01Lesson 1 · Module 2

Future money is not the same as today's money.

A company may receive cash next year. A bond may pay interest for decades. A career may generate salary for 20 years. Present value is the tool that converts future cashflows into today's terms.

  • Turn assets into cashflow timelines
  • Convert future cashflows into present value
  • Decide whether projects create value
  • Prepare for perpetuities, annuities, compounding, and inflation
M2Module map

Present Value Relations

Four connected lessons turn future cashflows into value today. Complete the first three to unlock the integrated CFO Decision Room.

02Part I

Cashflows, Assets, and the Present Value Operator

Lesson objectives

What you should understand in this lesson

Finance starts by translating assets into cashflows. A factory, a patent, a stock, a bond, a business, a brand, and a career are different on the surface, but from a finance perspective they can all be analyzed as current and future cashflows.

What is an asset?

In everyday language, an asset sounds like something you own. In finance, that is not precise enough. A finance analyst asks: What cash will this asset generate, and when will that cash arrive?

Definition · Asset
An asset is a sequence of current and future cashflows.
value
Business entity
cashflow
Property, plant & equipment
market
Patents and R&D
market
Stocks, bonds & options
value
Knowledge, reputation, opportunities
cashflow
Future salary stream

A sequence of negative cashflows may be a liability, but it still fits the cashflow framework.

Try itAsset scanner
Motivation — scan the cashflow lens

Each surface looks different — a jet program, an equity index, an employee option. Activate the cashflow lens on each to see what a finance analyst actually values.

Asset 01

Boeing regional jet

Boeing is evaluating whether to develop a regional jet. Development takes 3 years, costs roughly $850 million, unit costs may fall to $33 million, and Boeing expects to sell 30 planes per year at an average price of $41 million.

What future cashflows matter?
Asset 02

S&P 500 dividends and earnings

Firms in the S&P 500 are expected to earn $66 and pay dividends of $24 per share, adjusted to the index. Dividends and earnings historically grew 6.6% nominally, or about 3.2% in real terms, since 1926.

What future cashflows matter?
Asset 03

HP stock options

A new HP employee receives 50,000 stock options with a strike price of $24.92 and expiration in 10 years. HP stock ranged from $16.08 to $26.03 over the prior two years.

Why is this an asset?

Always draw a timeline

Before calculating anything, draw a timeline. A cashflow today is not the same as a cashflow in Year 1 or Year 2. If the cashflow is placed on the wrong date, the formula may look correct but the answer will be wrong.

t = 0
Today
t = 1
Year 1
t = 2
Year 2
t = 3
Year 3
t = T
Final date
Try itTimeline builder
Tap a card, then tap a year

Place each cashflow onto the correct date. The cost happens today. The two inflows arrive in Year 1 and Year 2. Build the timeline before you discount anything.

Cashflows
Timeline
Year 0
Today
Year 1
Year 1
Year 2
Final date

The present value operator

The present value operator takes a sequence of cashflows and returns a value at a chosen date. In this lesson, the chosen date is usually today.

Cashflows at different dates are different currencies

You would not directly add ¥150 and £300. You first convert them into the same currency. The same is true for money at different dates. You cannot directly add money today and money in Year 2 until both are converted into the same date.

¥150 + £300 = ?Meaningless until converted to a common currency.
Definition · Numeraire date
the date used as the common unit of measurement. Usually today, t = 0.

Net present value

Present value converts future cashflows into today's terms. Net present value includes the initial cost or investment.

If there is an initial investment, CF0 < 0. Any future CFt can also be negative.

Value creator

If NPV > 0, accept.

Value destroyer

If NPV < 0, reject.

Where does r come from?

The discount rate reflects the opportunity cost of capital: what investors could earn on comparable opportunities in financial markets. It is not chosen arbitrarily.

Opportunity costComparable alternativesMarket-determined
Try itWorked example 01
Step 1 of 4

Worked Example: Current investment, future cashflows

Year 0 · Today
−$10.0M
Investment today
Year 1
+$5.0M
Inflow
Year 2
+$7.0M
Inflow
$1 in Year 1 = $0.90 today$1 in Year 2 = $0.80 today
  1. 1Draw the timeline
    Year 0
    −$10.0M
    Year 1
    +$5.0M
    Year 2
    +$7.0M
Try itWorked example 02
Step 1 of 4

Worked Example: Future investment

Year 0 · Today
+$2.0M
Inflow today
Year 1
+$5.0M
Inflow
Year 2
−$8.0M
Future investment
$1 in Year 1 = $0.90 today$1 in Year 2 = $0.80 today
  1. 1Draw the timeline
    Year 0
    +$2.0M
    Year 1
    +$5.0M
    Year 2
    −$8.0M

What this lesson gives you

You can now value known cashflows if cashflow amounts, signs, timing, and exchange rates are known and there are no conversion frictions. Later lessons relax these assumptions.

Try itPart I mastery check
Pass with 4 of 5 correct

Answer all questions, then check your work. You can retry any time — mastery is based on correctness, not speed.

  1. 01

    Select all that are assets under the cashflow definition.

  2. 02

    Place the cashflow on a timeline: a $5.0M inflow received one year from now goes on which date?

  3. 03

    Why can ¥150 + £300 not be added directly? (Mention conversion or currency.)

  4. 04

    Which is the correct NPV formula?

  5. 05

    A project has NPV = −$50,000. Do you accept or reject?

Lesson summary
  1. 1Assets are sequences of cashflows.
  2. 2Cashflows at different dates are different economic units.
  3. 3Present value converts future cashflows into today's dollars.
  4. 4NPV is the present value of benefits minus costs.
  5. 5Positive-NPV projects create value.
  6. 6Perpetuities and annuities are special cashflow patterns.
  7. 7Compounding affects the true annual rate.
  8. 8Inflation changes purchasing power.
  9. 9Real and nominal cashflows must be discounted consistently.