Corporate finance is about how firms make financial decisions. Those decisions fall into three categories, and understanding what they are is the first step to understanding how the rest of this course fits together.
Capital budgeting is deciding what long-term investments to make. Should a firm build a new factory? Launch a product? Acquire a competitor? The core challenge is always the same: does the expected future payoff justify the upfront cost? This question sounds simple but answering it well requires tools for comparing dollars received at different points in time — which is exactly what we'll start building in the second half of this week. We'll return to capital budgeting formally in Weeks 6 and 7 when we study net present value.
Capital structure is deciding how to pay for those investments. A firm can use retained earnings (profits it already has), borrow money (bank loans, bonds), or sell ownership stakes (issuing stock). Each source has different costs and implications. Debt requires fixed payments regardless of how the business performs — miss those payments and the firm can end up in bankruptcy. Equity doesn't require fixed payments, but issuing new shares dilutes existing shareholders' ownership. The tradeoff between debt and equity is one of the central questions in finance. We'll quantify the cost of each funding source when we calculate the weighted average cost of capital in Weeks 9 and 10.
Working capital management is managing the firm's short-term assets and liabilities — cash on hand, inventory, accounts receivable (money customers owe the firm), and accounts payable (money the firm owes suppliers). The goal is to ensure the firm can meet its short-term obligations while not tying up excess cash unproductively. A firm can be profitable on paper and still fail if it runs out of cash to pay its bills this month.
If you're the financial manager, what are you actually trying to accomplish? The answer used in finance is shareholder wealth maximization — making decisions that increase the market value of the firm's stock.
You might wonder: why not maximize profit? The problem is that "profit" as an accounting concept is ambiguous in two critical ways.
First, timing matters. A project that earns $1 million in profit spread over the next 20 years is not the same as one that earns $1 million next year. Accounting profit doesn't distinguish between the two. But investors care deeply about when they receive cash, because cash received sooner can be reinvested. Stock prices reflect the timing of expected cash flows; accounting profit does not.
Second, risk matters. A guaranteed $1 million is more valuable than a 50/50 chance at $2 million or nothing, even though the "expected profit" is identical in both cases. Investors are generally risk-averse — they prefer certainty. Stock prices reflect this by discounting risky cash flows more heavily. Accounting profit doesn't adjust for risk at all.
Because stock prices incorporate both the timing and riskiness of future cash flows, maximizing stock price is a more complete objective than maximizing accounting profit. This doesn't mean managers should manipulate stock prices in the short run — it means they should make decisions that genuinely increase the long-run value of the firm to its owners.
The organizational form a business takes determines who makes decisions, who bears liability for the firm's debts, how the firm is taxed, and how easily it can raise capital. There are three main forms, and the tradeoffs between them matter.
A sole proprietorship is owned by a single individual. It's the easiest form to establish — in many cases you just start doing business. The owner has complete control and keeps all the profits. But there are two significant drawbacks. First, the owner has unlimited personal liability: if the business can't pay its debts, creditors can go after the owner's personal assets (house, savings, car). Second, the firm's ability to raise capital is limited to the owner's personal wealth and borrowing capacity. It's hard to grow a sole proprietorship beyond a certain scale.
A partnership has two or more owners. General partners share management responsibility and unlimited liability. A limited partnership adds partners whose liability is capped at their investment, but those limited partners typically can't participate in day-to-day management. Partnerships can pool more capital than a sole proprietorship, but transferring ownership is difficult (you generally can't sell your partnership interest without the other partners' consent), and the unlimited liability problem persists for general partners.
A corporation is a separate legal entity from its owners. This separation is the key feature. Limited liability means shareholders can lose their investment but creditors cannot seize their personal assets. Corporations can raise very large amounts of capital by issuing stock to the public. Ownership is easily transferable — shares trade on exchanges without disrupting the business. The primary disadvantage is double taxation: the corporation pays income tax on its profits, and shareholders pay income tax again on any dividends they receive. There is also significantly more regulatory overhead — reporting requirements, board governance rules, and compliance costs.
In a sole proprietorship, the owner is the manager. Interests are perfectly aligned. But in a corporation, the owners (shareholders) hire managers to run the firm on their behalf. This creates a principal-agent relationship: shareholders are the principals, managers are the agents. The risk is that agents may pursue their own interests at the expense of principals.
What does this look like in practice? Managers might overspend on perks (lavish offices, corporate jets), pursue acquisitions that grow their personal empire rather than create shareholder value, or avoid risky but high-value projects because failure might cost them their job. These are all manifestations of the agency problem.
Several mechanisms exist to align managers' interests with shareholders':
Compensation design — Tying a significant portion of executive pay to stock price performance through stock options, restricted stock grants, or performance bonuses. If the manager's personal wealth rises and falls with the stock price, they have a direct financial incentive to maximize it.
Board of directors — The board is elected by shareholders to monitor management. An effective board hires and fires the CEO, approves major strategic decisions, and sets executive compensation. The quality of board oversight varies enormously across firms.
The threat of takeover — If managers run the firm poorly and the stock price drops, the firm becomes an attractive acquisition target. A hostile acquirer can buy the undervalued shares, take control, and replace the management team. This threat alone can discipline managers even if a takeover never actually occurs.
The labor market for managers — Managers who develop reputations for destroying shareholder value will find it harder to land their next position. Career concerns can substitute for formal monitoring.
Here's a question: would you rather have $1,000 today or $1,000 one year from now? The answer is today — and you don't even need to think about it. This intuition is the foundation of everything we'll do for the rest of this course.
A dollar today is worth more than a dollar in the future for three reasons. First, you could invest today's dollar and earn a return on it, so by next year you'd have more than a dollar. Second, inflation erodes purchasing power — the dollar will likely buy less next year. Third, the future is uncertain — there's always a chance the promised future dollar won't materialize.
Even if we set aside inflation and risk and focus purely on the investment opportunity, the logic holds: money has a time dimension, and ignoring that dimension leads to bad decisions. The time value of money (TVM) is the framework for making that time dimension precise and quantitative. Every valuation model in this course — for bonds, stocks, projects, entire companies — is ultimately an application of TVM.
Suppose you deposit $100 in an account earning 10% per year. After one year, you have $110 — your original $100 plus $10 of interest. Nothing surprising yet.
But what happens in year two? You earn 10% on $110, not just on the original $100. That gives you $110 × 1.10 = $121. The extra dollar (compared to $120 you'd have with simple interest) is interest earned on the first year's $10 of interest. This is compounding: the process by which interest earns interest over time.
The amount your investment grows to after t periods is the future value (FV):
The expression (1 + r)t is called the future value interest factor. It tells you how many dollars you'll have in the future for each dollar invested today. For example, at r = 8% and t = 10, the factor is (1.08)10 = 2.1589. Each dollar invested today becomes $2.16 in ten years.
With simple interest, you earn interest only on the original principal — the interest itself never earns interest. The total after t years is just PV + (PV × r × t). With compound interest, each period's interest is added to the balance and earns interest in subsequent periods.
Over short horizons the difference is small. Over long horizons it becomes enormous, because compound growth is exponential while simple growth is linear.
Of all the variables in the future value formula, time has the most dramatic effect. This is because compounding is exponential — the growth curve bends upward, and the longer you're on that curve, the steeper it gets. This is the reason financial advisors constantly emphasize starting to save early. The difference between starting at 22 and starting at 32 is not just 10 years of contributions — it's 10 years of compounding on everything that came before.
A $5,000 investment became over $200,000 — and you never added another dime. Note that the interest rate matters enormously over long horizons too. We'll see shortly that doubling the rate more than doubles the ending balance, because the exponential effect amplifies the rate difference over time. We'll return to retirement planning with much more powerful tools (annuities) in Week 2, where we can model regular contributions over a career.
The interest rate is in the exponent of the future value formula, which means small changes in the rate produce large changes in the outcome — especially over long horizons. This is worth seeing concretely.
Future value answers "what will my money grow to?" Now flip the question: if you need a specific amount in the future, how much do you need to invest today to get there? This is the present value (PV) question.
