Valuation Basics, Cash Flows, and Discount Rates
What is Valuation?
The objective of most firms is to create wealth. To create wealth, we must manage investments that generate cash flows that are worth more than what was invested.
Our goal, as management, is to avoid making investment decisions based on incorrect or incomplete analysis. Valuation provides us a toolset to evaluate new investment opportunities. It is more than just discounting cash flows, we have to look at the whole story (market analysis, comparable multiples, strategic fit, etc.)
Our Learning Objectives
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Investment Evaluation Process
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Relevant Cash Flows (Incremental Cash Flows)
- These are cash flows directly generated by the investment, these could be:
- Projected revenues and costs of the new project
- Potential cannibalization (when the new project steals sales away from another product line. Example: Less people are likely to buy an iPhone 15(s) when the 16 comes out.)
- Sunk costs are not part of the incremental cash flows and should be ignored.
- Opportunity costs
- Include everything that is invested, including resources that might have other productive uses or market value (Land, Natural Resources, and Buildings)
- Time and Labor should also be included
How to Calculate a Project/Firm's Free Cash Flows (FCF)
- Gross Profit =
- + Sales
- - Costs of Goods Sold (COGS)
- Earnings before Interest and Taxes (EBIT) =
- + Gross Profit
- - Operating Expense
- Net Operating Profit After Taxes (NOPAT) =
- + EBIT
- - Taxes
- Project Free Cash Flows =
- + NOPAT
- + Depreciation Expense (DA)
- - Capital Expenditures (CAPEX)
- - Changes in Net Working Capital (ΔNWC)
NOTE: Notice that we don't ever subtract Interest Expense from EBIT. This is because we are interested in the cash generated by a project's assets BEFORE financing. Financing effects will be accounted for in later steps through the discount rate, not through the cash flow itself.
Snow Cone Sales, Seasonality, and Risk (CAPM Intuition)
The image above shows monthly snow cone sales for two locations: Columbus, Texas and Columbus, Ohio. Although total annual sales are the same in both cities (1,000 snow cones), the pattern of sales over the year differs significantly.
Sales in Texas are relatively smooth and consistent throughout the year, while sales in Ohio are highly seasonal—concentrated in the summer months and very low during the winter.
If we think like lenders or investors, the Ohio location would likely face higher borrowing costs or worse loan terms. This is because its cash flows are less reliable throughout the year, making loan repayment more uncertain during off-season months. In contrast, the Texas location generates steadier cash flows, reducing repayment risk.
Connection to CAPM and Beta
This example illustrates a core idea behind the Capital Asset Pricing Model (CAPM)
If we treat Texas as the baseline or “market,” Ohio’s sales move in the same direction (both peak in summer and decline in winter), but Ohio’s swings are much larger. This means Ohio has higher covariance (also known as Theta) with the seasonal cycle, analogous to a higher beta in CAPM.
As a result:
Importantly, the higher required return is not because Ohio is more volatile in isolation, but because its performance is more sensitive to the underlying cycle.
Sales in Texas are relatively smooth and consistent throughout the year, while sales in Ohio are highly seasonal—concentrated in the summer months and very low during the winter.
If we think like lenders or investors, the Ohio location would likely face higher borrowing costs or worse loan terms. This is because its cash flows are less reliable throughout the year, making loan repayment more uncertain during off-season months. In contrast, the Texas location generates steadier cash flows, reducing repayment risk.
Connection to CAPM and Beta
This example illustrates a core idea behind the Capital Asset Pricing Model (CAPM)
- Risk is not about total volatility or variability on its own.
- Risk is about covariance with the broader cycle (the “market”).
If we treat Texas as the baseline or “market,” Ohio’s sales move in the same direction (both peak in summer and decline in winter), but Ohio’s swings are much larger. This means Ohio has higher covariance (also known as Theta) with the seasonal cycle, analogous to a higher beta in CAPM.
As a result:
- Ohio requires a higher expected return
- Texas can accept a lower required return
Importantly, the higher required return is not because Ohio is more volatile in isolation, but because its performance is more sensitive to the underlying cycle.
How Capital Structure Effects Investor Demand
As we learned in accounting:
Consider the 2 capital structures:
- Assets = Debt + Equity
Consider the 2 capital structures:
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1)Unlevered Project - 0% Debt, 100% Equity 2) Mixed Project - 20% Debt, 80% Equity |
Between these two projects which is more risky? (2) Is more risky because the debt component must be paid back first before any of the equity holders can lay claim to the rest. Even for the same asset, as you increase debt % the equity holders will want a higher return.
There are 2 things that determine what your required returns have to be for your investors:
There are 2 things that determine what your required returns have to be for your investors:
- The asset you are selling
- How you own it
How to Calculate Investor Demand? (WACC)
The Weighted Average Cost of Capital (WACC) is a % that defines the average of the estimated rates of returns for a firm's interest-bearing debt (kd) and common equity (ke). The weights (w's) used for each source of funds are equal to the proportion in which funds are raise (so wd +we = 1). Notice the (1-T) part, that is the tax shield benefit (T = Tax Rate) companies get from having debt. But how do we calculate each of these variables?
Ways to calculate kd (Cost of Debt):
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Ways to calculate ke (Cost of Equity):
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If a firm were to own its assets fully in the form of debt (known as "Fully Levered") then we could simply use our Kd as the discount rate when discounting future cash flow back to the present value. Or if a firm owned all of its assets in the form of equity (known as "Fully Unlevered") then we could simply use Ke as our discount rate. However, when a firm owns its assets partially in the form of debt and equity, we must use the WACC as the discount rate.
