Chapter 2: Marginal and Investment Analysis#

Every manager faces two types of decisions every day. Some are about tiny adjustments—should we make one more cup of lemonade? Others are big, one-time choices—should we buy that new delivery truck? This chapter gives you the tools to think clearly about both, and then shows you how to value anything that pays off over time.

The Big Picture#

Imagine you run a small bakery. You can tweak the number of cookies you bake, or you might decide whether to open a whole second shop. The first kind of choice is about the margin—how much extra benefit you get from one more unit. The second is a jump to a whole new setup. Both hinge on comparing extra benefits and extra costs. When the payoffs stretch into the future, you also need to respect a simple truth: a dollar today is worth more than a dollar tomorrow. This chapter builds a complete mental toolkit for making those comparisons. With it, you can decide “yes or no,” “how much,” and “is it worth it over time” with confidence.

Marginal Analysis: The MB = MC Rule#

Think about how you decide how long to spend mowing a lawn. You’ll keep going as long as the extra time makes the lawn noticeably better. At some point, another five minutes barely improves anything, but you’d rather stop and have a cold drink. That’s marginal thinking in everyday life.

In business, a marginal benefit (MB) is the extra revenue or benefit you get from one more unit. The marginal cost (MC) is the extra cost of producing that unit. The basic rule is simple:

MB = MC Rule: Keep increasing the activity as long as marginal benefit is greater than marginal cost. Stop when they are equal. If MB is less than MC, you’ve gone too far and should reduce the activity.

Why does equality mark the right stopping point? When MB > MC, the next unit adds more benefit than it costs, so doing more increases total net gain. When MB < MC, the last unit cost more than it brought in, so you’ve actually lost ground. The best point—where net gain is highest—is exactly where MB = MC.

Let’s make it concrete. Suppose you run a taco stand. Each taco sells for $3.00, so the marginal benefit from selling one more is a steady $3.00, at least up to a point. The marginal cost, though, might rise. The first few tacos might cost you $1.50 each in ingredients and labour. But as you get busier, you have to pay workers overtime or they get slower, so the 50th taco might cost $2.80, and the 100th taco $3.20. You’d happily make the 50th taco (MB = $3.00 > MC = $2.80) but you’d avoid the 100th (MB = $3.00 < MC = $3.20). The best number is where the extra revenue from the last taco just equals the extra cost—around the point where MC rises to exactly $3.00. Maybe that’s 85 tacos.

We can also express this with simple math. Let be quantity. The total benefit from selling tacos is and total cost is . Marginal benefit is the change in total benefit when you change a little: . Marginal cost is . The rule says: set so that

In many real situations, marginal benefit falls as you produce more (maybe because you have to lower the price to sell extra units) and marginal cost rises. The logic stays the same: keep doing more while MB > MC, and stop right at the crossover.

A mental shortcut: if you are ever unsure whether to increase or decrease an activity, ask “Will the very next unit bring in more than it costs?” If yes, go ahead; if no, cut back. That’s all the rule is.

📝 Section Recap: Marginal analysis says to expand any activity as long as the extra benefit exceeds the extra cost, and to stop when MB = MC. This single rule tells a manager the profit‑maximising level of any continuous decision.

Incremental Analysis for Discrete Choices#

Not every choice is as simple as picking a number, like exactly how many tacos to make. Some choices are “all or nothing” or involve big, stepwise changes. For those, we use incremental analysis. This is a close cousin of marginal analysis, but it’s designed for jumps.

Incremental analysis asks: “If we take this step—say, launching a new product, adding a second shift, or buying a new machine—will the total change make us better off?” You compare total revenues and costs with and without the change. The difference is the incremental profit.

Incremental Decision Rule: If the incremental revenue minus incremental cost (including any opportunity costs) is positive, go ahead. If it’s negative, don’t.

Remember: ignore costs that you cannot change regardless of your decision. These are sunk costs—money already spent that cannot be recovered. For example, if you already paid for market research last month, that money is gone. Whether you launch the new product or not, you cannot get the research cash back. So it should not influence your go/no-go call. Only the future, avoidable costs matter.

