7 Free Cash Flow (to Firm)

This unit is the last in your “road trip” through finance.

You speak the language of cash-flows, you’ve mastered the tools of TVM. You understand the ins-and-outs of stocks and bonds and can evaluate which projects to buy and which to avoid.

Your last task now, is to get a better understanding of cash-flows.

You know that the inputs to the capital budgeting process are the:

  1. cash flows and

  2. cost of capital (= discount rate)

When these two components are provided, the capital budgeting process is purely mechanical. To make quality decisions it is critical that the firm obtain quality estimates for these two inputs.

Remember: garbage in –>>>> garbage out

You saw how to obtain the cost-of-capital in an earlier unit. Now we want to get some insight into how much cash our operations will provide our investors. Specifically, we want to estimate the free-cash flows of the firm.

When we use the term free cash-flow we mean the cash that is available to distribute to the investors after all fixed and variable cost have been paid and capital expenditures have been made. There are a lot of qualifiers there. The formula for Free Cash Flow is given as

\[Free\;Cash\;Flow=EBIT(1-tax\;rate)+Depreciation\;Expense\] \[-\;Change\;in\;wroking\;capital-Capital\;Expenditures \]

Working capital is equal to short term assets minus short term liabilities. For simplicity we have omitted adjustments to working capital other than changes in accounts receivable and changes in accounts payable.

To illustrate the idea, let’s follow the cash-flows from revenue to free-cash flow.

Assume you have a retail merchandise store. We are going to follow a transaction from the retail sales to how much cash we can finally distribute to investors. We’ll use the figure below to get us started.

From Revenue to After-Tax Income


We start with the firm’s revenue. Your retail customers buy $200,000 worth of your product and pay with cash, with checks, and with debit cards. With these sales you have been paid, and the sales count as income and an increase in cash for your firm.

In contrast, some of your commercial customers buy on credit, where the customer agrees to settle (pay for) the purchase with cash at some future date. Sales on credit are recorded by your firm as accounts receivable and are treated as income for the firm just like a sale with cash. However, while an increase in accounts receivable increases the firm’s income, the firm’s cash-balances do not increase at the time the revenue is recorded. Assume your commercial customers buy $50,000 worth of your product on credit which you record as an increase in accounts receivable. In the figure we will indicate non-cash items in red so they are easy to identify.

The total amount of revenue at this date is the sum of your cash and non-cash (accounts receivable) sales. In this case we have $200,000 plus $50,000 for total revenue of $250,000. Now we need to take into account our costs.

Fixed Cost

After you have your revenue figures, you need to subtract out your costs. The first costs we will address are your company’s fixed costs. Fixed costs are those costs that are associated with your firm, but that do NOT vary with the amount of product that you produce. One category we can consider a fixed cost is overhead expenses. An example of a fixed cost could be the heating bill for your facilities. You have to heat your buildings no matter how much product you sell. Another common example would be management and support services. For example, the amount you have to pay your accountants and management teams does not depend on the level of your sales.

For our example, we’ll assume your firm has fixed costs of $12,500. We’ll assume that these expenses are paid at the time the expense is incurred and therefore, these require cash immediately (you can think of the company paying these expenses from its checking account).

Variable Costs

Next we need to account for the costs associated with the volume of our sales. The distinguishing feature of variable costs is that variable costs depend on the volume of the product produced. An example of these types of costs would be raw materials. With raw materials it’s likely that your firm is working with another commercial business and so you are more likely to make your purchases on credit. That is to say, you would purchase the materials at one point in time, but not actually pay for them until later. The purchase counts as an expense at the time of the purchase, but your firm’s cash balances do not decrease until the liability is settled. The transaction therefore appears as a non-cash expense. For this example, we’ll assume you purchased $75,000 on credit.


