Chapter 2

What Matters and What Doesn’t: Relevant Revenues and Costs

The primary goal of a firm is to maximize profits. This implies, of course, that each decision a manager makes is consistent with that goal. Although managers are expected to rely on internally produced reports to help them make decisions, most of the information that appears on these statements is period based rather than decision based. A balance sheet shows the sum total of a firm’s assets and liabilities at a given point in time. If the firm sold off all of its assets at book value and used the proceeds to pay its liabilities, what remains is owner’s equity, which is the amount that is owed to shareholders. An income statement is the difference between revenues and expenses between two points in time.

A myriad of useful pieces of information can be gleaned from these statements: the current ratio, inventory ratio, and liabilities ratio may be determined from balance sheets. Net sales to inventory and net profits to net sales are obtained from income statements. But as useful as this information can be to managers, the critical element is that the balance sheet and income statement represent the collective results of previous decisions. The balance sheet indicates where the firm stands as a result of all past decisions. The income statement reports the revenues received and expenses incurred between two distinct dates. Some of the revenues may flow from decisions made in previous periods. Some of the expenses that are incurred may not generate revenue until a future period. There is nothing in the statement that reports the results of a specific decision.

But managers need to know how to make profitable decisions. Economists and accountants assert that managers should compare the relevant revenues and relevant costs associated with a decision.¹ Relevant revenues refer to any revenues that will change if the decision is implemented. Any revenue that will remain unchanged is irrelevant and should be disregarded in evaluating a course of action. Relevant costs refer to any costs that will change if the decision is implemented. Any costs that remain unchanged should not be factored into the firm’s decision.

Let’s use several contrasting examples. A local group decides to hold a fundraiser by selling boxes of chocolate chip cookies. Each box costs the group $3. Historically, it charged a price of $10/box and sold 300 boxes. This year, the group is considering lowering its price to sell more boxes. It believes it could sell 400 boxes at a price of $8/box. The decision is whether to lower the price to $8 to sell more boxes. If the decision is implemented, revenues will rise from $3,000 to $3,200, or by $200. The $200 increase in revenue is the relevant revenue. The relevant revenue, however, is not simply the revenues generated by the additional 100 boxes. If that were true, revenues would rise by $8 × 100 boxes, or $800. Instead, the relevant revenues incorporate the fact that the 300 boxes that could have been sold for $10 will also be sold for $8. In other words, to sell the additional 100 boxes for $800, the group sacrificed $600 on the first 300 boxes. Hence, the decision caused the group’s revenue to rise by $800 – $600, or $200.

The relevant cost in this example is the change in the group’s cost if the decision to lower the price is implemented. Because each box costs the group $3, if it lowers the price to $8, it will sell 100 additional boxes at a cost of $3, causing costs to rise by $300.

If we compare the relevant revenues with the relevant costs, we can see that the group should not lower its price. If it does, its revenues will rise by $200, whereas its cost will increase by $300. It will be $100 worse off by lowering its price.

This can also be seen by examining total revenues and costs. At a price of $10, the group’s revenue is $10 × 300, or $3,000 and its costs are $3 × 300, or $900, leaving a profit of $2,100. If it charges $8, its revenues will be $3,200 ($8 × 400) and its costs will be equal to $1,200 ($3 × 400), for a profit of $2,000. By lowering its price, its profits decline by $100. This is summarized in Table 2.1.

Although this is a relatively simple example, one might see how poor decisions might have been made without relying on relevant revenues and costs. For example, each box costs the group $3 and would be priced at $8. At face value, one might be deluded into thinking that the group’s profits would rise by $500 ($5 profit/box times 100 additional boxes) if the price were lowered. In fact, the decision would have caused the group’s profits to fall because the first 300 boxes would also be sold at the lower price. Let’s expand on the previous example to show how relevant revenues and costs can become complicated. Suppose the group is considering offering a senior citizen discount on boxes. The seniors will pay $8, whereas everyone else will pay $10. Consistent with the previous example, 300 boxes can be sold for $10 and 100 additional boxes can be sold for $8. In this case, the relevant revenue is $800. The group will collect an additional $800 from the 100 boxes, and none of that will be offset by lower prices charged on the first 300 boxes. Because the relevant costs associated with the decision to set a separate price for senior citizens is $300, the group’s net income will rise by $500. This is illustrated in Table 2.2.

