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[latex]\begin{array}{l}\text{Budget}={P}_{1}\times{Q}_{1}+{P}_{2}\times{Q}_{2}\\\text{Budget}=\$10\\\,\,\,\,\,\,\,\,\,\,\,\,{P}_{1}=\$2\left(\text{the price of a burger}\right)\\\,\,\,\,\,\,\,\,\,\,\,\,{Q}_{1}=\text{quantity of burgers}\left(\text{variable}\right)\\\,\,\,\,\,\,\,\,\,\,\,\,{P}_{2}=\$0.50\left(\text{the price of a bus ticket}\right)\\\,\,\,\,\,\,\,\,\,\,\,\,{Q}_{2}=\text{quantity of tickets}\left(\text{variable}\right)\end{array}[/latex] For Charlie, this is [latex]{\$10}={\$2}\times{Q}_{1}+{\$0.50}\times{Q}_{2}[/latex] Step 3. Simplify the equation. At this point we need to decide whether to solve for [latex]{Q}_{1} [/latex] or [latex]{Q}_{2} [/latex]. Remember, [latex]{Q}_{1} = \text{quantity of burgers} [/latex]. So, in this equation [latex]{Q}_{1} [/latex] represents the number of burgers Charlie can buy depending on how many bus tickets he wants to purchase in a given week. [latex]{Q}_{2}=\text{quantity of tickets} [/latex]. So, [latex]{Q}_{2} [/latex] represents the number of bus tickets Charlie can buy depending on how many burgers he wants to purchase in a given week. We are going solve for [latex]{Q}_{1} [/latex]. [latex]\begin{array}{l}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10=2Q_{1}+0.50Q_{2}\\\,\,\,10-2Q_{1}=0.50Q_{2}\\\,\,\,\,\,\,\,\,\,\,\,\,-2Q_{1}=-10+0.50Q_{2}\\\left(2\right)\left(-2Q_{1}\right)=\left(2\right)-10+\left(2\right)0.50Q_{2}\,\,\,\,\,\,\,\,\,\text{Clear decimal by multiplying everything by 2}\\\,\,\,\,\,\,\,\,\,\,\,\,-4Q_{1}=-20+Q_{2}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,Q_{1}=5-\frac{1}{4}Q_{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{Divide both sides by}-4\end{array}[/latex] Step 4. Use the equation. Now we have an equation that helps us calculate the number of burgers Charlie can buy depending on how many bus tickets he wants to purchase in a given week. For example, say he wants 8 bus tickets in a given week. [latex]{Q}_{2}[/latex] represents the number of bus tickets Charlie buys, so we plug in 8 for [latex]{Q}_{2}[/latex], which gives us [latex]\begin{array}{l}{Q}_{1}={5}-\left(\frac{1}{4}\right)8\\{Q}_{1}={5}-2\\{Q}_{1}=3\end{array}[/latex] This means Charlie can buy 3 burgers that week (point C on the graph, above). Let’s try one more. Say Charlie has a week when he walks everywhere he goes so that he can splurge on burgers. He buys 0 bus tickets that week. [latex]{Q}_{2}[/latex] represents the number of bus tickets Charlie buys, so we plug in 0 for [latex]{Q}_{2}[/latex], giving us [latex]\begin{array}{l}{Q}_{1}={5}-(\frac{1}{4})0\\{Q}_{1}={5}\end{array}[/latex] So, if Charlie doesn’t ride the bus, he can buy 5 burgers that week (point A on the graph). If you plug other numbers of bus tickets into the equation, you get the results shown in Table 1, below, which are the points on Charlie’s budget constraint.
Step 5. Graph the results. If we plot each point on a graph, we can see a line that shows us the number of burgers Charlie can buy depending on how many bus tickets he wants to purchase in a given week.  Figure 2. Charlie’s Budget Constraint. We can make two important observations about this graph. First, the slope of the line is negative (the line slopes downward from left to right). Remember in the last module when we discussed graphing, we noted that when when X and Y have a negative, or inverse, relationship, X and Y move in opposite directions—that is, as one rises, the other falls. This means that the only way to get more of one good is to give up some of the other. Second, the slope is defined as the change in the number of burgers (shown on the vertical axis) Charlie can buy for every incremental change in the number of tickets (shown on the horizontal axis) he buys. If he buys one less burger, he can buy four more bus tickets. The slope of a budget constraint always shows the opportunity cost of the good that is on the horizontal axis. If Charlie has to give up lots of burgers to buy just one bus ticket, then the slope will be steeper, because the opportunity cost is greater. This is easy to see while looking at the graph, but opportunity cost can also be calculated simply by dividing the cost of what is given up by what is gained. For example, the opportunity cost of the burger is the cost of the burger divided by the cost of the bus ticket, or [latex]\frac{$2.00}{$0.50}=4[/latex] [latex]\frac{$0.50}{$2.00}=0.25[/latex]
Opportunity costs represent the potential benefits that an individual, investor, or business misses out on when choosing one alternative over another. Because opportunity costs are unseen by definition, they can be easily overlooked. Understanding the potential missed opportunities when a business or individual chooses one investment over another allows for better decision making.