Our next major expense is from the depreciation of our Plant & Equipment. When we started our company we had to make certain capital expenditures. The plant and equipment we purchase to start our business are assets for the company, and they are expected to last for more than one accounting period (quarter or year). Since these assets last more than one period, one way to account for the expense of these assets is to “depreciate” them over time. The tax authority classifies different assets based on their useful lives and determines a “depreciation schedule” for each asset. The depreciation schedule determines how much of the purchase price of the asset our firm can treat as an expense in each reporting period for the asset’s lifespan. For example, an asset with a 4 year life might have the following depreciation schedule:

To see how this might work, let’s say that we needed to purchase a $20,000 machine for our business. We buy the machine for $20,000 today, but we do not record a $20,000 expense today. Instead we allocate the $20,000 expense over the four years according to the depreciation schedule.

Based on the first year of the depreciation schedule, we can count $6,600 (0.33 x $20,000) as a depreciation expense as shown in the figure. Since we did not actually pay $6,600 from our firm’s checking account in year 1, this is a non-cash expense.


After we subtract our fixed and variable costs from our revenue, we have our firm’s “Earnings Before Interest and Taxes” or EBIT.*

Assume that your company has an income tax rate of 23%. Based on this your tax liability would be (0.23)x($155,900) = $35,857. You will need to write the IRS a check for $35,857 to cover your tax bill so the tax expense will lower your cash balances.

  • Note that for the calculation of Free Cash Flow we are assuming the firm has no debt. We will account for the firm’s debt when we calculate the value of the firm or via the discount rate if we use the free cash-flows for capital budgeting.

The Bottom Line

The “bottom line” of $120,043 is what your company would report as its earnings for the period. However, this is NOT how much your company’s cash balances have changed.

The reason? Some of the revenue items and expense items were non-cash.

To move toward our goal of finding the “free cash-flow” we need to make some adjustments for the these non-cash items.

Adjusting for Non-Cash Items

The first adjustment for non-cash items we will make is to add back the depreciation expense. We had a depreciation expense of $6,600 but no cash actually left our checking account. We therefore add $6,600 to the after-tax income figure of $120,043 to get $126,643 ($120,043+$6,600).

We also have to take into account our sales that we recorded as accounts receivable and our purchases that we recorded as accounts payable.

We recorded $50,000 of revenues as accounts receivable. Since we have not actually collected the cash for this yet, the $126,643 overstates how much cash these transactions actually generated. To adjust for the accounts receivable we subtract $50,000 from the $126,643 to get $76,643.

We still have one more non-cash transaction to take into account and that’s the $75,000 purchase we made on credit and recorded as accounts payable. Since we treated this $75,000 as an expense, but didn’t actually write a check, we need to adjust the $76,643 upward by $75,000 to get $151,643.

The $151,643 is the amount these transactions increased our cash balances.

Another adjustment we need to make is related to our collection or payment of accounts receivable or payable from previous periods. When you collect on an accounts receivable, your accounts receivable decrease (come off the books) but your cash balances increase.

When you pay off an accounts payable, your accounts payable decrease (come off your books), but your cash balances decrease.

Let’s say that this period you collect $5,000 from accounts receivable from previous periods. You would need to add this $5,000 to the $151,643 because the $5,000 is an inflow of cash this period. You would then have generated $156,643 ($151,643 + $5,000) this period.

Continuing with the adjustments, let’s assume that this period you payoff $9,000 of your accounts payable from previous periods. You would write a check for $9,000 which you would need to subtract from the free cash-flow of $156,643. You would then have $147,643 ($156,643 - $9,000) for free cash-flow.

This finishes the adjustments to free cash-flow for non-cash revenues and expenses.

Even though our cash balances increased $147,643, this is not necessarily what we could pay our investors (i.e., our free cash-flow).

To get our free cash flow we must take into account whether we need to make any capital expenditures. As a reminder, capital expenditures account for purchases of machinery that contribute to the production of the firm’s goods. The assets of the firm must be replaced or expanded for the company to stay operating and/or grow.

To continue with our example, let’s say that you need to make capital expenditures of $30,000 in this reporting period. You write a check for $30,000 and purchase new machinery.

This would reduce your cash balances to $117,643 ($147,643 - $30,000).

From this example, your firm would have $117,643 available this period to distribute to your firm’s investors. These investors would include bond holders as well as stockholders.

