When a new business opens its doors, its owners and investors want to know: How long is it going to take until I get my initial investment back and start pulling in a profit? This payback period determines the value of a business opportunity by the amount of time it takes the business venture to recover the initial investment costs.

Here’s the mathematical formula for payback period analysis:

**PP: Cost of Project or Investment / Annual Cash Inflows**

Simple, right? How much went out compared to how much came in. Let’s look at an example. We want to figure out the payback period on an enterprise into which we plan to place a $200,000 investment. The expected annual cash inflows,which is really the amount being returned on the investment, is $40,000 per year. When you divide $200,000 by $40,000, you learn that the payback period is five years if the investment performs as anticipated.

Although the payback period is the easiest to compute and the simplest to understand, this method of analysis has weaknesses. The payback period analysis does not compute any benefits or profits that may have been earned or acquired after the payback period. Payback period analysis also does not account for the time value of money, that is, what the money could have been earning had it been invested elsewhere.

**Internal rate of return**

The internal rate of return (IRR), according to Investopedia, is the growth rate expected to be generated by a specific project. Generally speaking, the higher a project’s internal rate of return, the more desirable it is to undertake the project. This ratio is also sometimes called the economic rate of return or ERR. The IRR is an analysis of how much sales volume a business must achieve in order to begin making profit. This information is crucial in developing a pricing strategy. By knowing the number of sales required at a given price in order to break even, an entrepreneur can identify whether the price structure being considered will allow the business to thrive.

When a business obtains bank financing to purchase equipment or gets a loan to provide operating capital, the money borrowed carries a cost, or interest, that must be paid in addition to the principal amount. The income generated by the use of this capital compared to the cost of the capital generates the IRR. In most spreadsheet software applications such as Excel, the formula for IRR is a built-in function and you simply choose the formula by using the formula wizard. You can also use online calculators to perform the calculations.

Here’s an example of how IRR can help you make solid business decisions. Suppose you wish to purchase equipment that costs $100,000.You will have to pay 14 percent interest on the money borrowed to pay for the equipment. Your best estimates show that by adding this equipment, you’ll increase your revenues by 22 percent. The IRR in this case is 8 percent, the difference between the cost of capital and the revenue increase generated by the capital investment.

On the other hand, let’s say that you are considering the same equipment purchase at a cost of $100,000 and you’ll pay the same 14 percent on the money borrowed, but your best estimates of the revenue generated by adding this equipment show that your revenue will increase only 3 percent, putting the IRR in negative territory. Then clearly the investment is not a good idea.

**Break-even analysis**

Another way to estimate profitability of a business venture and to determine some uncertain variables you undoubtedly will run into somewhere along your business path is called the break-even analysis. Break-even analysis can help determine the income estimation when certain variables may still be unknown. The simple equations that represent a break-even analysis are below.

First, you need to determine the contribution margin. The contribution margin consists of the revenue minus any variable costs (costs that change from month to month such as electricity). The result is the amount that is available to pay for fixed costs (costs that do not vary from month to month but are always a set amount such as the payment on a fixed-rate mortgage) and the remainder provides the profit the business earns. Once you know the contribution margin, you can then subtract the fixed costs from the contribution margin to obtain the before-tax earnings from the business.

Second, you can now calculate the break-even point. In order to do so, you must divide the total fixed costs by the contribution margin that you defined using the formula above. Commonly, break-even is expressed as a percent of revenue. It can also be expressed as a number of units required to achieve the break-even point.

Here’s what we mean: Current financial statements for Joe’s Bakery show that the fixed costs are $49,000 and variable costs per loaf of bread are $0.30. Let’s assume the sales revenue is $1.00 per loaf of bread. We can easily see that after the $0.30 per loaf variable costs are covered, each loaf of bread contributes $0.70 toward covering the fixed costs of the business. By dividing fixed costs by the contribution of $0.70 made by each loaf of bread sold – $49,000/$0.70 — we see that 70,000 loaves must be sold in order for Joe’s Bakery to break even.

If fewer than 70,000 loaves of bread are sold, the business will experience a loss.

In the case of Joe’s bakery, a 10,000-loaf increase in sales over the break-even point to 80,000 loaves will produce a $7,000 profit, and a 30,000 loaf increase to 100,000 loaves will produce a $21,000 profit. On the other hand, a decline in sales of 10,000 loaves from break-even to 60,000 loaves will produce a loss of $7,000, and a 30,000 decrease from the 70,000 break-even point produces a $21,000 loss.

Being able to successfully manipulate these types of calculations can be the difference between a thriving business and a failed enterprise.