Opportunity Cost = FO − CO where: FO = Return on best forgone option CO = Return on chosen option \begin{aligned}&\text{Opportunity Cost}=\text{FO}-\text{CO} \\&\textbf{where:} \\&\text{FO}=\text{Return on best forgone option} \\&\text{CO}=\text{Return on chosen option} \\\end{aligned} Opportunity Cost=FO−COwhere:FO=Return on best forgone optionCO=Return on chosen option The formula for calculating an opportunity cost is simply the difference between the expected returns of each option. Consider a company is faced with the following two mutually exclusive options: Option A: Invest excess capital in the stock market to potentially earn capital gains. Option B: Invest excess capital back into the business for new equipment to increase production efficiency. Assume the expected return on investment (ROI) in the stock market is 12% over the next year, and your company expects the equipment update to generate a 10% return over the same period. The opportunity cost of choosing the equipment over the stock market is 2% (12% - 10%). In other words, by investing in the business, the company would forgo the opportunity to earn a higher return.
While financial reports do not show opportunity costs, business owners often use the concept to make educated decisions when they have multiple options before them. Bottlenecks, for instance, often result in opportunity costs. Opportunity cost analysis plays a crucial role in determining a business’s capital structure. A firm incurs an expense in issuing both debt and equity capital to compensate lenders and shareholders for the risk of investment, yet each also carries an opportunity cost. Funds used to make payments on loans, for example, cannot be invested in stocks or bonds, which offer the potential for investment income. The company must decide if the expansion made by the leveraging power of debt will generate greater profits than it could make through investments. A firm tries to weigh the costs and benefits of issuing debt and stock, including both monetary and nonmonetary considerations, to arrive at an optimal balance that minimizes opportunity costs. Because opportunity cost is a forward-looking consideration, the actual rate of return (RoR) for both options is unknown today, making this evaluation tricky in practice. Assume that the company in the above example forgoes new equipment and instead invests in the stock market. If the selected securities decrease in value, the company could end up losing money rather than enjoying the expected 12% return. For the sake of simplicity, assume that the investment yields a return of 0%, meaning the company gets out exactly what is put in. The opportunity cost of choosing this option is 10% to 0%, or 10%. It is equally possible that, had the company chosen new equipment, there would be no effect on production efficiency, and profits would remain stable. The opportunity cost of choosing this option is then 12% rather than the expected 2%. It is important to compare investment options that have a similar risk. Comparing a Treasury bill, which is virtually risk free, to investment in a highly volatile stock can cause a misleading calculation. Both options may have expected returns of 5%, but the U.S. government backs the RoR of the T-bill, while there is no such guarantee in the stock market. While the opportunity cost of either option is 0%, the T-bill is the safer bet when you consider the relative risk of each investment. When assessing the potential profitability of various investments, businesses look for the option that is likely to yield the greatest return. Often, they can determine this by looking at the expected RoR for an investment vehicle. However, businesses must also consider the opportunity cost of each alternative option. Assume that, given $20,000 of available funds, a business must choose between investing funds in securities or using it to purchase new machinery. No matter which option the business chooses, the potential profit that it gives up by not investing in the other option is the opportunity cost. If the business goes with the first option, at the end of the first year, its investment will be worth $22,000. The formula to calculate RoR is [(Current Value - Initial Value) ÷ Current Value] × 100. In this example, [($22,000 - $20,000) ÷ $20,000] × 100 = 10%, so the RoR on the investment is 10%. For the purposes of this example, let’s assume it would net 10% every year after as well. At a 10% RoR, with compounding interest, the investment will increase by $2,000 in year 1, $2,200 in year two, and $2,420 in year three. Alternatively, if the business purchases a new machine, it will be able to increase its production of widgets. The machine setup and employee training will be intensive, and the new machine will not be up to maximum efficiency for the first couple of years. Let’s assume it would net the company an additional $500 in profits in the first year, after accounting for the additional expenses for training. The business will net $2,000 in year two and $5,000 in all future years. Since the company has limited funds to invest in either option, it must make a choice. According to this, the opportunity cost for choosing the securities makes sense in the first and second years. However, by the third year, an analysis of the opportunity cost indicates that the new machine is the better option ($500 + $2,000 + $5,000 - $2,000 - $2,200 - $2,420) = $880.
