The Discounted Cash Flow Method

Lucas S. Macoris (FGV-EAESP)

Disclaimer

Disclaimer

The information presented in this lecture is for educational and informational purposes only and should not be construed as investment advice. Nothing discussed constitutes a recommendation to buy, sell, or hold any financial instrument or security. Investment decisions should be made based on individual research and consultation with a qualified financial professional. The presenter assumes no responsibility for any financial decisions made based on this content.

All publicly available content used in this lecture is available and also shared on my GitHub page. Participants are encouraged to review, modify, and use it for their own learning and research purposes. However, no guarantees are made regarding the accuracy, completeness, or suitability of the code for any specific application.

For any questions or concerns, please feel free to reach out via email at lucas.macoris@fgv.br

Moving past relative valuation

As you saw in the previous lecture, although Relative Valuation can provide a ballpark estimate of what would have been the firm value as-if it was priced similarly to other comparable firms, there were a series of drawbacks and limitations:
1. Sensitive to market mood and choice of comparables
2. Captures market sentiment and industry positioning
3. Generally backward-looking
To that matter, we need a way to estimate the intrinsic value of a company taking into account specific information regarding its ability to generate future profits

Analyzing (expected) future performance

So far, we’ve been concerned about the firm’s past performance:
1. How profitability was trending?
2. How does working capital was financed?
Now, we’ll turn our attention to focus on (expected) future performance:
1. How much value can a new project bring to the firm?
2. What are the expected future cash inflows/outflows?
In what follows, you will learn how to estimate the future cash-flows that will serve as a input to our analysis!

The Discounted Cash Flow (DCF) Method

Definition

Valuation method that estimates the present value of an asset based on its expected future cash flows.. It takes into account measures of expected profits ($\small 1,2,...,\infty$ periods ahead) and its underlying risk to come up with an estimate of the opportunity value in $\small t_0$.

Core Idea: if we are able to estimate the firms’ future cash flows, we can adjust them to present value using a discount rate
Key Inputs: Cash flow projections, discount rate (often WACC), and terminal value assumptions
Strengths: Grounded in fundamentals; flexible to different scenarios
Weaknesses: time-consuming, fully dependend on the forecast assumptions

The Discounted Cash Flow (DCF) Method

Let $CF_t$ be the amount of cash flow available in period $t$ to all owners of the company, for periods $\small t=1,2,3,...,\infty$. The Discounted Cash Flow method estimates the intrinsic value of a company, $V_i$, as:

\[ V_i = \sum_{t=1}^{\infty} \dfrac{CF_i}{(1+r_i)}, \]

where $r_i$ is the opportunity cost of capital associated with undertaking the project
Question: how can we use such rationale to estimate the value of a new investment opportunity?

Introducing the Free Cash Flow (FCF)

How to measure the incremental gains/losses due to the acceptance of a project? For this, we’ll use the Free Cash Flow measure

Definition

The Free Cash Flow is a measure of the project’s available cash to be repaid to its investors after all costs and investments needed to sustain the business plan were taken into account. It is calculated by:

Projecting direct expected Revenue and Cost Estimates
Considering indirect revenues/expenses
Calculating EBIT, Taxes, and NOPAT
Adjusting for non-cash effects
Considering future investments
Determining eventual adjustments, if needed

We’ll be doing this in using a case study that will guide us through all the steps

Case walkthrough

Cia. Amazônia is a manufacturer of sports shoes that is analyzing the possibility of investing in a new line of sneakers, having even incurred research and market testing costs worth $\small \$125,000$. The shoes would be manufactured in a warehouse next to the company’s factory, fully depreciated, which is vacant and could be rented for $\small\$38,000$ per year.
The cost of the machine is $\small \$200,000$, depreciated over five years using the straight-line method. Its market value, estimated at the end of five years, is $\small \$35,000$
The company needs to maintain a certain investment in working capital. As it is an industrial company, it will purchase raw materials before producing and selling the final product, which will result in an investment in inventories. The firm will maintain a cash balance as protection against unforeseen expenses. Credit sales will generate accounts receivable. In sum, working capital will represent $\small10\%$ of sales revenue.

Case walkthrough, continued

The company projects the following sales over a $\small5$-year horizon
- Year 1: $\small 7,000$
- Year 2: $\small 9,000$
- Year 3: $10,000
- Year 4: $\small11,000$
- Year 5: $\small9,000$
The unit price is $\small\$28$, and the unit cost is $\small\$14$. It is estimated that its operating costs will rise at an average rate of $\small6\%$ each year
On the other hand, the company knows that due to market competition, it will not be able to fully pass this on to prices and projects an average increase in sales prices of $\small4\%$ each year

Step 1: Revenue and Cost Estimates

Earnings are not actual cash flows. However, as a practical matter, to derive the forecasted cash flows of a project, financial managers often begin by forecasting earnings
Thus, we begin by determining the incremental earnings of a project—that is, the amount by which the firm’s earnings are expected to change as a result of the investment decision.
In our case, we begin by determining the direct earnings and cost estimates from the operation:

\[ \small \text{Gross Profit}_{t}=\text{Sales}_t\times(\text{Price per Unit}_t-\text{Cost per Unit}_t) \]