Example 2

-   You buy a machine for $30,000 with some of the firm's available cash.
-   Your sales from retail consumers of $275,000. These customers pay immediately. 
-   You also have commercial customers that purchase $60,000 of your product, but they purchase the product on credit. 
-   The cost of your overhead is $27,000 which you pay for immediately. 
-   You have variable costs of  $80,000  which you pay on credit. 
-   Your firm's tax rate is 28%.
-   Finally, you collect on past accounts receivable for $3,000 and pay off past accounts payable for $2,000

With this information, what is your firm’s free cash-flow as a result of all of these transactions?

From Revenue to After-Tax Income

We’ll use the figure below to guide our calculations.

First, calculate the depreciation schedule since we will need that for later.

Trace the cash-flows associated with the narrative.

You will have after-tax income of $157,032

To move toward free cash-flows we add back in depreciation to get

$157,032 + $9,900 = $166,932

Again, we also have to take into account our sales that we recorded as accounts receivable and our purchases that we recorded as accounts payable.

We recorded $60,000 of revenues as accounts receivable. Since we have not actually collected the cash for this yet, the $166,932 overstates how much cash these transactions actually generated. To adjust for the accounts receivable we subtract $60,000 from the $166,932 to get $106,932.

We still have one more non-cash transaction to take into account and that’s the $80,000 purchase we made on credit and recorded as accounts payable. Since we treated this $80,000 as an expense, but didn’t actually write a check, we need to adjust the $106,932 upward by $80,000 to get $186,932.

The $186,932 is the amount these transactions increased our cash balances.

Then pay for our machine (a capital expenditure) of $30,000 to get

$186,932 - $30,000 = $156,932

And finally take into account paying off our past accounts payable (uses $2,000 of cash) and collecting on our past accounts receivable (provides $3,000 in cash) gives us free cash-flow of $157,932.

In this second example, by conducting the transactions as stated in the narrative, the company would have an additional $157,932 available to pay out to its investors.

7.1 Which cash flows to include?

When you are conducting an estimate of the free cash-flows of a firm or project, not all cash-flows are included. Here we will consider four concepts related to which cash-flows to include and which to leave out. We’ll consider:

1.  Incremental cash-flows
2.  Sunk Costs
3.  Opportunity Costs
4.  Spillover Effects
5.  Incremental cash-flows

In any capital budgeting project we have to be careful to only consider the incremental cash-flows. The incremental cash-flows are the difference in the cash-flows from doing something new vs. continuing with your current activity (which includes doing nothing). You might recall from your micro-economics classes that an incremental cash-flow would be called a marginal cash-flow.

For example, say you have a job with an annual salary of $50,000 and you are considering a different job that will have an annual salary of $60,000. Whether you take the new job or stay with your current job depends on $10,000 ($60,000 - $50,000) NOT the $60,000 or the $50,000 per se. The benefit from the new job is $10,000. It wouldn’t matter whether the change in job moved your income from $30K to $40K or $50K to $60K. The benefit is still $10K.

This may seem obvious, but in complex situations it can be difficult. This is the same idea of making decisions based on marginal costs and marginal benefits you learned from microeconomics.

Sunk Costs

Capital budgeting often involves choosing between alternatives (e.g., keep the current machine or buy a new one). A sunk cost is a cost associated with the situation, but that will be the same amount no matter which alternative you choose and the cost cannot be recovered. Here are some examples.

Example 1

Your company purchases a new software package for your employees at a cost of $2 million. After installing the system, you discover that there are bugs in the system. In the meantime, the company that sold you the system goes out of business, so you cannot get back any of the $2 million. You now have two choices:

  1. spend $500K to de-bug the software you just bought

  2. spend $200K to buy a different system.

The $2 million you originally spent on the first system should not have any influence on your decision of what to do. The $2 million cannot be recovered and you have spent the $2 million no matter which alternative you do.

Example 2

You are on the City Council and must vote whether the city should build an arena. You commission a feasibility study that costs $400K.

Part of the study is to create a budget that includes all of the costs to build the arena. Should you include the $400K as part of the arena costs?

No. It is of course a cost that must be paid, but the $400K will be spent whether the arena is built or not built. Therefore it meets the definition of a sunk cost: it cannot be recovered and it does not depend on which choice we make (build or don’t build the arena).

Opportunity Costs

An opportunity cost arises when a resource can be used in more than one way, and one is considering which of the ways to use the resource.

