Corporate Finance

Corporate finance is the study of how a company obtains money and puts it to work. Every firm, from a food truck to a global airline, faces the same three financial questions, and the person who answers them is the financial manager.

The three big questions

1. Capital budgeting - what long-term investments should the firm make? Should it build a new plant, launch a product, or buy a rival? These are the decisions that create value, and Module 6 is devoted to them.
2. Capital structure - how should the firm pay for those investments? What mix of debt (borrowed money) and equity (owners' money) should it use?
3. Working capital management - how should the firm handle its day-to-day cash, inventory, and short-term bills so it never runs dry?

The goal: maximize value

You might guess the goal of a business is to "maximize profit," but finance is more precise. The accepted goal of financial management is to maximize the current value of the owners' stake - for a public company, to maximize the current share price. Why not just profit? Because profit is slippery. It ignores three things that value captures: timing (a profit next decade is worth less than one this year), risk (a risky profit is worth less than a safe one), and cash (accounting profit can differ from the cash actually available). Maximizing value forces the manager to weigh all three.

Whose money is it? The agency problem

In a large corporation, the owners (the shareholders) are usually not the people running the company (the managers). Managers are hired agents of the owners, and their interests can diverge - a manager might prefer a bigger empire, a plush office, or a quiet life over the hard choices that lift the share price. This conflict is the agency problem, and the costs it creates are agency costs. Companies fight it with tools such as tying pay to the stock price, oversight by a board of directors, and the discipline of takeover threats.

Why finance is its own subject

Accounting, which you may have studied, looks backward and records what has already happened. Finance looks forward and asks what a stream of future cash flows is worth today, and whether a decision will add to that value. To do that, we need one master tool that lets us compare dollars arriving at different times. That tool is the time value of money, and it is the heart of this course.

Finance is forward-looking, but the raw material for its forecasts comes from a firm's financial statements. A financial manager must read them fluently. Three statements matter most.

• The balance sheet is a snapshot on one date of what the firm owns and owes. It obeys the identity Assets = Liabilities + Equity. Assets are listed roughly in order of liquidity (cash first); the right side shows how those assets were financed - by creditors or by owners.
• The income statement measures performance over a period: Revenues minus Expenses equals Net Income. Net income (the "bottom line") is the accountant's measure of profit.
• The statement of cash flows tracks the actual cash that moved in and out, split into operating, investing, and financing activities.

Profit is an opinion; cash is a fact

A finance manager cares about cash flow, not just net income, and the two are not the same. Net income includes non-cash charges such as depreciation (spreading an asset's cost over its life), and it records sales made on credit as revenue before the cash arrives. A rough but useful measure, operating cash flow, adds the non-cash depreciation back to profit:

Operating cash flow ≈ Net income + Depreciation

Suppose a firm reports net income of $120,000 after subtracting $30,000 of depreciation. No cash left the building for that depreciation, so cash generated by operations is closer to 120,000 + 30,000 = 150,000. A company can be profitable on paper yet run out of cash, which is why finance never loses sight of the cash statement.

Ratios: turning statements into judgments

Absolute dollars are hard to judge, so we use ratios that divide one figure by another. Three families recur throughout this course:

Ratio	Formula	Measures
Current ratio	Current assets / Current liabilities	Liquidity - can it pay bills soon?
Debt-to-equity	Total debt / Total equity	Leverage - how much borrowing?
Return on equity (ROE)	Net income / Total equity	Profitability per owner dollar
Profit margin	Net income / Sales	Profit kept per sales dollar

For a firm with current assets of $200,000 and current liabilities of $100,000, the current ratio is 200,000 / 100,000 = 2.0, meaning $2 of short-term assets back every $1 of short-term debt. If that same firm earned net income of $90,000 on equity of $600,000, its ROE is 90,000 / 600,000 = 0.15, or 15%. A ratio is only meaningful in context - compared with the firm's own past, a competitor, or an industry norm - but ratios are the vocabulary finance uses to describe a company's health.

Here is the idea the whole course turns on: a dollar today is worth more than a dollar received in the future. A dollar in hand can be invested to earn interest, so it grows; a dollar promised next year cannot. The rate at which money grows over time is the interest rate, often written r and also called the discount rate or the required return.