The Gross Profit is our starting point for estimating incremental earnings

Step 1: Revenue and Cost Estimates

Your Gross Profit estimation should look like the following:

Before we calculate tax expenses, we need to deduct all other costs that may affect taxes:
1. For example, depreciation and amortization are non-cash items, but they are generally tax-deductible
2. Furthermore, all other incremental costs, even if they are indirect, need to be taken into account

Step 2: Consider indirect effects

When computing the incremental earnings of an investment decision, we should include all changes between:
1. The firm’s earnings with the project;
2. The firm’s earnings without the project
There are two important sources of indirect costs that need to be considered:
1. Opportunity Costs: many projects use a resource that the company already owns. However, in many cases the resource could provide value for the firm in another opportunity or project.
2. Project externalities: indirect effects of the project that may increase or decrease the profits of other business activities of the firm

Step 2: Consider indirect effects

In our case, we saw that the firm will use existing assets that otherwise would yield $38,000 yearly. Because of that, we need to take into consideration as an opportunity cost
What about the $\small\$125,000$ R&D expenses incurred? This is an example of a sunk cost:
1. Sunk costs have been or will be paid regardless of the decision about whether or not to proceed with the project
2. Therefore, they are not incremental with respect to the current decision and should not be included in its analysis
3. If our decision does not affect the cash flow, then the cash flow should not affect our decision!
Examples of sunk costs may include, but are not limited to: past R&D expenses, fixed overhead costs, and unavoidable competition effects

Step 3: EBIT and Taxes

Before we calculate tax expenses, if we assume that depreciation is tax-deductible, we can then use the $\small\$40,000$ value from the straight-line depreciation to deduct our taxable earnings:

\[ \small EBIT_{t}= [\text{Sales}_t\times(\text{Price per Unit}_t-\text{Cost per Unit}_t)-\text{Depreciation}_t-\text{Other Costs}_t] \]

And the Income Tax that we’ll deduct is:

\[ \small \text{Income Tax}_{t}= EBIT_{t}\times\tau_t \]

Which tax-rate to use? The correct tax rate to use is the firm’s marginal corporate tax rate, which is the tax rate it will pay on an incremental dollar of pre-tax income

Step 3: EBIT and Taxes

What if part of the upfront investment was financed using debt? Do we need to include interest expenses in the calculation?
Because the Free Cash Flow is the measure of available resources to all investors of the firm (creditors + equityholders), whenever we evaluating a capital budgeting decision, we do not include interest expenses in the calculation
1. We wish to evaluate the project on its own, separate from the financing decision
2. Furthermore, the cost of debt (along with its tax shield) can be considered in an appropriate estimate of the cost of capital for the project
3. For these reasons, we also call our incremental earnings as unlevered net income

$\rightarrow$ Therefore, in our Free Cash Flow estimations, we’ll be focusing on the operating portion as if it were financed without any debt!

Step 3: EBIT and Taxes

Considering both Depreciation and the Opportunity Costs, our Unlevered Net Income is:

Step 4: Adjust for non-cash effects

As discussed in previous lectures, earnings are merely an accounting measure of the firm’s performance:
1. They do not represent real profits
2. As a consequence, the firm cannot use its earnings to buy goods, pay employees, fund new investments, or pay dividends to shareholders
On the other hand, cash does!
1. Because of this, to evaluate a capital budgeting decision, we must determine its consequences for the firm’s available cash
2. The incremental effect of a project on the firm’s available cash, separate from any financing decisions, is the project’s Free Cash Flow

Step 4: Adjust for non-cash effects

There are important differences between earnings and cash flow:
1. Earnings include non-cash charges, such as depreciation…
2. But do not include the cost of capital investment!
To determine the Free Cash Flow, we must adjust for these differences by:
1. Adding back Depreciation: because depreciation is not a cash flow, we do not include it in the cash flow forecast
2. Capital Expenditures (CAPEX): to account for the cash that will be used to fund the equipments, we include the actual cash cost of the asset when it is purchased.

Step 4: Adjust for non-cash effects

In our case, we have the following adjustments:

For Depreciation, we need to add back $\small\$50,000$ across Year 1-5 to account for non-cash items
On the other hand, to consider the actual cost of the machinery by the time that it was bought, we need to include $\small\$200,000$ in Year 0 of the analysis

With these adjustments in place, we should have the following values:

Step 5: Consider future investments in working capital

Now that we have considered all cash effects from the investment that is needed, is there anything else that needs to be taken into consideration?
Most projects will require the firm to continuosly invest in net working capital as time goes by:
1. Firms may need to maintain a minimum cash balance to meet unexpected expenditures
2. Inventories of raw materials and finished products are needed to accommodate uncertainties and demand fluctuations
3. Finally, customers may not pay for the goods they purchase immediately, and the firm may have credit with its suppliers
Although it is difficult to consider all potential fluctuations on working capital, it is expected that a portion of it should be positively correlated with sales:
1. As sales go up, firms may want to keep its past terms with suppliers and customers
2. All else equal, an increase in sales should increase the amount of working capital needed

Step 5: Consider future investments in working capital

In our case, we summarized this idea by taking into consideration that working capital is 10% of the Sales revenue
Therefore, our year-over-year change in net working capital reflects the additions/deductions on the amount of net working capital for each year:

\[ \small \Delta NWC_{t}=NWC_{t}-NWC_{t-1} \]

In our case, our net working capital should look as follows:

Step 5: Consider future investments in working capital

In the beginning of Year 0, we forecast Year 1’s sales and invest in working capital
For each Year 1-4, we look forward to period $\small t+1$ to determine the adequate level of working capital in $t$
At the end of Year 5, we know that the $\small NWC=0$, assuming that the project ends
Therefore, $\small \Delta NWC_{t=5}$ shows that the firm can recover its investment in working capital

Step 6: Calculating the Free Cash Flow

We can summarize what we have so far by:

(+) Revenues
(-) Costs
(-) Depreciation
(=) EBIT
(-) Tax Expenses
(=) Unlevered Net Income
(+) Depreciation
(-) CAPEX
(-) $\Delta$ NWC
(=) Free Cash Flow

This is the standard estimate of a Free Cash Flow, which is the amount of incremental cash that a project can actually bring to the firm!

Step 6: Calculating the Free Cash Flow

We can summarize the Free Cash Flow calculation as follows:

\[ \small FCF_{t}= \underbrace{(\text{Revenues}-\text{Costs}-\text{Depreciation})\times(1-\tau)}_{\text{Unlevered Net Income}}+\text{Depreciation}-\text{CAPEX}-\Delta NWC \]

Note that we first deduct depreciation when computing the project’s incremental earnings, and then add it back (because it is a non-cash expense) when computing Free Cash Flow
Thus, the only effect of depreciation is to reduce the firm’s taxable income!
Because of this, we can rewtrite the same equation as:

\[ \small FCF_{t}= (\text{Revenues}-\text{Costs})\times(1-\tau)-\text{CAPEX}-\Delta NWC+\tau\times\text{Depreciation} \]

Where the last term is the depreciation tax shield

Step 7: Adjustments to the Calculating the Free Cash Flow

Our standard Free Cash Flow estimates should look like the following:

Step 7: Adjustments to the Calculating the Free Cash Flow

Our final step is to account for any eventual adjustments needed. Some examples include (but are not limited) to:
1. Other non-cash items: amortization of intangibles, for example, can be taken into consideration
2. Timing of cash flows: can be estimated on a monthly or quarterly basis
3. Different depreciation patterns: straight line depreciation may not apply to all cases
4. Liquidation or Salvage value: assets that are no longer needed often have a resale value, or some salvage value if the parts are sold for scrap
5. Termination Value: value for the subsequent periods whenever we have infinite-horizon projects

Step 7: Adjustments to the Calculating the Free Cash Flow

In our case, we know that the market-value of the machinery is $\small 35,000$. Since it has been fully depreciated at Year 5, we know that the capital gain is simply $\small 35,000 - 0 = 35,000$
Therefore, we also need to consider that, in Year 5, as the project has ended, we can sell the machine, pay taxes on it, and recover part the liquidation value of our investment:

\[ \small \text{Liquidation Value}= 35,000 \times (1-\tau)\rightarrow 35,000\times(1-34\%)=23,100 \]

Adding this value as a cash-inflow in the last year of the project:

\[ \small FCF_{t=5}=107,584+23,100=130,684 \]

Final Result

Bridging NPV and Free Cash Flow

We can finally use our FCF estimates in the NPV formula to gauge the value of the project:

\[ \small NPV= \dfrac{-219,000}{(1+15\%)^0}+\dfrac{46,592}{(1+15\%)^1}+\dfrac{69,266}{(1+15\%)^2}+\dfrac{80,218}{(1+15\%)^3}+\dfrac{101,293}{(1+15\%)^4}+\dfrac{130,684}{(1+15\%)^5}=48,922.22 \]

What else needs to be done? See the Appendix for a detailed discussion on some of the most common adjustments and extensions¹:
1. Adjust FCF estimates to incorporate different depreciation patterns
2. Incorporate long-term value for projects that have an infinite-horizon (for example, a firm!)
3. Take uncertainty of the inputs that we’re using into account through Sensitivity, Break-Even, and Scenario Analysis

Supplementary Reading

See Note on Capital Budgeting for a detailed discussion on more aspects of the capital budgeting process in practice

$\rightarrow$ All contents are available on eClass®.

Appendix

Different Depreciation Patterns

Suppose that instead of using foreign suppliers when buying your machinery, you have received an offer to use new, national supplier, which can provide machinery that is supposedly as efficient as the original one. Notwithstanding, because you’re financing a national capital good, you have access to an accelerated depreciation benefit:

The market-value of the machine is still worth $\small \$200,000$, to be paid in Year 0
You’ll fully depreciate the machine in the first three years: $\small 30\%$ in the first year, and $\small 35\%$ in the second and third year

Would you accept the offer?