Example 1

You own a piece of farmland on the edge of a growing city. Your current farm is expected to provide an income to you of $50,000 per year forever. You apply a discount rate of 5% to this cash-flow to determine the farm is worth $1,000,000. If a developer offers you $1,200,000 for the land, you should only consider the $200K in your decision of whether to sell the land or not ($1,200,000 - $1,000,000 = $200,000).

Example 2

One day you are taking a walk and notice a coin on the ground. You pick it up and discover that it is a 1 oz. gold coin. On the day you find the coin the price of gold is $1,200 per oz. You decide to give the coin to your favorite nephew and tell him “it didn’t cost me anything, I found it on the ground.”

While it was very generous of you to give your nephew the coin, it DID cost you something. It cost you $1,200.

Example 3

You are currently employed as a CPA and earning $65,000 per year. You are considering quitting your job to go to law school. Law school will cost $34,000 per year, for three years, starting in one year. If you go to law school you will graduate and start practicing as a lawyer from year 4 onward. As a lawyer you will earn $130,000 per year. If you are trying to decide the value of going to law school, what should the cash-flows look like?

Each year of law school costs you $99,000, composed of the direct costs of $34,000 plus the opportunity cost of your lost income because you had to quit your job. This example also illustrates our earlier idea of “incremental.” The benefit from the law school is the amount above what you would have made as a CPA.

Spillover Effects

When a firm undertakes any action there may be “spillover” effects that result. Here we use the term spillover to mean a consequence of any action that is NOT directly intended. A spillover can be beneficial to the firm (or others) or detrimental to the firm (or others). You may be familiar with the phrase “unintended consequences.” For example, you build a wood burning fire pit on your deck to provide a nice place to sit around at night. The negative spillover or unintended consequence is that your house smells like smoke for days. A spillover can also be positive. For example, you plant a honeysuckle bush to provide privacy in your yard. The bush attracts humming birds, which you like. Here the humming birds are an unintentional benefit.

Firms face similar consequences when they adopt new plant & equipment. When we conduct a capital budgeting analysis we need to be conscious of taking into account both the direct costs and benefits, AND the spillover costs and benefits.

The spillovers can affect the firm itself or they can affect parties outside the firm. Spillovers can result at least one of three ways:

  1. The action affects a complimentary product in the firm.

  2. The action affects a substitute product in the firm.

  3. The action has an unforeseen effect on the firm

Consider the following as an example of how a spillover may result from complimentary goods in the firm. You own a bookstore and are considering whether to add a coffee service within the store. You conduct a capital budgeting analysis on the direct costs and benefits of selling coffee. You find that the NPV of the coffee shop is positive so you decide to add the coffee service. Once the coffee service is in the store, you notice that you are selling more books as well. In this case coffee services and books are complimentary goods. Your NPV analysis would have underestimated the value to you of adding the coffee services, because you ignored the benefits of the additional book sales.

The classic example of a substitute product spillover is known as corporate cannibalism. In this case the company introduces a new product that by itself, may have a positive NPV and would thus appear beneficial to the firm’s stockholders. However, if the new product is a substitute for one of the firm’s existing products, the positive cash-flows from the new product may be offset by the reduced cash-flows of the existing product. For example, consider when Apple introduces a newer model iPhone. Some customers that would have purchased an older model iPhone will purchase the newer model instead. When Apple performs a capital budgeting analysis for the new i-phone it may find that it has a positive NPV. However, if sales on the older model iPhones decrease, then the NPV will overstate the benefit to the shareholders of Apple. Corporate cannibalism often arises when a firm introduces additional sales channels, such as additional store locations or adding online sales to a brick-and-mortar operation.

Finally, some spillovers for a firm’s actions are entirely unrelated to the product associated with the capital budgeting analysis. Often these types of spillovers affect parties outside of the firm. These could include byproducts of the production process. For example, a production process could affect the quality of the air or water near the facility. Noise and unsightliness can affect property values.

Spillovers can also be beneficial to parties outside the firm. For example, a movie theater could attract business to a nearby restaurant. The restaurant would benefit from the theater even though it is a separate company.