Compounding: earning interest on interest

Put $1,000 in an account paying 10% per year. After one year you have 1,000 × 1.10 = 1,100. In year two you earn 10% not just on the original 1,000 but on the whole 1,100, giving 1,100 × 1.10 = 1,210. That extra $10 - interest earned on last year's interest - is the magic of compounding. The general formula for the future value of a single sum is:

FV = PV × (1 + r)ⁿ

where PV is the present amount, r is the interest rate per period, and n is the number of periods.

Worked example

What will $1,000 grow to in 3 years at 8% per year? Apply the formula:

FV = 1,000 × (1.08)3 = 1,000 × 1.259712 = 1,259.71

The $1,000 becomes $1,259.71. Of the $259.71 of growth, $240 is simple interest (3 years × $80) and the extra $19.71 is interest earned on interest.

Simple vs. compound interest

Simple interest pays only on the original principal, so $1,000 at 8% simple for 3 years earns a flat 1,000 × 0.08 × 3 = 240, reaching $1,240. Compound interest reaches $1,259.71. Over long horizons the gap explodes.

The Rule of 72

A handy shortcut: money roughly doubles in 72 / r years, where r is the percentage rate. At 8%, that is about 72 / 8 = 9 years. Check it: 1,000 × (1.08)9 ≈ 1,999, almost exactly double. The Rule of 72 lets you gauge growth in your head.

Future value pushes money forward in time. Present value does the reverse: it pulls a future cash flow back to today, telling you what it is worth right now. This process is called discounting, and it is the workhorse of finance, because valuing anything - a project, a bond, a company - means discounting the cash it will produce.

The present value formula

Just rearrange the future-value formula to solve for PV:

PV = FV / (1 + r)ⁿ

The term 1 / (1 + r)n is the discount factor, always less than 1, which shrinks a future amount down to its worth today.

Worked example

How much must you invest today at 6% to have $5,000 in 4 years? Discount the $5,000 back:

PV = 5,000 / (1.06)4 = 5,000 / 1.262477 = 3,960.47

You need $3,960.47 today. Put another way, a promise of $5,000 in 4 years is worth only $3,960.47 to you now, if 6% is the return you could otherwise earn.

What moves present value

Two forces push present value down:

• A higher discount rate lowers PV. At 10% instead of 6%, that same $5,000 in 4 years is worth only 5,000 / (1.10)4 = 3,415.07. The more you could earn elsewhere, the less a fixed future sum is worth today.
• A longer wait lowers PV. The farther off the money, the more the discount factor shrinks it. $5,000 in 10 years at 6% is worth just 5,000 / (1.06)10 = 2,791.97.

Solving for rate or time

The same equation solves for a missing rate or horizon. If $3,960.47 grows to $5,000 in 4 years, the implied rate satisfies (1 + r)4 = 5,000 / 3,960.47 = 1.2625, so r = 1.26251/4 - 1 = 0.06, confirming 6%. This one relationship - four quantities (PV, FV, r, n) with any three giving the fourth - underlies almost every calculation in the rest of the course.

You know	You want	Use
PV, r, n	FV	FV = PV(1 + r)n
FV, r, n	PV	PV = FV / (1 + r)n
PV, FV, n	r	r = (FV/PV)1/n - 1

Many real cash flows are not one lump sum but a series of equal payments - a car loan, a mortgage, a pension, rent. A stream of equal payments made at equal intervals is an annuity. Rather than discount each payment separately, we use compact formulas.

Present value of an ordinary annuity

In an ordinary annuity, payments arrive at the end of each period. Its present value is:

PV = PMT × [ 1 - (1 + r)^-n ] / r

where PMT is the payment per period. Example: you will receive $2,000 at the end of each year for 5 years, and the discount rate is 7%. The present value is:

PV = 2,000 × [1 - (1.07)-5] / 0.07 = 2,000 × 4.100197 = 8,200.39

The five payments are worth $8,200.39 today - less than the $10,000 of raw dollars, because most of it arrives years from now.

Future value of an ordinary annuity

If instead you save $2,000 at the end of each year for 5 years at 7%, the accumulated future value is:

FV = PMT × [ (1 + r)ⁿ - 1 ] / r

FV = 2,000 × [(1.07)5 - 1] / 0.07 = 2,000 × 5.750739 = 11,501.48

Saving $10,000 in deposits grows to $11,501.48; the extra $1,501.48 is compound interest.