Let’s go back to the single price example, but make adjustments on costs. A local supermarket is allowing the group to sell its cookies outside the store, but requires the group to pay $1 for each box it sells. The group has already sold 300 boxes. It is going to purchase 100 more boxes, but is considering lowering its price from $10 to $8 to sell them. Because 300 boxes have already been sold, the relevant revenue is $8 × 100, or $800. What is the relevant cost? The $300 paid to the supermarket for the first 300 boxes is a sunk cost. A sunk cost is a cost that will not change if the decision is implemented. Sunk costs are never relevant to any decision. In this case, the relevant costs are equal to $400: each of the 100 additional boxes cost the group $3. In addition, the group must pay the supermarket $100 for the additional unit sales ($1/box multiplied by 100 boxes). If the group lowers its price, its net income will increase by $400. This result is seen in Table 2.3.

Let’s make another change to the scenario. This time, the group preorders 400 boxes in the belief it can sell them for $10 each. Once ordered, the boxes cannot be returned for a refund. Unit sales are slower than anticipated. The group sees that it will sell no more than 300 boxes unless it lowers its price to $8. Should the price be lowered? Our assumption is that 300 boxes have already been sold for $10. The relevant revenues will be equal to the additional revenues generated by the extra 100 boxes, or $800. What are the relevant costs? Under the arrangement with the supermarket, the group will have to pay $1/box or an additional $100. What about the cost of the boxes? Indeed, the group paid $3 for each of the 400 boxes. However, because the boxes cannot be returned for a refund, this cost is now a sunk cost and not relevant to the decision. Thus, the relevant cost is $100. If the group lowers its price to $8 to sell the additional 100 boxes, its net income will increase by $700.

If this seems confusing, let’s examine the overall ramifications. If the price remains at $10, the group will sell 300 boxes and generate $3,000 in revenue. The costs will consist of the $1,200 paid for the boxes ($3 × 400) and also $300 paid to the supermarket ($1 × 300) for a total of $1,500. The fundraiser will generate net income equal to $1,500. Suppose the group lowers its price to $8 to sell the additional 100 boxes (keep in mind that 300 boxes have already been sold for $10), its revenues will total $3,800. The group’s costs will equal $1,600 ($4 × 400). Net income will rise to $2,200, an increase of $700, as shown in Table 2.4.

Let’s take this last example and give it another twist. The fundraiser is nearly over. The group realizes it ordered too many boxes of cookies and is considering lowering its price to sell them. What is the lowest price the group should charge? At first glance, one might assume the breakeven price is $4. After all, the group paid $3/box and each additional box sold requires a $1 payment to the supermarket. So the group will lose money on each box sold for less than $4. But this is where the importance of sunk costs comes into play. The group prepaid for 400 boxes and cannot return any unsold boxes for a full or partial refund. Although the decision to order 400 boxes may be one they regret, the cost of the 400 boxes is not relevant to any subsequent decision. The only additional cost the group will bear by selling more boxes is the $1/box paid to the supermarket. This means the group should be willing to lower its price to no less than $1.

How could this be? Doesn’t this imply the group will be selling the additional boxes below cost? Table 2.5 illustrates the results. The first 300 boxes were sold for $10/box. Because the group did not want to leave with unsold boxes, it drops the price to $1.50/box for the remaining 100 boxes. Because the relevant cost of the last 100 boxes is $1/box, the group increases its net income by $50 when it lowered the price of the remaining boxes to $1.50.

It is critical to note that relevant cost cannot be determined a priori. Rather, relevance is defined by the decision. In the last example, we decided that the $3/box cost of the cookies was a sunk cost and, therefore, irrelevant. This is why it made sense for the group to lower the price to $1.50 to dump the remaining boxes. Suppose the group had only ordered 300 boxes. Once the fundraiser got under way, the group believed it could sell more. Assume the supplier is local, allowing the group to purchase additional cookies to sell. If the group were to consider purchasing 100 additional boxes, what is the lowest price it should consider charging? Note that in this case, the $3/box cost is no longer sunk. It represents a relevant cost associated with selling 100 more boxes. Coupled with the $1/box payment to the supermarket, if the group wishes to purchase 100 more boxes, it must be willing to charge a price no less than $4 to make the effort worthwhile. This is shown in Table 2.6. Let’s assume the additional boxes are sold for $5 each. The increase in profit is simply the difference between the relevant revenues ($5/box multiplied by 100 additional boxes) and the relevant costs ($4/box multiplied by 100 additional boxes). The critical notion is that a cost is sunk only if it cannot be changed by the decision under consideration; if the decision may cause it to change, the cost is relevant. As this example illustrates, a cost that was not considered relevant to one decision may be relevant to another.