One of the most famous examples of opportunity cost is a 2010 exchange of Bitcoin for pizza. The opportunity cost of exchanging the 10,000 bitcoins for two large pizzas peaked at almost $700 million based on Bitcoin's 2022 all-time high price. A sunk cost is money already spent in the past, while opportunity cost is the potential returns not earned in the future on an investment because the capital was invested elsewhere. When considering opportunity cost, any sunk costs previously incurred are ignored unless there are specific variable outcomes related to those funds. Buying 1,000 shares of company A at $10 a share, for instance, represents a sunk cost of $10,000. This is the amount of money paid out to invest, and getting that money back requires liquidating stock. The opportunity cost instead asks where that $10,000 could have been put to better use. From an accounting perspective, a sunk cost also could refer to the initial outlay to purchase an expensive piece of heavy equipment, which might be amortized over time, but which is sunk in the sense that you won’t be getting it back. An opportunity cost would be to consider the forgone returns possibly earned elsewhere when you buy a piece of heavy equipment with an expected ROI of 5% vs. one with an ROI of 4%. Again, an opportunity cost describes the returns that one could have earned if the money were instead invested in another instrument. Thus, while 1,000 shares in company A eventually might sell for $12 a share, netting a profit of $2,000, company B increased in value from $10 a share to $15 during the same period. In this scenario, investing $10,000 in company A returned $2,000, while the same amount invested in company B would have returned a larger $5,000. The $3,000 difference is the opportunity cost of choosing company A over company B. As an investor who has already put money into investments, you might find another investment that promises greater returns. The opportunity cost of holding the underperforming asset may rise to the point where the rational investment option is to sell and invest in the more promising investment. In economics, risk describes the possibility that an investment’s actual and projected returns are different and that the investor loses some or all of the principal. Opportunity cost concerns the possibility that the returns of a chosen investment are lower than the returns of a forgone investment. The key difference is that risk compares the actual performance of an investment against the projected performance of the same investment, while opportunity cost compares the actual performance of an investment against the actual performance of another investment. Still, one could consider opportunity costs when deciding between two risk profiles. If investment A is risky but has an ROI of 25%, while investment B is far less risky but only has an ROI of 5%, even though investment A may succeed, it may not. If it fails, then the opportunity cost of going with option B will be salient. Therefore, decision-makers rely on much more information than just looking at just opportunity cost dollar amounts when comparing options.
In 1962, a little known band called The Beatles auditioned for Decca Records. The label decided against signing the band. This decision would have been made because the opportunity cost to sign them did not outweigh the opportunity cost to pass on them. Opportunity cost is used to calculate different types of company profit. The most common type of profit analysts are familiar with is accounting profit. Accounting profit is the net income calculation often stipulated by Generally Accepted Accounting Principles (GAAP). Only explicit, real costs are subtracted from total revenue. Companies or analysts can future manipulate accounting profit to arrive at an economic profit. The difference between the calculation of the two is economic profit includes opportunity cost as an expense. This theoretical calculation can then be used to compare the actual profit of the company to what the theoretical profit would have been. Economic profit (and any other calculation above that considers opportunity cost) is strictly an internal value used for strategic decision-making. There are no regulatory bodies that govern public reporting of economic profit or opportunity cost. Whereas accounting profit is heavily dictated by reporting rules and frameworks, economic profit factors in vague assumptions and estimates from management that do not have IRS, SEC, or FASB oversight. Before making big decisions like buying a home or starting a business, you probably will scrupulously research the pros and cons of your financial decision, but most day-to-day choices aren’t made with a full understanding of the potential opportunity costs. When feeling cautious about a purchase, for instance, many people will check the balance of their savings account before spending money. But they often won’t think about the things that they must give up when they make that spending decision. The problem comes up when you never look at what else you could do with your money or buy things without considering the lost opportunities. Having takeout for lunch occasionally can be a wise decision, especially if it gets you out of the office for a much-needed break. However, buying one cheeseburger every day for the next 25 years could lead to several missed opportunities. Aside from the missed opportunity for better health, spending that $4.50 on a burger could add up to just over $52,000 in that time frame, assuming a very achievable 5% RoR. This is a simple example, but the core message holds for a variety of situations. It may sound like overkill to think about opportunity costs every time you want to buy a candy bar or go on vacation. But opportunity costs are everywhere and occur with every decision made, big or small.
Opportunity cost is often overlooked by investors. In essence, it refers to the hidden cost associated with not taking an alternative course of action. If, for example, a company pursues a particular business strategy without first considering the merits of alternative strategies available to them, they might fail to appreciate their opportunity costs and the possibility that they could have done even better had they chosen another path.
Opportunity cost does not show up directly on a company’s financial statements. Economically speaking, though, opportunity costs are still very real. Yet because opportunity cost is a relatively abstract concept, many companies, executives, and investors fail to account for it in their everyday decision making.
Consider the case of an investor who, at age 18, was encouraged by their parents to always put 100% of their disposable income into bonds. Over the next 50 years, this investor dutifully invested $5,000 per year in bonds, achieving an average annual return of 2.50% and retiring with a portfolio worth nearly $500,000. Although this result might seem impressive, it is less so when one considers the investor’s opportunity cost. If, for example, they had instead invested half of their money in the stock market and received an average blended return of 5%, then their retirement portfolio would have been worth more than $1 million.
The downside of opportunity cost is it is heavily reliant on estimates and assumptions. There's no way of knowing exactly how a different course of action may have played out financially. Therefore, to determine opportunity cost, a company or investor must project the outcome and forecast the financial impact. This includes projecting sales numbers, market penetration, customer demographics, manufacturing costs, customer returns, and seasonality. This complex situation pinpoints the reason why opportunity cost exists. It may not be immediately clear to a company the best course of action; however, after retrospectively assessing the variables above, they may further understand how one option would have been better than the other and they have incurred a "loss" due to opportunity cost. |
How to calculate opportunity cost from one point to another
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