This simplified worksheet illustrates the basic principle behind the merger of two entities. It is common knowledge that a merger will always be accretive is the target's price-earnings-ratio ('PER') is lower than the buyer's PER.

Think of PER as a *reverse yield* on the business - intuitively, buying a company with a higher income yield will always make a good deal for shareholders of the buyer.

In reality, not all target companies have lower PER than the acquirer. In some cases, the target company's PER could be marginally lower, which dilutes the effect of accretion. And if the deal can be funded with bank debt, this will also help improve the case for an earnings accretive acquisition.

See the spreadsheet below in which company A is the buyer and company B is the target.

The spreadsheet below enables you to calculate the selling price (or exit value) of any investment based on a *specific IRR*. You will need the following inputs:

The initial investment outlay (or purchase price)

Holding period of the investment

Any cash flows received during the holding period

The target IRR

NPV (Net Present Value) gives us the value of a business based on a set of projected cash flows. This is used in the income approach of valuation.

Because these cash flows occur in the future, there is an element of *uncertainty,* quantified by the *discount rate* and the year in which they are being generated. The further out these cash flows occur, the greater the discounting effect i.e. the *lower* the present value of those cash flows.

In the below example, we take a series of future cash flows ($100 annually for up to 6 years) and apply a discount rate of 10%. The values in the 'discount factor' row is applied to each year of cash flows to arrive at the *"present value of cash flows". *

It can be seen that similar cash flows in the later years have a significantly lower value than those in the earlier years.

To calculate the value of those cash flows, we add up all the present value of cash flows from year 1 to year 6 to arrive at 435.53. This is equivalent to the *NPV* of those cash flows.

**But what does the NPV of 435.53 mean?**

"If I invest $435.53 in this project and expect to receive $100 every year for six years, my investment return on this project will be10%"

Or, another way to look at this is:

"If my expected return is 10% and I can expected to receive $100 from this project for the next 6 years, I should invest no more than $435.53"

The NPV gives you an indication of how much you should be paying for the business based on the discount rate. Loosely speaking, the discount rate is sort of an expected *return on investment*. Assuming the estimated cash flows are fairly consistent and fixed, in order to get a return that is __higher than 10%__, one has to invest __less than $435__ in order to achieve this.

This is obviously more hairy in reality because:

Every investor has a different required rate of return (i.e. the discount rate) and;

Future cash flows can be

*vastly*different, which makes it more complicated because this ultimately also drives the rate of return.

If we plug $435.53 into the series of cash flows per below in row 12, we can calculate the Internal Rate of Return (IRR) based on the:

(i) initial capital outlay in cell C12; and

(ii) the future cash flows as shown in row 12 from column D to I

The IRR based on this series of cash flows yields a value of ** 10%,** which is equivalent to the discount rate of the project.

**Additional reading:**

If you have held an investment for a few years now i.e. you know the acquisition price and the set of cash flows over the period, you can also calculate the **minimum exit value** based on a specific desired IRR (__see this post__).

Not happy with a 10% IRR on your investment? This __post__ talks about cost of capital and how to increase investor returns with leverage.