Using the WAAC
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Givens:
So WAAC = 0.4(0.05)(1-0.2) + 0.6(0.14) = 10% |
Calculating Cost of Debt (Kd)
There are 3 ways to estimate the Cost of Debt:
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1️⃣ If the company’s bonds are publicly traded:
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2️⃣ If the debt is NOT publicly traded:
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3️⃣ If there is default risk:
You must account for
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Calculating Cost of Equity (Ke)
One of the most common ways to calculate Ke is to the Capital Pricing Model (CAPM) which uses the following equation:
- Krf is the Risk Free Rate (This is typically the % return from US Treasury Bonds)
- Be (Equity Beta) is the covariance of the return of the firm and the market
- Km is the Market Rate of Return (This is typically the S&P 500 Average Rate of Return)
2 Types of Risk
- Systematic Risk (or Non-Diversifiable Risk, example would be changes in interest rates influence almost all stocks, cannot be canceled out)
- Non-Systematic Risk (Diversifiable Risk, risk from randomness, can be canceled out)
How do we figure out βe?
We can estimate βe by using historical return data. Plot the Firm's excess return (excess return = subtract out the risk free rate after calculating return) % vs. the S&P500's excess returns. The slope of these data points is the estimated βe.
NOTE: βe is subject to random error. Common fix: Use an average of Be estimates for "similar" companies, then:
- Unlever the βe
- Relever the average unlevered βe
Fama French Model
While the CAPM model is a good estimate of the expected return of a security (Ke). However, it only considers one factor which is systematic risk due to how the stock changes in relation to how the market changes ( βe). However, the Fama French 3 Factor Model attempts to take this a step further by considering two more aspects of a security. Specifically factoring the stock's size known as "Small Minus Big" (SMB)(small market cap vs large market cap) and a stock's Book to Market (BTM) ratio (being a low BTM = "growth stock" vs. high BTM = "value stock")
Unlevering
Unlevering is about figuring out how risky a business really is, without letting debt confuse the picture.
Debt doesn’t change what a company’s products, customers, or operations do. What it does change is how risky the stock looks.
So when a company uses more debt:
Debt doesn’t change what a company’s products, customers, or operations do. What it does change is how risky the stock looks.
So when a company uses more debt:
- Equity looks riskier
- Equity beta goes up
Even if the business itself hasn’t changed at all.
3 Different Betas:
Why this matters
Unlever → get business risk → re-lever for the situation you care about.
- Equity beta: how risky the stock is (business risk plus debt risk)
- Debt beta: how risky the loans are (usually small)
- Asset beta: how risky the business itself is (Same as βe_Unlevered)
Why this matters
- Two companies can look very different only because one uses more debt
- Projects don’t have debt — companies do
- If leverage changes, equity risk must change too
Unlever → get business risk → re-lever for the situation you care about.
Internal Rate of Return (IRR)
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Companies use WACC as their minimum acceptable return when deciding whether a project is worth doing. You can think of it as the company’s “cost to use money.” If a project can’t beat this rate, it’s not worth taking on.
IRR is the project’s own built-in return — it tells you what percentage return the project is expected to generate based on its future cash flows. So the decision is simple: If the project’s IRR is higher than the WACC, the project makes more money than it costs to fund → good project If the IRR is lower than the WACC, the project doesn’t earn enough to cover its cost → bad project |
What can we use the WACC for?
Let's say you have the following future cash flows:
If you wanted to figure out how much these future cash flows are worth together in today's dollars we'd use the Net Present Value (NPV) formula:
The above example is if the cash flow had no initial investment amount. However, as is typically the case, a project will have some initial investment amount, the NPV formula subtracts out that investment amount:
The variable 𝑟 is known as the discount rate. It represents the annual rate used to convert future cash flows into their present value.
CORE CONCEPT:
As mentioned before, one of the most challenging aspects of valuing a project is determining the appropriate discount rate. The WACC provides a appropriate discount rate because it represents the weighted average required return demanded by the firm’s debt and equity holders.
The usefulness of WACC extends beyond valuing individual projects. It is also used to value entire companies by discounting Free Free Cash Flows (FFCF) at the WACC to estimate Enterprise Value (EV)!
CORE CONCEPT:
As mentioned before, one of the most challenging aspects of valuing a project is determining the appropriate discount rate. The WACC provides a appropriate discount rate because it represents the weighted average required return demanded by the firm’s debt and equity holders.
The usefulness of WACC extends beyond valuing individual projects. It is also used to value entire companies by discounting Free Free Cash Flows (FFCF) at the WACC to estimate Enterprise Value (EV)!
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In a very niche case you can actually use a simplified version of this equation. Only if:
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However, it is seldom ever the case that there is no growth... which is where the Gordon Growth Model comes in.
The Gordon Growth Model
The problem with the first EV equation given above is that it only calculates today's value of a company based on a set of cash flows up until some end forecasting point N in time (and pretending that the company dies after year N). The 2nd equation considers time after N, but assumes no growth in cash flows. However, the truth is that most of a company's value comes from the growth after time N.
A true Enterprise value is:
A true Enterprise value is:
But we cannot realistically forecast to time Infinity. So the Gordon Growth Model adds a Terminal Value (TV) variable to our first equation to factor in the growth after t=N:
