# An Introduction to Capital Budgeting : Brief Discussion on Payback Period, NPV and IRR with Examples

Mr. Issac, an owner of a small firm wanted to buy a machine that would improve the productivity of his firm. The machine would be operated for the long term. As it was a kind of investment for the long term, Mr. Issac was worried whether the decision of investment would end up being successful. So, he went to his friend who knew a bit about finance. After discussing with his friend, Mr. Issac learned a new term called Capital Budgeting. It was a new idea for him. He googled capital budgeting. So let’s check what he found!

## A very brief discussion on **Capital Budgeting **

As you guessed, **capital budgeting** aka **investment appraisal ***is a process of plan and assessment whether the long-term investment proposals are worthy enough to be selected.*

As large amounts of capital are tied up for the long term, any error certainly has greater consequences. So forecast must be accurate.

Capital budgeting techniques will guide you whether you should replace your old machine, or whether you should need a new machine. When there are mutually exclusive projects, you can evaluate which one is worthy to be taken by using capital budgeting techniques.

Capital budgeting techniques sort out your cash inflows (the money you will receive) and outflows (the money you spend for projects). Then it analyzes the cash inflows and outflows to assume whether the proposal meets the benchmark you set. So capital budgeting is a tool for evaluating long-term investment proposals.

There are a couple of techniques in capital budgeting. Some are time-consuming, some are complicated and effective. **The payback period, NPV, IRR** are notable ones.

## Payback Period

Oh, we forgot about Mr. Issac who wanted to invest CU (cost Unit) **46,000** in equipment. He was informed that the machine would last for **4** years. He estimated he could sell it for CU 4,000 four years later. Mr. Issac is now ready to apply **payback period **as he finds out that this is the easiest method by which he can know the length of time it takes to retrieve the cost of the initial investment which was CU **46,000**.

**The payback period*** will tell you when you will recover the initial investment cost.*

Mr. Issac chose the payback period out of other capital budgeting techniques because it is pretty simple and quick to calculate. Mr. Issac easily understood the concept. He now knows that if his payback is for long period, the investment will be riskier.

So let’s see how he calculated payback. As he knows exactly how much money he will be benefited each year from buying the machine, he arranged forecasted operating profit yearly. Operating Profits as follow:-

#### Step 1: Adding depreciation to profits

The profits we are seeing above are subtracted by depreciation. As previously depreciation was deducted from revenue to calculate net profit, now Mr. Issac needs to add the depreciation to get the cash inflows. Mr. Issac has to separate the profit from depreciation to get the cash inflows as depreciation is a non-cash item.

###### How he calculated depreciation:

Annual depreciation: Asset cost- salvage value aka scrap value/ useful life.

Mr. Issac’s machine depreciation: Machine cost **46,000**– salvage value **4,000**/ useful life **4** years= **10,500**.

#### Step 2: calculating cumulative cash inflows

**Mr. **Issac now needs to calculate cumulative cash flows in each year to find the payback period. Each year’s cumulative cash inflows are calculated by adding the current year’s cash inflows with the previous year’s cumulative figures.

#### Step 3: Getting results

- At first, Issac needs to determine which year his cumulative cash flows are initially more than the
**original/initial investment.**We can call it the**Year of Full Recovery**.**The year of recovery**for Issac’s investment was two years. - Then he checked the previous year’s cumulative CF of the
**Year of Full Recovery**was CU 27,000. - Then he noted the
**Cash flow**during the**year of full recovery**which was CU 34,000. - Finally, he put all the figures into the formula to find the payback period.

The payback period was**1 year 6 months.**

## Net Present Value (NPV)

Mr. Issac told his finance expert friend that he calculated the payback period. But his friend criticized the effectiveness of the payback period. He said that the payback period isn’t a sophisticated capital budgeting method.

Yes, **the payback period **is not a sophisticated method as it ignores the time value of money. And the method does not consider the variability of cash flows.

What if two mutually exclusive projects result in the same payback period? The users will not be able to distinguish which one they will choose by the payback period.

Then Mr. Issac’s friend suggested **NPV** which is an acronym of **Net Present Value**.

**Net present value** is calculated by using **discounted cash flow technique** where forecasted discounted cash inflow and discounted cash outflow are differentiated.

To be more specific, it is just the difference between the present value of projected cash inflow and the present value of outflow or original investment.

The present value of outflow is normally the same as the investment has already been incurred. But the main issue here is projected or forecasted cash inflow. The projected cash inflow will be received in the future. So we need to use discounting techniques to know what the present value is.

We have to consider the time value of money as the issues of the uncertain future, inflation, ignoring the pleasure of having current benefits arise. So all those issues are considered in Net Present Value.

It does take into account the fact of maximizing shareholder’s wealth. Moreover, NPV is a clear-cut method in making capital budgeting decisions.

Now Mr. Issac wants to evaluate his investment proposal using NPV. He decided that his required rate of return (minimum amount of profit) would be **10%. **

#### Step 1: finding the present value of projected cash inflows

There is a formula to convert the future values into the present values. The process is known as **discounting.
**The formula is, PV=FV/(1+i)n

1st Year PV= 2700/(1+0.10)1 =24543

where, FV(Future Value)=2700

i(required rate of return)=10%

N(no. of periods)=1

The **PV table ****(click on the link to see the table) **makes it easier as we can easily find out the present value from the table. The present value of cash inflows is 76,798.

#### step 2: Subtracting the present value of projected cash inflows from the present value of cash outflow

**Net Present Value (NPV)= 76,798- 46,000= 30,798. **

Does, Mr. Issac choose his investment? Let’s see the criteria.

- If the
**Net Present Value**is positive, it means that the project will generate a return more than the cost of capital. The project will be accepted. - On the other hand, if the
**Net Present Value**is negative, it means the cost of capital is not over the return generated by the cash flows. So the project should be rejected.

Mr. Issac can accept the project as its NPV is positive.

## IRR (Internal Rate of Return)

Let’s talk about another important capital budgeting technique called IRR.

The **internal rate of return** is considered as the discount rate at which, the **Net Present Value** is equal to zero.

**IRR method** is a discounted cash flow technique but it is a relative appraisal technique where NPV is an absolute measure.

Because of being a relative appraisal technique, it is more understandable than NPV.

Managers or users who belong to the non-finance background can understand **IRR** more easily.

Let’s get back to Mr. Issac. He has a new project where he wants to know the IRR. Cash flows of the project as follows:

#### Step 1: Calculating two net present values that are close to zero

To find **IRR**, we need to calculate two NPV. Creating one NPV negative and the other positive is the first task to be exercised to calculate **IRR**.

Calculation of IRR has been done with trial and error exercise as satisfactory findings can not easily be obtained. We have to make several attempts to get the rate we want.

#### Step 2: Application of The IRR interpolation Formula

IRR must be more than 14% and less than 16%. And the formula also generates 15% IRR where NPV is zero.

These three appraisal techniques help investors to make better decisions. As the capital has been tied for a long period of time, sophisticated evaluation is much needed.

Here, a very basic idea of capital budgeting techniques is given. Hopefully, it may help the beginners.