Annuity due: payments at the start

An annuity due pays at the beginning of each period, so every payment sits one period longer and earns one more period of interest. Just multiply the ordinary-annuity answer by (1 + r). The $2,000, 5-year, 7% stream as an annuity due is worth 8,200.39 × 1.07 = 8,774.42 today - more than the ordinary annuity, because the money arrives sooner.

Perpetuities: payments forever

A perpetuity pays a fixed amount every period forever. Remarkably, an infinite stream has a finite value:

PV = PMT / r

A perpetuity paying $100 a year when the discount rate is 5% is worth 100 / 0.05 = 2,000. If the payment grows at a constant rate g each year, it is a growing perpetuity worth PMT / (r - g). This growing-perpetuity formula returns in Module 4 to value a share of stock.

We can now value a whole investment. The method is discounted cash flow (DCF): forecast every cash flow a project will produce, discount each back to today, and add them up. Compared against what the project costs, this gives its net present value (NPV) - the single most important tool in capital budgeting.

The NPV formula

If a project costs CF0 today (a cash outflow, so a negative number) and returns cash flows CF1, CF2, ... CFn over its life, then at discount rate r:

NPV = CF₀ + CF₁/(1+r) + CF₂/(1+r)² + ... + CF_n/(1+r)ⁿ

Worked example

A project costs $10,000 today and is expected to generate $4,000, $5,000, and $6,000 at the end of years 1, 2, and 3. The firm's discount rate is 10%. Discount each inflow:

Year	Cash flow	Discount factor at 10%	Present value
1	$4,000	1 / 1.10 = 0.9091	$3,636.36
2	$5,000	1 / 1.102 = 0.8264	$4,132.23
3	$6,000	1 / 1.103 = 0.7513	$4,507.89
Total present value of inflows			$12,276.48

Now subtract the cost:

NPV = -10,000 + 12,276.48 = 2,276.48

The NPV is +$2,276.48.

The NPV rule

The decision rule is beautifully simple:

• If NPV > 0, accept the project - it is worth more than it costs and adds value.
• If NPV < 0, reject it - it destroys value.
• If NPV = 0, the project exactly earns its required return; you are indifferent.

Because our project has NPV of +$2,276.48, the firm should accept it. That figure is not abstract: it is the dollar amount by which the project is expected to increase the value of the firm today, in current dollars, above and beyond the 10% return the firm demanded. NPV directly measures value created, which is exactly the manager's goal from Module 1. A closely related measure, the profitability index, divides the present value of inflows by the initial cost: 12,276.48 / 10,000 = 1.23. A profitability index above 1 signals a positive-NPV project.

NPV answers "how much value?" in dollars. Managers often also want a percentage return, and that is the internal rate of return (IRR). The IRR is the discount rate that makes a project's NPV exactly zero - the break-even rate at which the project's inflows just cover its cost.

What IRR means

Formally, the IRR is the rate r* that solves:

0 = CF₀ + CF₁/(1+r*) + ... + CF_n/(1+r*)ⁿ

Take the same project from the last lesson: cost $10,000, inflows of $4,000, $5,000, and $6,000. We found its NPV is positive at 10%. As we raise the discount rate, NPV falls; the rate at which it hits zero is the IRR. Solving (by trial or a financial calculator) gives an IRR of about 21.6%. We can check it near the answer: at 21% the NPV is a small positive +107.70, and at 22% it is a small negative -57.76, so the crossing point sits between - about 21.65%.

The IRR rule

Compare the IRR to the firm's required return (also called the hurdle rate or cost of capital):

• If IRR > required return, accept - the project earns more than the firm demands.
• If IRR < required return, reject.

Our project's IRR of 21.6% comfortably beats the 10% hurdle, so we accept - the same verdict NPV gave. For a single, standard project, NPV and IRR always agree, because "NPV positive at 10%" and "IRR above 10%" are two ways of saying the same thing.

A cleaner example

IRR is easiest to see with one future cash flow. If you invest $1,000 today and receive $1,120 in one year, the IRR solves 1,000 = 1,120 / (1 + r*), giving r* = 1,120/1,000 - 1 = 0.12, or exactly 12%. The project earns a 12% return; accept it if your hurdle rate is below 12%.

Where IRR can mislead

IRR is intuitive but has traps that NPV avoids:

• Scale. A tiny project can have a huge IRR yet add little dollar value. A 50% return on $100 adds less than a 15% return on $1,000,000.
• Ranking mutually exclusive projects. When you must choose one of several projects, IRR can rank them differently from NPV; when they conflict, trust NPV, because it measures value directly.
• Unusual cash flows. A project whose cash flows switch sign more than once can have multiple IRRs or none at all.

