, the actual formula for IRR is given as:

…………………………………………. (3)

It can be noticed that the ERR equation is the same as the one used for the NPV method. In the NPV method, the required rate of return, k, is known and the net present value is found, while in the IRR method the value of r has to be determined at which the net present value becomes zero.

The acceptable IRR can be calculated using trial and error and interpolation.

**5)** **Profitability Index**

Profitability Index is a capital budgeting technique which can be defined as the ratio of the present value of cash flows at the required rate of return to the initial cash outflow on the investment. It is also called the benefit –cost ratio because it shows the present value of benefits per dollar of the cost. It is therefore a relative means of measuring a project’s return. It thus can be used to compare projects of different sizes.

- The profitability index (PI) is an investment appraisal method used to determine the attractiveness of a project.
- The PI is calculated by dividing the present value of future expected cash flows of an investment by the initial cash outlay of the investment.
- The investment is acceptable if the PI is greater than 1.0. Projects with higher values are more attractive.
- Under capital constraints and mutually exclusive projects, only those with the highest PIs should be undertaken.

A PI of less than 1 indicates that the present value of the investment’s inflows is less than its initial investment cost.

The components of profitability index are:

- Present value of future cash flows
- Initial investment cost

**How to Calculate Profitability Index**

PI can be calculated using the following formula:

Profitability Index = PV of future cash flows/initial investment

Based on the above formula, future cash flows of an investment requires the use of time value of money to get the present value. Future cash flows are discounted based on the number of periods of the project to get their present monetary value.