Let’s work through a typical discrete decision. You own a pizza shop. You’re thinking about adding a delivery service. The new service will bring in extra sales of $2,000 a week. But you’ll need to hire a driver, buy a delivery car, and pay for extra insurance and fuel—total incremental cost of $1,500 a week. The incremental profit is $500 per week. That looks good. But you also have to consider any hidden costs: maybe you’ll lose some in-store customers because the kitchen is busier, which might reduce existing profit by $200 a week. Then the true incremental cost is $1,700, and the net gain shrinks to $300. Still positive, so you would adopt the service. If the net gain turned negative, you’d reject it.

Notice that we never included the money you spent three years ago on a delivery feasibility study. That’s sunk and irrelevant.

Incremental analysis is incredibly practical because most business choices are discrete: open a new store, drop an old product line, accept a special one-time order. The logic always boils down to: “Does this move, and only this move, add more to revenue than it adds to cost?” If yes, do it. If not, walk away.

📝 Section Recap: Incremental analysis guides yes/no decisions by comparing the extra revenue from a discrete change to the extra cost, ignoring sunk costs. The rule is simple: if incremental profit > 0, accept the change; if < 0, reject it.

Present Value and the Time Value of Money#

So far we’ve acted as if time doesn’t matter. But a dollar received today is worth more than a dollar received a year from now. Why? Because you could invest today’s dollar and earn interest, making it grow. If you let me borrow your money for a year, you lose that opportunity. Receiving cash sooner is better, and paying cash later is better (from the payer’s point of view). This idea is the time value of money.

The tool that makes future money comparable to today’s money is present value (PV). It answers: “How much would I have to put in the bank today, at a given interest rate, to end up with that future amount?”

To find the PV of a single future sum received in years, when the interest rate (also called the discount rate) is , we use:

The expression is called the discount factor. It is always less than 1 for any positive , so it shrinks future values down to their equivalent today‑value.

Let’s try a small example. Suppose your friend promises to give you $110 in exactly one year. You can earn 10% per year in a safe savings account. What is that promise worth to you today? You’d compare it with putting some amount in the bank today. In one year, that grows to . You want this to equal $110, so 100110 one year from now at 10% is exactly $100. If your friend offered to sell you the promise for $95, you’d buy it, because you’d be getting something worth $100 for only $95. If they asked $105, you’d say no—the promise is worth less than what you give up.

The same logic applies to any stream of cash over many years. We discount each future amount back to today separately and add them up. For years, the present value of a stream is:

Picking the right discount rate matters a lot. It should reflect the opportunity cost of capital—the return you give up by tying up money in this project rather than in the next best alternative of similar risk. For low-risk projects, might be a safe bond yield. For riskier ventures, you’d use a higher rate to reflect the extra uncertainty.

The further in the future a cash flow is, the more it gets shrunk by the discount factor. That’s why $100 promised 50 years from now is almost worthless at any reasonable interest rate. This sharp decline makes far-off promises much less valuable than near-term ones.

📝 Section Recap: A dollar received in the future is worth less than a dollar today because you could invest today and earn interest. Present value converts future cash to today’s money by discounting at the appropriate interest rate. Only by putting everything in present‑value terms can you fairly compare cash flows at different times.

Computing Net Present Value for Project Evaluation#

When we combine the idea of present value with incremental analysis, we get net present value (NPV). NPV is the single most important tool for evaluating projects, investments, and pretty much any decision with cash flows spread over time.

The recipe is straightforward. For a project, list all the cash inflows and outflows in each year, from today (year 0) to the end of the project. Then compute the present value of each year’s net cash flow—inflows minus outflows—using your chosen discount rate. Finally, sum all those present values. The result is the NPV.

NPV Decision Rule: If NPV > 0, the project adds value and should be accepted. If NPV < 0, it destroys value and should be rejected. If NPV = 0, you are indifferent—the project just earns exactly the required return.

