Unit 13 · Lesson 2 Corporate finance

$10,000 now for $15,000 later. Is that a good deal?

The story so far Both shops are open. Now you want a repair van, so you can fix bikes at people's homes. The van costs $10,000 today. You expect it to bring in $3,000 of extra cash a year for 5 years, then it's worn out. That's $15,000 back for $10,000 spent. Sounds like an easy yes. But the $15,000 comes slowly, over five years, and money later is worth less than money now (Lesson 10.2). This lesson shows the tool every company uses to decide what to build: net present value.

What

Net present value (NPV) is what a project's future cash is worth today, minus what it costs today.

Why

Every company has more ideas than money. NPV tells you which ideas make the business more valuable and which ones quietly lose money.

How

List the cash the project brings each year, shrink each amount back to today's dollars, add them up, and subtract the cost.

Who

Corporate finance analysts run NPV on new stores, machines and products. CFOs use it to pick which projects get money. Investment bankers use the same math to value whole companies.

What you're looking at: the van as a timeline. The orange bar is the $10,000 you pay today. The green coins are the $3,000 it brings each year. The dashed rings show $3,000; the solid coins show what it's worth in today's dollars, which shrinks the further away it is.

01 See it

Bring every dollar back to today.

You can't compare $10,000 today with $3,000 in year 5 directly. They're different kinds of dollars. So you turn every future dollar into today's dollars first.

Project cash flows

A project's cash flows are the real money it brings in or costs each year. Use cash, not profit, for the same reason as in Lesson 12.3: you can only spend cash.

In this example

Today: −$10,000 for the van.
Years 1 to 5: +$3,000 each year: $3,000 × 5 = $15,000 in total, before thinking about time.

The discount rate

To shrink future cash into today's dollars, you need a discount rate: the return your money has to earn to be worth tying up. Companies also call it the hurdle rate, because a project has to jump over it. Lesson 13.3 shows how companies set it.

In this example

Your rate: 10% a year. Between the bank loan at 8% and what your investor expects, you need the van to earn at least 10%.

Present value of each year

Divide each year's cash by 1.10 once for every year you wait. That's the present value from Lesson 10.2.

Present value = cash that year(1 + rate)^year

In this example

Year 1: $3,0001.10 = $2,727
Year 2: $3,0001.21 = $2,479
Years 3, 4, 5: $2,254, $2,049 and $1,863. The later the $3,000, the less it's worth today.

Net present value

Add up every year's present value and subtract the cost. That's the net present value, or NPV. The NPV rule: if NPV is above zero, do the project. It earns more than your discount rate, and the business becomes worth that much more. Below zero, skip it.

NPV = present value of all future cash − cost today

In this example

Add them up: $2,727 + $2,479 + $2,254 + $2,049 + $1,863 = $11,372.
NPV: $11,372 − $10,000 = $1,372. Above zero, so buy the van. The $15,000 is really worth $11,372 today, and that still beats the $10,000 price.

Internal rate of return

Raise the discount rate and NPV falls. At some rate, NPV hits exactly zero. That rate is the internal rate of return, or IRR: the yearly return the project really earns. If the IRR beats your discount rate, the NPV is above zero. Slide the rate below and find it.

In this example

The van's IRR: About 15.2%. At 15%, NPV is +$56. At 16%, it's −$177. Since 15.2% beats your 10%, the van is worth it.

Discount rate 10%

What you're looking at: the van's five years of cash. Each dashed outline is the $3,000 that arrives; the green bar inside is what it's worth today at the rate you pick. The total at the bottom compares all five green bars with the $10,000 cost.

The payback period

Many small businesses ask a simpler question: how long until I get my money back? That's the payback period. It's easy, but it has two blind spots: it treats a dollar in year 3 like a dollar today, and it ignores everything after the money comes back.

Payback = costcash per year (when the cash is the same every year)

In this example

The van: $10,000$3,000 = about 3.3 years. It says nothing about years 4 and 5.

02 Hear it

Two minutes. Just listen.

Tap any line to jump to it.

03 Play it

Build it or skip it?

Eight project decisions. Each one gives you the numbers. One try each.

Question 1 of 8

Right0 of 0

What you're looking at: made-up projects at made-up businesses. Each lists the numbers, then asks one question.

04 Break it down

The logic, step by step.

Every NPV, from a bike van to a new factory, takes the same four steps.

Step 1: List the cash, year by year

Cost today, then the cash each year

In this example

The van: −$10,000, then $3,000 a year for 5 years.

Step 2: Pick the discount rate

The return your money must earn

In this example

The shop: 10% a year.

Step 3: Bring each year back to today

Divide by 1.10 once per year of waiting

In this example

Total: $2,727 + $2,479 + $2,254 + $2,049 + $1,863 = $11,372.