The process of translating future dollars into today's dollars is called discounting. It's compounding in reverse. Instead of multiplying by (1 + r)t, you divide by it:
The discount rate (r) in a present value calculation represents the opportunity cost of capital — the return you could earn on an alternative investment of similar risk. A higher discount rate means future cash flows are worth less today. This makes intuitive sense: if you have excellent investment opportunities available right now, a promise of money in the future is less attractive because you're giving up more by waiting.
Here's a useful check: present value and future value undo each other. If Red Acre invests $13,611.66 at 8% for 5 years, it should grow to exactly $20,000: $13,611.66 × (1.08)5 = $20,000.00. Whenever you calculate a present value, you can verify it by compounding back to the future value.
The higher the discount rate, the lower the present value. This is one of the most important relationships in finance, and it will appear again and again — in bond pricing (Week 3), stock valuation (Week 4), and project evaluation (Weeks 6–7).
Notice how sensitive present value is to the discount rate. The same $50,000 future payment is worth $30,696 or $12,359 depending on the rate — a $18,000 difference. When we get to bond and stock valuation, interest rate changes will drive price changes through exactly this mechanism.
So far we've used the TVM formula to find future values and present values, treating r as a known input. But sometimes you know the beginning value, the ending value, and the time, and you want to find the implied rate of return. This is common in investment analysis: you bought something, you sold it later for more, and you want to know what annual return you earned.
Rearranging FV = PV × (1 + r)t to isolate r:
The quantity FV ÷ PV tells you the total multiple on your investment. The t-th root converts that total multiple into a per-period rate. This is sometimes called the compound annual growth rate (CAGR) in investment contexts.
The final rearrangement: you know how much you have, how much you need, and what rate you can earn, but you want to know how long it will take. To solve for t, you need logarithms. Starting from FV = PV × (1 + r)t:
A useful shortcut: to estimate how long it takes for an investment to double, divide 72 by the interest rate (expressed as a whole number). This is the Rule of 72.
At 6%, money doubles in approximately 72 ÷ 6 = 12 years. The exact answer (using our formula) is ln(2) ÷ ln(1.06) = 11.90 years — the rule is remarkably accurate. At 9%, money doubles in about 72 ÷ 9 = 8 years (exact: 8.04 years). The Rule of 72 is a quick mental check — useful for back-of-the-envelope calculations and for catching errors in more detailed work.
| Future Value | FV = PV × (1 + r)t |
| Present Value | PV = FV ÷ (1 + r)t |
| Solving for Rate | r = (FV ÷ PV)1/t − 1 |
| Solving for Time | t = ln(FV ÷ PV) ÷ ln(1 + r) |
| Rule of 72 | Doubling time ≈ 72 ÷ r (where r is in %) |
You invest $12,000 today in an account earning 8% per year. (a) What is the balance after 10 years? (b) What is the balance after 30 years? (c) How much of the 30-year balance is attributable to compounding (interest earned on interest) versus simple interest?
You will receive $1,000 in 15 years. What is the present value of this payment if the discount rate is (a) 6%? (b) 3%? (c) In a sentence or two, explain why the present value is higher when the discount rate is lower.
Your parents want to set aside money today to help pay for college. They estimate they'll need $100,000 in 18 years. If they can earn 7% per year, how much do they need to invest now?
A vintage guitar was purchased for $4,500 and sold 8 years later for $7,200. What compound annual rate of return did the guitar earn?
Green Acre Industries is offered two payment options for a piece of land it is selling: $8,000 today, or $13,000 in 5 years. The company's investments typically earn 9% per year. Which option should Green Acre choose? Show your work.
The CEO of Red Acre Industries is evaluating two projects. Project A generates $500,000 in profit over 2 years. Project B generates $500,000 in profit over 5 years. The CEO argues they're equally valuable because total profit is the same. (a) Explain why this reasoning is flawed from the perspective of shareholder wealth maximization. (b) If the CEO prefers Project B because it ensures her job security for 5 years rather than 2, what kind of problem does this illustrate, and what mechanisms might the board use to address it?