Lesson 2.6: Discounted Cash Flow (DCF)

Lesson Overview

By now you’ve learned the building blocks of Time Value of Money: future value, present value, annuities, and perpetuities. A Discounted Cash Flow (DCF) model puts all of that together.

A DCF answers one of the most important questions in finance: What is this asset, business, or project worth today based on the cash it will produce in the future?

The core idea is simple: estimate future cash flows, discount each one to present value, and add them up.

Learning Objectives

• Define a Discounted Cash Flow (DCF) valuation.
• Set up a timeline and identify cash flows by period.
• Calculate PV of multiple cash flows and sum them to get total value.
• Explain the meaning of NPV (Net Present Value) and interpret it for decisions.
• Understand why discount rate selection matters.
• Explain terminal value intuition and when it is used.
• Identify common DCF errors (timing, rate mismatch, double-counting).

What Is DCF (In Plain Language)?

A DCF is a structured way to say: “Future cash is valuable, but less valuable than cash today so let’s convert all future cash into today’s dollars.”

You can apply DCF thinking to:

• Investments: stocks, bonds, real estate
• Businesses: valuing a company based on cash generation
• Projects: should we build the factory, launch the product, buy the machine?
• Personal decisions: “Is this deal worth it?”

The DCF Formula (General Form)

If you expect cash flows CF₁, CF₂, ..., CF_n over time, the present value is:

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

This is just “PV of each cash flow” repeated and summed.

Step 1: Draw a Timeline

DCF is easiest when you organize the problem visually:

• t = 0: today (often includes an initial cost or purchase price)
• t = 1, 2, 3...: future periods where cash flows occur

Then you discount cash flows back to t = 0.

Step 2: Identify the Cash Flows (CFs)

In a DCF, cash flow is the money you can actually take out and use (or must pay in). For Finance 101 problems, cash flows are typically given to you directly.

Common patterns:

• Initial investment: a negative cash flow at t=0 (cash outflow)
• Benefits: positive cash flows later (cash inflows)
• Final sale value: a lump sum at the end (sometimes called salvage value)

Step 3: Choose a Discount Rate (r)

The discount rate reflects the return required for the risk of the cash flows. At a basic level it captures:

• Opportunity cost: what you could earn elsewhere
• Inflation: compensation for lost purchasing power
• Risk: uncertainty of receiving the cash

A higher discount rate makes future cash worth less today.

Step 4: Discount Each Cash Flow and Sum

For each period t:

PV(CF_t) = CF_t / (1 + r)^t

Then:

Total Value Today = Sum of PVs

Worked Example: A Simple DCF

Suppose you can pay $1,000 today to receive the following cash flows:

• Year 1: +$400
• Year 2: +$400
• Year 3: +$400

If the discount rate is 10%, the present value of the inflows is:

• PV₁ = 400 / (1.10)¹
• PV₂ = 400 / (1.10)²
• PV₃ = 400 / (1.10)³

Add them to get PV of benefits, then compare to the $1,000 cost (NPV concept below).

Net Present Value (NPV): The Decision Rule

When there is an upfront cost, DCF naturally leads to Net Present Value (NPV):

NPV = PV(of all future inflows) - PV(of all costs)

In many problems, the main cost is at t=0, so it’s already in present value terms.

Basic decision rule:

• If NPV > 0: value created (worth doing at that discount rate)
• If NPV = 0: break-even (exactly meets required return)
• If NPV < 0: value destroyed (not worth it at that discount rate)

DCF as “PV of Pieces” (A Useful Mental Model)

A DCF is just a sum of familiar building blocks:

• Single lumps sums (PV of a future amount)
• Annuities (PV of equal repeating payments)
• Perpetuities (PV of payments that extend indefinitely)

Sometimes you can simplify a DCF by recognizing patterns. For example, if Years 1–5 are equal payments, that portion is an annuity.

Terminal Value (Intuition)

In real valuation, cash flows can continue beyond the explicit forecast period. Rather than modeling every year forever, analysts often estimate a terminal value at the end of the forecast.

Two common intuition-friendly approaches:

• Perpetuity method: assume cash flows continue at a stable level or grow at a stable rate.
• Exit multiple method: estimate a resale value based on a market multiple (learned later).

In Finance 101, think of terminal value as: a shorthand for “all the value after the forecast horizon.”

Period Matching: The Most Common DCF Mistake

Your discount rate must match your cash flow timing:

• Annual cash flows → use an annual discount rate and yearly periods.
• Monthly cash flows → use a monthly discount rate and monthly periods.

If you mix them, your result can be wildly wrong even if the math is “correct.”

Common DCF Pitfalls (and How to Avoid Them)

• Off-by-one timing: discounting a Year 1 cash flow as if it happens today.
  Fix: Put cash flows on a timeline. If it’s in Year 1, discount by (1+r)¹.
• Double-counting: adding a terminal value that already includes cash flows you forecasted.
  Fix: Terminal value should represent cash flows beyond the forecast horizon.
• Using the wrong rate: discounting risky cash flows at a risk-free rate.
  Fix: Match the discount rate to the risk of the cash flow stream.
• Ignoring sign conventions: forgetting that costs are negative cash flows.
  Fix: Use + for inflows and - for outflows consistently.

Practice: Check Your Understanding

1. In one sentence, what is a DCF used for?
2. What does NPV tell you and what is the basic decision rule?
3. If the discount rate rises, does the PV of future cash flows increase or decrease? Why?
4. Why is drawing a timeline so important in DCF problems?
5. What is terminal value trying to capture?

Key Takeaways

• DCF values an asset by discounting each future cash flow and summing present values.
• NPV compares PV of benefits to costs to decide if value is created at a given discount rate.
• Discount rate selection matters because it reflects opportunity cost, inflation, and risk.
• Timelines prevent the most common errors (timing and period mismatch).
• Terminal value is a shortcut for value beyond the explicit forecast period.

What’s Next?

In Lesson 2.7: TVM in the Real World, you’ll apply TVM and DCF ideas to common financial decisions such as mortgages, bonds, retirement planning, and investment choices.