Step 4: Subtract the cost and decide

NPV above zero → do it

In this example

NPV: $11,372 − $10,000 = $1,372. Buy the van.

Worked example: you can only afford one

You have $10,000 and two ideas. Here are the facts:

The van: costs $10,000 and brings $3,000 a year for 5 years.
A parts booth at the market: costs $10,000 and brings $6,600 in year 1, $4,235 in year 2 and $1,331 in year 3.
Your rate: 10%.

Payback. The booth gets your money back in about 1.8 years ($6,600 + $4,235 = $10,835 by year 2). The van takes about 3.3 years. Payback says: booth.
The booth's present values. $6,6001.10 = $6,000, $4,2351.21 = $3,500, $1,3311.331 = $1,000.
The booth's NPV. $6,000 + $3,500 + $1,000 − $10,000 = $500.
Compare. The van's NPV is $1,372; the booth's is $500.
The answer. Buy the van. When you can only do one, pick the higher NPV. The booth pays back faster, but the van adds $872 more value, because payback ignores the van's years 4 and 5.

05 Nature link

Bees pay up front for wax.

Honeybees build their comb from wax they make inside their bodies. It's expensive: a colony eats about 6 to 8 pounds of honey to make 1 pound of wax. But a good comb stores honey and raises young bees for years. So colonies build most of their comb when flowers are full of nectar, when the payoff is biggest.

What you're looking at: an illustration, not data. On the left, the honey a colony spends today. On the right, the comb it builds with that honey, which pays the colony back for years.

Why this sticks. The colony pays a big cost now for a stream of benefits later, and builds most when the future payoff is largest. That's an NPV decision.

06 Notes

The page you'd copy down.

Cash flows: cost today, then cash each year. Van: −$10,000, then $3,000 × 5.
Discount rate (hurdle rate): the return the money must earn. 10%.
Present value = cash that year(1 + rate)^year. Year 1: $3,0001.10 = $2,727.
NPV = all present values − cost. $11,372 − $10,000 = $1,372. Above zero: do it.
IRR: the rate where NPV = 0. Van: about 15.2%. Beats 10%, so do it.
Payback = $10,000$3,000 = 3.3 years. Ignores time value and later years.
Only one? Pick the higher NPV: van $1,372 beats booth $500.

Fill in the blanks

1. A project's present value of future cash minus its cost today is its .

2. At a 10% rate, $1,100 arriving in one year is worth dollars today.

3. The discount rate that makes NPV exactly zero is the .

4. The number of years it takes to earn back a project's cost is its period.

07 Together

Grab a friend or a study group.

Shark tank, NPV style

Each person invents a small project with a cost and yearly cash. Swap, compute each other's NPV at 10%, and fund only the ones above zero.

Is college worth it?

List the cost of a degree today and the extra pay it might bring each year. Pick a discount rate and argue about which numbers are fair.

Find the IRR

Using the slider above, find the two whole-number rates where the van's NPV flips from positive to negative.

08 On your own

Just you and your money.

These stay on this device. Nobody else sees them.

Think of something you paid for once that paid you back over time, like a tool, a course or a bike. Was it worth it?

What return would you need to tie up $1,000 for five years?

What's a big purchase you're considering? What cash would it save or bring in each year?

09 Check

Exam-style questions.

Written the way a college exam would ask them. Each right answer on the first try is worth 10 xp.

On the job: you're a corporate finance analyst

A coffee chain is thinking about a new espresso machine for its busiest store. Here's the situation:

Cost today: $50,000.
Extra cash: $12,000 a year from faster service, for 6 years.
After 6 years: the machine is worth nothing.
The company's discount rate: 8%.

Your task: what's the payback period? What's the NPV at 8%? Should the company buy it? What if the CFO says the rate should be 12%?

See a model answer

Payback: $50,000$12,000 = about 4.2 years.

NPV at 8%: bringing each $12,000 back to today gives $11,111, $10,288, $9,526, $8,820, $8,167 and $7,562, which add up to about $55,475 (each year is rounded). NPV = $55,475 − $50,000 = $5,475. Above zero, so buy it.

At 12%: the same six years are worth only about $49,337 today, so NPV is about −$663. Now it's a skip. The decision depends on the rate, which is why the next lesson is about setting it.

10 Where it leads

Is it worth it?

What you're looking at: a map of where this lesson fits in the course. Read it left to right: the lessons it builds on, this lesson in the middle, and the lesson that comes next.

Back · Unit 10The time value of money
Back · Unit 12How the three statements connect
Back · Unit 13Raising money
You are herePicking projects with NPV
Next · Unit 13The cost of capital

Next lesson: The cost of capital →Course map