For these reasons finance treats NPV as the gold standard and IRR as a useful companion. When the two disagree, follow NPV.

A bond is a loan sliced into a tradable security. When a firm or government issues a bond, it promises the holder two things: a fixed interest payment called the coupon each period, and repayment of the face value (or par value, usually $1,000) at the maturity date. Because a bond is just a set of future cash flows, we value it the way we value everything else - by discounting.

The bond pricing formula

A bond's price is the present value of its coupons (an annuity) plus the present value of its face value (a single sum), both discounted at the market's required return, the yield to maturity (YTM):

Price = C × [1 - (1+y)^-n] / y + Face / (1+y)ⁿ

where C is the coupon per period, y is the yield per period, and n is the number of periods.

Worked example

Value a 3-year bond with a $1,000 face value and a 5% annual coupon (so C = $50) when the market yield is 6%. Discount the two pieces:

Component	Calculation	Present value
Coupons ($50 for 3 yrs)	50 × [1 - (1.06)-3] / 0.06	$133.65
Face value ($1,000 in 3 yrs)	1,000 / (1.06)3	$839.62
Bond price		$973.27

The bond is worth $973.27, below its $1,000 face value. It trades at a discount because its 5% coupon is stingier than the 6% the market now demands, so buyers will only pay less than par to make up the difference.

Rates and prices move in opposite directions

This is the central fact of bond investing: when interest rates rise, bond prices fall, and vice versa. The coupon is fixed, so the only way an old bond can offer a competitive return when rates change is for its price to adjust. The pattern is:

• Coupon rate > yield → price above par (a premium bond). An 8% coupon at a 6% yield on our 3-year bond prices at $1,053.46.
• Coupon rate = yield → price equals par. A 6% coupon at a 6% yield prices at exactly $1,000.
• Coupon rate < yield → price below par (a discount bond), as in our example.

Longer-maturity bonds swing more when rates change, because more of their cash flow is discounted over more periods. Most bonds also pay coupons twice a year; you simply halve the coupon and yield and double the number of periods. The logic never changes - a bond is worth the discounted value of the cash it will pay.

A share of common stock is part ownership of a company. Its cash flows to an investor are the dividends the company pays, plus whatever price the share can eventually be sold for. But that future selling price itself depends on the dividends the next owner expects. Follow the logic to its end and a share's value today is simply the present value of all future dividends, discounted at the return r that investors require for the stock's risk.

The constant-growth model

Forecasting an endless dividend stream sounds impossible, but one assumption tames it: suppose dividends grow at a constant rate g forever. Then the stream is a growing perpetuity, and its value collapses to the elegant Gordon growth model (also called the dividend discount model):

P₀ = D₁ / (r - g)

Here D1 is next year's expected dividend, r is the required return, and g is the constant dividend growth rate (which must be less than r for the formula to work).

Worked example

A company is expected to pay a dividend of $2.00 next year. Investors require a 10% return, and the dividend is expected to grow 4% per year forever. The stock's value today is:

P0 = 2.00 / (0.10 - 0.04) = 2.00 / 0.06 = 33.33

The share is worth $33.33. Notice how sensitive this is to the inputs: because we divide by the small number (r - g), a growth estimate that is even one point too high sharply inflates the value. If D0 (this year's dividend just paid) were given instead of D1, we would first grow it: D1 = D0 × (1 + g).

Zero-growth stock

If dividends never grow (g = 0), the growing perpetuity becomes an ordinary perpetuity and the formula simplifies to P0 = D / r. A stock paying a level $3 dividend forever, with a required return of 12%, is worth 3 / 0.12 = 25, or $25 per share. Preferred stock, which pays a fixed dividend, is often valued exactly this way.

Where the model strains

The dividend discount model is powerful but assumes a company pays dividends and grows them steadily - untrue for a young firm that pays nothing yet, or one whose growth is lumpy. In those cases analysts forecast the early years explicitly and apply the constant-growth formula only to the stable years that follow, or turn to other approaches such as discounting free cash flow. The core idea, though, is unshaken: a stock is worth the present value of the cash it will return to its owners.

Every valuation so far assumed we knew the discount rate - the required return. Where does that rate come from? It comes from risk. Investors dislike uncertainty, so they demand a higher expected return to bear more of it. This lesson makes "risk" and "return" precise.

Expected return

The return on an investment over a period is its gain (price change plus any dividend) divided by the starting price. When the future is uncertain, we work with the expected return: the probability-weighted average of the possible returns. If the economy might boom, stay normal, or fall into recession, we weight each scenario's return by its probability.

Consider a stock with these forecasts:

Scenario	Probability	Return	Probability × Return
Boom	0.30	+25%	+7.5%
Normal	0.40	+12%	+4.8%
Recession	0.30	-5%	-1.5%
Expected return			+10.8%

The expected return is 0.30(25%) + 0.40(12%) + 0.30(-5%) = 10.8%. It is not any single outcome; it is the average you would expect over many repetitions.

Risk as standard deviation

Two investments can share an expected return yet differ wildly in how spread out their possible returns are. Finance measures that spread with the variance and its square root, the standard deviation. The bigger the standard deviation, the more the actual return is likely to stray from the expected return - and the riskier the investment. For the stock above, squaring each scenario's deviation from 10.8%, weighting by probability, and taking the square root gives a standard deviation of about 11.7%. Roughly speaking, returns will often land within a band of about one standard deviation around the 10.8% mean.

The risk-return trade-off

The foundational pattern of investing is that higher expected returns come only with higher risk. History bears this out: over the long run, stocks have delivered higher average returns than bonds, and bonds more than Treasury bills - and in exactly that order, riskier assets have swung more violently along the way. The extra return a risky asset offers above the safe rate is its risk premium, the reward for bearing risk. No investment reliably offers high return with low risk; if one seems to, look harder.

The most important free lunch in finance is diversification: holding many different assets reduces risk without necessarily reducing expected return. When you combine assets whose returns do not move in lockstep, their ups and downs partly cancel, and the portfolio's swings shrink below the average swing of its parts.

Why diversification works

Imagine two stocks each with a return standard deviation of 20% and 30%. If you split your money evenly, a naive guess for the portfolio's risk is the average, 25%. But that is only true if the two stocks move perfectly together (correlation +1). If they are uncorrelated, the portfolio's standard deviation falls to about 18%; if they moved perfectly opposite (correlation -1), risk could shrink to as low as 5%. The less correlated the assets, the more risk diversification removes.

Two kinds of risk

Diversification splits risk into two types:

• Unsystematic risk (also firm-specific or diversifiable risk) is unique to one company - a lawsuit, a failed product, a factory fire. Across a large portfolio these events are independent and wash out, so unsystematic risk can be diversified away.
• Systematic risk (also market risk) affects nearly all assets at once - recessions, interest-rate shifts, wars. It cannot be diversified away, so it is the only risk investors are ultimately rewarded for bearing.

The key insight: because unsystematic risk is free to eliminate, the market pays a risk premium only for systematic risk. An asset's contribution to the systematic risk of a diversified portfolio is measured by its beta (β). A beta of 1.0 means the asset moves with the market; a beta of 1.5 means it swings 50% more than the market; a beta of 0.5 means it is half as volatile.

The Capital Asset Pricing Model

The Capital Asset Pricing Model (CAPM) turns beta into a required return. It says an asset's expected return equals the risk-free rate plus a risk premium proportional to its beta:

E(R) = R_f + β × (E(R_m) - R_f)

Here Rf is the risk-free rate, E(Rm) is the expected market return, and (E(Rm) - Rf) is the market risk premium - the reward per unit of beta.

Worked example

Suppose the risk-free rate is 3%, a stock's beta is 1.2, and the market risk premium is 5%. The required return is:

E(R) = 3% + 1.2 × 5% = 3% + 6% = 9%

Investors should require 9% to hold this stock. That 9% is exactly the kind of number we plugged in as the "required return" when valuing stocks and projects - the CAPM is where discount rates come from. A stock with a higher beta would demand a higher return; a safer, low-beta stock would demand less.

Every technique in this course needed a discount rate. For a whole firm, that rate is its cost of capital - the return the firm must earn on its investments to satisfy everyone who funded it. Since a firm raises money from two sources, lenders and shareholders, its overall cost is a blend of the two, weighted by how much of each it uses. That blend is the weighted average cost of capital (WACC).