Why does a positive NPV mean “go”? Because it shows that the project’s cash inflows are enough to cover all its costs and also deliver a return above your opportunity cost. In other words, you’d be better off taking the project than putting your money in the next best alternative.

Let’s walk through a realistic example. Suppose you’re considering buying a new espresso machine for your café. The machine costs $4,000 today. You expect it to boost your net cash inflows by $2,500 at the end of year 1 and another $2,500 at the end of year 2. After that, the machine wears out and has no scrap value. Your café’s discount rate is 8% per year (maybe that’s the interest rate you pay on a loan, or the return you could earn elsewhere). We compute NPV:

• Year 0 cash flow: -$4,000 (outflow today, no discounting needed).
• Year 1 cash flow: +$2,500. Its PV = 2,314.81$.
• Year 2 cash flow: +$2,500. Its PV = 2,143.35$.

Add them: 458.16458.16 of value in today’s money. You should buy it.

If the machine had cost $4,500 instead, NPV would be about -$41.84, saying “no”. This precision helps you avoid emotional decisions and focus purely on value creation.

Many real projects have more cash flows and a salvage value at the end. You just discount that final receipt too. The framework always works the same.

Watch out: a higher discount rate makes future cash worth less in PV, so projects with big early outflows and late inflows look less attractive. That’s sensible—if you can earn a high return elsewhere, you need a very compelling project to tie up your money for years. Always match the discount rate to the risk of the project; otherwise NPV can mislead you.

📝 Section Recap: Net present value is the sum of the present values of all incremental cash flows from a project. A positive NPV means the project increases wealth; a negative NPV means it destroys wealth. This rule works for any multi‑period decision, from machine purchases to marketing campaigns.

Valuing a Firm as the Present Value of Its Profit Stream#

Now step back and think about an entire business. At its core, a firm is just a collection of projects and activities that throw off profits over time. If we can value a project by discounting its future cash flows, we can value a whole firm the same way. The fundamental value of a firm is the present value of all the future net profits (or free cash flows) investors expect it to generate.

If we denote expected profit in year as and a suitable discount rate as , the firm’s value is:

In principle, this continues forever. This is the bedrock idea behind stock prices: a share of a firm is worth what you think the discounted stream of future earnings per share is worth.

For a business that is expected to earn a steady profit every year into the foreseeable future, the formula simplifies dramatically. A constant perpetual stream, or perpetuity, has a present value:

This is one of those simple but powerful formulas you’ll come back to constantly. For example, imagine a small software firm that is expected to generate annual profits of $200,000 with no growth, and the owners require a 10% return (discount rate). The firm’s value is:

Why does this make sense? Think of it as: if you had $2 million in the bank at 10%, you’d earn $200,000 a year in interest forever. Buying the firm for anything less than $2 million gives you a better deal than the bank, so its value is exactly $2 million.

What if profits are growing? Suppose profits start at and grow at a constant rate each year (with ). The value becomes that of a growing perpetuity:

A small growth rate can massively increase the value. If that software firm’s profits grow at 3% a year, 2,857,14385 per year in the first year seems tiny, but the fact that it compounds forever raises the value by over $850,000.

This valuation perspective connects directly to the NPV rule. Every project with a positive NPV increases the firm’s value by exactly that NPV amount. So when you accept a project with NPV of $458, you are adding $458 to the firm’s total worth. Managers who maximise the sum of positive‑NPV projects are implicitly maximising the value of the firm for its owners. That’s the ultimate benchmark for good decisions.

📝 Section Recap: A firm’s true worth is the present value of all its expected future profits, discounted at a rate that reflects risk. A constant profit stream is worth , and growing profits are worth . Any project with positive NPV directly increases the firm’s value.

Summary#

We’ve covered a lot of ground, but the ideas are connected: every smart business decision compares extra benefits with extra costs, either at the margin or for discrete jumps. When time is involved, we bring those future amounts back to today using discounting so we can compare apples to apples. The NPV rule then becomes a clear test for value creation, and it scales all the way up to pricing an entire company.

The following table captures the core concepts in a pocket guide you can refer back to.