Let’s make another change in the analysis. We will return to the assumption that 400 boxes were preordered and cannot be returned for a partial refund. Moreover, rather than pay $1/box, the supermarket charges a flat fee of $400. If the group wishes to lower the price to dump the remaining 100 boxes, what is the lowest price it should entertain?

Although the flat fee ($400) divided by 400 boxes is still $1, the breakeven price is no longer $1. In this instance, the entire fee becomes a sunk cost. The group will pay $400 to the supermarket regardless of whether it sells 300 boxes or 400 boxes. The $3 cost per box is also a sunk cost because unsold boxes cannot be returned for a refund. This implies that the group could lower the price to $0 without being worse off. We can illustrate this in Table 2.7. We will assume the first 300 boxes were sold for $10/box and the remaining 100 boxes were sold for 1¢ each.

As the table indicates, if the firm does not lower its price for the remaining boxes, it will generate $3,000 in revenue. Selling the remaining 100 boxes at $.01/box generates an additional $1 in revenue. Four hundred boxes were prepaid at a cost of $3/box. In addition, the group paid a flat fee of $400 for the right to hold its fundraiser on supermarket property. This implies the group bears costs of $1,600 regardless of how many boxes it sells. Lowering the price on the remaining 100 boxes does not force the group to incur any additional costs, so the relevant cost associated with the decision is $0. Thus, the decision adds $1 to the net income of the group.

Let’s try one more example that will bring us in focus with the theme of this book. The group has a treasurer who collects past expenses. The group will rely on her cost data to set prices. She gathered data from the previous year’s fundraiser. In that year, the group paid a flat fee of $200 to hold its fundraiser. The cost of each box was $3. Promotional and other miscellaneous expenses totaled $100. As the previous year’s fundraiser resulted in 300 boxes being sold, she reports the cost/box to be $4, as shown in Table 2.8. Based on her estimates, she advises selling the boxes for a price no less than $4/box.

Is the treasurer correct in her analysis? What is the relevant cost associated with selling one box of cookies? If none of these expenses have yet been incurred, then one might surmise that they are all relevant costs. That’s not quite correct. They are all relevant costs if the decision is whether to hold a fundraiser at all. In that case, the group’s relevant cost would be $300 + $3Q, where Q is the number of boxes sold. Because the revenue generated from sales is P × Q, the lowest feasible price for holding the fundraiser would be determined by setting total revenue equal to total cost and solving for the price. In other words,

Keep in mind that this equation does not determine what price the group should charge. Rather, it indicates the minimum price the group should charge if it wants to sell a given quantity of boxes and break even. For example, if the group wants to sell 100 boxes, it would need to be able to charge ($300 + $3 × 100)/100, or $6 to break even. If the group wishes to sell 400 boxes, it would have to sell the boxes at a price of at least ($300 + $3 × 400)/400, or $3.75 to break even.

It is important to note that the equation does not imply that the group can sell the desired quantity of boxes at that price; rather, it only indicates the minimum price necessary to generate enough money to cover its costs. Managers need to understand that breakeven pricing is not an indication of consumer demand. In this circumstance, the group would need to determine if selling 100 boxes at $6/box or 400 boxes at $3.75/box was feasible.

This can be illustrated with an exaggerated example. Suppose the group wanted to sell only two boxes. The minimum price necessary to hold the fundraiser would be ($300 + $3 × 2)/2, or $153. Clearly, the group cannot expect to be able to charge $153 for a box of cookies and expect to sell them.²

The group decides to go ahead with the fundraiser. At this point, the supermarket fee and the promotional expenses become sunk costs.³ They are no longer relevant to the pricing of a box of cookies. From this point forward, only the $3 cost/box is relevant to pricing decisions.

If the reader is still unconvinced, let’s make a change in the analysis. Suppose last year’s fundraiser took place in a pounding rain with 35 MPH winds. As a result, the group only sold ten boxes. If so, the average cost per box would be $33, as shown in Table 2.9.

Would you follow the treasurer’s advice to charge no less than $33/box for this year’s fundraiser? If we eliminate the irrelevant costs, we see that the only cost relevant to price setting is the $3 cost of each box.