The cost of debt

The cost of debt is the interest rate the firm pays on its borrowing - essentially the yield on its bonds. It has one twist: interest is tax-deductible, so borrowing shelters some income from tax. The relevant figure is therefore the after-tax cost of debt:

After-tax cost of debt = r_d × (1 - Tax rate)

A firm borrowing at 8% with a 25% tax rate has an after-tax cost of debt of 8% × (1 - 0.25) = 6%. The tax deduction makes debt cheaper than its stated rate.

The cost of equity

The cost of equity is the return shareholders require, and we already know how to find it: the CAPM from Module 5. If the risk-free rate is 3%, the firm's beta is 1.2, and the market risk premium is 5%, the cost of equity is 3% + 1.2 × 5% = 9%. Equity is not free - shareholders demand a return for their risk, and it is almost always higher than the cost of debt because equity holders are paid last and bear more risk.

Weighting them: the WACC

WACC weights each source by its share of the firm's total financing (based on market values):

WACC = (E/V) × r_e + (D/V) × r_d × (1 - Tax)

where E is the market value of equity, D the value of debt, and V = E + D the total.

Worked example

A firm is financed with $6,000,000 of equity and $4,000,000 of debt, so V = $10,000,000. Its cost of equity is 12%, its cost of debt is 6%, and the tax rate is 25%. The weights are E/V = 0.60 and D/V = 0.40. Then:

Source	Weight	Cost	Weight × Cost
Equity	0.60	12%	7.2%
Debt (after tax)	0.40	6% × (1 - 0.25) = 4.5%	1.8%
WACC			9.0%

The firm's WACC is 9.0%. This is the hurdle rate the firm should use to discount its projects: an investment must earn more than 9% to create value for the mix of investors who financed it. The WACC ties the whole course together - it is built from the cost of debt (bond valuation), the cost of equity (CAPM), and it becomes the discount rate for NPV.

We close by putting every piece together. Capital budgeting is the process of deciding which long-term projects to fund, and it is where the financial manager creates - or destroys - value. The recipe is now familiar: estimate the project's cash flows, discount them at the firm's cost of capital, and apply the NPV rule.

Getting the cash flows right

The hardest part is not the discounting but choosing which cash flows to count. Three rules keep you honest:

• Use incremental cash flows - only cash flows that change because you take the project. If a cost occurs whether or not you invest, ignore it.
• Ignore sunk costs - money already spent and unrecoverable (like a past market study) is irrelevant to today's decision.
• Include opportunity costs - if a project uses a warehouse you could have rented out, the forgone rent is a real cost of the project.

Use after-tax cash flows, and remember from Module 1 that cash flow is not accounting profit - add back non-cash charges like depreciation.

Putting it together

Recall our Module 3 project: it costs $10,000 and returns $4,000, $5,000, and $6,000 over three years. Suppose the firm's WACC, which we computed as 9%, is the right discount rate (rather than the 10% we used earlier). Discounting the inflows at 9%:

Year	Cash flow	PV at 9%
1	$4,000	$3,669.72
2	$5,000	$4,208.40
3	$6,000	$4,633.10
Total PV of inflows		$12,511.23

The NPV is -10,000 + 12,511.58 = 2,511.58, or +$2,511.58. Because the firm now discounts at its true 9% cost of capital rather than 10%, the project looks even better than before - a lower hurdle rate raises NPV. Since NPV is positive, the firm creates value by accepting it.

Comparing the criteria

Managers use several yardsticks; know their strengths and flaws:

Method	Rule	Strength	Weakness
NPV	Accept if NPV > 0	Measures dollar value added; uses all cash flows and the time value of money	Requires a discount rate
IRR	Accept if IRR > WACC	Intuitive percentage return	Can mislead on scale and multiple sign changes
Payback period	Accept if it repays within a cutoff	Simple; highlights liquidity	Ignores the time value of money and all cash flows after the cutoff

The payback period counts how long until cumulative cash flows repay the cost. Our project recovers $4,000 then $5,000 (=$9,000) in two years, needing $1,000 more of the year-3 $6,000, so payback is about 2 + 1,000/6,000 = 2.17 years. Payback is a rough liquidity check, but because it ignores the time value of money and everything past the cutoff, it should never overrule NPV. The verdict of modern finance is firm: when methods conflict, follow NPV, because maximizing NPV is the same as maximizing the value of the firm - the goal we began with in Module 1.