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In: Finance

elaborate on the concept of compounding. Discuss how to calculate the net present value and the...

elaborate on the concept of compounding. Discuss how to calculate the net present value and the significance of this indicator for decision.

Solutions

Expert Solution

Compounding is when interest is earned both on the prinicipal amount as well as the interest earned in the prior periods. Under compounding the value of the asset or the liability increases faster.

For example:

Let's say you have $1000 which you deposit in bank at 10% for 2 years. In this case, the amount earns a simple interest.

So, after 2 years, the amount you'll receive is $1200 ($1000 + ($1000*0.1*2))

However, if you deposit the same amount in common stock and suppose you receive the same rate of return on a compounding basis for the same period of time.

You'll receive an accumulated amount of $1210 ($1000 * (1+0.1)^2)


So, for the same amount of time and on the principal, you'll receive a greater amount of $10. How? Because in the first year you received $1100 under both the methods. However, in the second year, you received $100 as interest under simple interest and $110 as interest under compounding method . The difference i.e. $10 is the amount of interest earned on the interest earned in the first year.

Now, let's get to the net present value. The net present value is the net present value of the future cashflows of a project. Just to make you understand through an example, suppose you are being asked to invest $1000 for a year and you expect the invest to generate $100 every month. However, that's an expectation of future which means it is highly uncertain in nature. So in order to consider whether you should invest or not, you calculate the present value of such cashflows i.e. if the present value is given to you today or the future value on the specified date, you'll be indifferent between both of such inflows. The net present value is the total present value of the cash inflows minus the total present value of the cash outflows.

It is calculated as follows:

Here, -C0 is the present value of the cash outflow while Cn is the cash inflow discounted at the rate i for a time period of n. The NPV is the net value of the both.

The basic requirement according to NPV is if your NPV > 0 then the project should be accepted while if your NPV < 0 the project should be rejected.

This because if your NPV < 0, then your project's cost will exceed your projects benefit and vice versa. NPV is one of the most common method used to evaluate project. If a project as cash flows that can be estimated and a rate of return that the company expects out of such project, NPV stands as one of the most simple yet insightful method to evaluate the project.


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