There is another element in the analysis worth noting. The supermarket charged a flat fee of $200 for the previous year’s fundraiser, but is raising the fee to $400 this year. Is this cost relevant to the decision to hold the fundraiser? Of course, it is. The flat fee for last year’s fundraiser has no bearing on this year’s fundraiser. Historical costs have no bearing on decisions. Only expected future costs matter.

This has a great deal of importance to managers. Unit cost estimates are invariably based on historical costs. But decisions take place in the future. Only if past cost patterns continue will the unit cost data correctly reflect expected future costs.

We can examine balance sheets from the same perspective. In theory, the balance sheet reveals how much money will be left over if the firm sells off all of its assets and uses the funds to pay its liabilities. But is this necessarily the case? Most accountants report their assets in terms of their book value, not their current market value. They also rely on a depreciation method to infer the current depreciated value of the asset. Accountants generally acknowledge that many assets wear out over time, diminishing their salvage value, but the rate at which they wear out is unknown. Consequently, accountants depreciate their assets according to one of many conventionally accepted methods. But the depreciation expense is only an estimate of the rate at which the assets wear out. Thus, the value of the asset, calculated as its book value less accumulate depreciation may be an inaccurate reflection of its true salvage value.

Many accountants have taken to mark-to-market accounting to better reflect the assets’ (or liabilities’) current value. Unfortunately, because the current market value of an asset could not always be objectively determined, this technique opened up the potential for accounting fraud, such as that revealed in the Enron scandal. In its original business model, the Enron relied on actual expenses incurred and actual revenues received. When mark-to-market accounting was implemented in its trading business, the present value of inflows from long-term contracts was recognized as revenues and the present value of expected future costs was expensed. Of course, one might expect the present value of future inflows to be rather speculative. As an example, Enron signed a 20-year deal with Blockbuster to provide video on demand to various markets. Pilot projects were set up in Portland, Seattle, and Salt Lake City. Based on the results of the pilot projects, Enron logged profits of $110 million even though there were questions about its viability and market demand.⁴

Our examples showed that determining relevant revenues and costs requires a bit of thought. Let’s break it down into its pieces. First, we need to distinguish between fixed costs and variable costs. Fixed costs are expenses that do not vary with output. Examples include the group’s promotional expenses or the flat fee that it might have paid the supermarket. We can also break fixed costs into two subcategories. Avoidable fixed costs are fixed expenses that are incurred only if the decision is implemented. Unavoidable fixed costs are fixed costs that remain unchanged if the decision is implemented. Unavoidable fixed costs are, by definition, sunk costs, and are not relevant to decisions.

It is important to note that categorizing an expense as avoidable or unavoidable cannot be done a priori. Rather, the decision defines the expense. For example, if the group is trying to determine whether to hold the fundraiser, the promotional expenses are avoidable fixed costs. If the fundraiser is held, the group will incur this expense; if the fundraiser is not held, there are no promotional expenses. Avoidable fixed costs are relevant costs. Once the group goes ahead with the fundraiser, the promotional expense becomes an unavoidable fixed cost. The group has committed to the expense and cannot recover it. Therefore, it is not relevant to any subsequent decision.⁵

Variable costs are expenses that vary with production. Each box of cookies cost the group $3. Consequently, the more boxes they wanted to sell, the higher the cost. Because most decisions involve changes in production, variable costs are usually relevant costs.

Categorizing avoidable fixed costs, unavoidable fixed costs, and variable costs allows us to understand relevant costs. Avoidable fixed costs are always relevant costs because they change if the decision is implemented. Unavoidable fixed costs are never relevant costs because they are sunk. Variable costs are relevant costs in most circumstances because the majority of decisions entail changes in production or the unit costs associated with production. An example of where variable costs are not relevant is when the firm wants to shift production from one facility to another because the lease offers more favorable terms. If unit costs are not going to be different and the firm does not expect to change production levels, the difference in the terms of the lease is the only relevant cost.

If we apply these definitions to the fundraiser examples, we can see why some costs were categorized as relevant and why others were not. When deciding whether to lower the price from $10 to $8, the $3/box cost was relevant because it was a variable that would rise with each additional box sold. When 400 boxes were prepurchased, the expenditure became an unavoidable fixed cost because the group had expended $1,200, and that cost would not change regardless of how many boxes went unsold. Similarly, the $1/box payment was a variable cost that would be relevant to the pricing decision. The flat fee to be paid to the supermarket would be an avoidable fixed cost if the group is considering whether to hold a fundraiser, but it would be an unavoidable fixed cost when it comes to pricing decisions.

Summary