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FIN 40153: Advanced Corporate Finance. Basic Valuation Techniques (Based on RWJ Chapter 18). Valuation Methodologies. Income approach Discounted cash flow Market approaches Comparable multiple and transaction analyses Cost approaches Replacement cost Adjusted book value or sum of assets.

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Fin 40153 advanced corporate finance
FIN 40153: Advanced Corporate Finance

Basic Valuation Techniques

(Based on RWJ Chapter 18)

Valuation methodologies
Valuation Methodologies

  • Income approach

    • Discounted cash flow

  • Market approaches

    • Comparable multiple and transaction analyses

  • Cost approaches

    • Replacement cost

    • Adjusted book value or sum of assets

Basic outline of a business analysis and valuation
Basic Outline of a Business Analysis and Valuation

  • Define the problem

  • General economic conditions

  • Industry analysis

  • Company’s position within the industry

  • Company financial analysis

    • Historical

    • Forecast

  • Preliminary valuation

  • Premiums/discounts

Valuation premises
Valuation Premises

  • The value of a business is equal to the present value of the future benefits of ownership.

  • Value is not always a single number.

  • Value is specific to a point in time.

Income approach estimating the total value of the firm
Income Approach:Estimating the Total Value of the Firm

  • The total value of a firm, VF, equals the present value of the free (net) cash flows, FCF, that the firm is expected to provide investors, discounted by the firm’s weighted average cost of capital, WACC.

What is FCF?

The total free cash flows are calculated as follows
The Total Free Cash Flows are Calculated as Follows


- Operating Expenses

Earnings Before Interest, Taxes, Dep & Amort (EBITDA)

- Depreciation and Amortization

Operating Profit (EBIT)

x (1 - Tax Rate)

Operating Profits After Tax

+ Depreciation and Amortization

- Capital Expenditures

- Additions to Working Capital

Free Cash Flows

The total free cash flows are calculated as follows1
The Total Free Cash Flows are Calculated as Follows

Simplified version:

Free Cash Flow =

EBIT×(1-T) Net Operating Profit After Tax

+ DA Depreciation and Amortization

- ΔNWC Change in Net Working Capital

- CAPX Capital Expenditures

Why ebit 1 t
Why EBIT×(1-T)?

  • We want to calculate cash flows generated by the assets independent from the way they are financed

  • Hence we look at earnings before interest and taxes and apply the tax rate to EBIT, which ignores the tax shield

EBIT = Revenues – CGS – Other Costs – Depreciation


Income Approaches to Valuation:Discounted Cash Flow (DCF) Analysis

  • The DCF approach considers the actual benefits that investors care about (e.g., cash-equivalent value)

  • The implementation of the DCF approach can be represented as follows:

  • V = PV(FCFT) + PV(TVT) + NOA [1]

  • V - value of the business

  • PV(FCFT) - PV of the total FCF through year T

  • PV(TVT) - PV of the terminal value in year T

  • NOA - market value of excess or non-operating assets (for us this will not be important)

Calculating pv fcf t
Calculating PV(FCFT)

  • PV(FCFT), in equation [1] is estimated by using the weighted average cost of capital (WACC) to discount the projected operating cash flows. The operating cash flows in period t are calculated as

    NOPATt = EBITt ×(1 - tc) [2]

    FCFt = NOPATt + DEPt - CAPEXt - DWCt [3]

    NOPATt - net operating profits after tax

    EBITt - projected earnings before interest and taxes

    tc - corporate tax rate

    CAPEXt - total capital expenditures

    DEPt - tax depreciation and amortization

    DWCt - additions to working capital

Where Do the Numbers Come From?

  • Cash flow forecasts are typically derived from pro-forma financials.

  • With Pro-forma financials, the process of forecasting cash flows involves

    • making explicit assumptions concerning revenues, operating costs, financial market conditions etc. and

    • modeling the inter-relationships between the various line items in the firm’s financial statements.

Determining capital expenditures depreciation
Determining Capital Expenditures & Depreciation

  • CAPEXt in equation [3] includes expenditures for R&R (repair and replacement/economic depletion) and capacity additions

    • Project these two items separately in the pro forma analysis

      • R&R capital expenditures tend to be relatively stable

      • Investments in new capacity must be consistent with the growth projections

  • Depreciation should be based on expected tax depreciation schedules.

  • Should be calculated for both the existing asset base and for future expenditures

Determining additions to working capital
Determining Additions to Working Capital

  • DWCt is the incremental working capital required in year t

    • As a business grows, cash, accounts receivable, inventory, and accounts payable also tend to grow

    • The historical relation between revenue and working capital can be used to estimate this percentage

    • You can also make adjustment in items, such as A/R or A/P that reflect what are expected to be future collection terms

Calculating the PV of the Terminal Value - PV(TVT):

  • The present value of the terminal value, PV(TVt) in equation [1], is frequently estimated by “capping” the cash flows at the end of a period for which detailed projections are produced.

    • Businesses are typically long-lived assets.

    • Detailed cash flows beyond 5 or 10 years tend to be highly uncertain.

    • Consequently, analysts usually prepare detailed cash flow projections for some finite period and then assume some terminal value at the end of that period.

Calculating PV(TVT)

  • The constant growth model is typically used to estimate the terminal value.

  • TVT = FCFT(1+g)/(WACCT - g) [4]

  • FCFT – operating cash flow in year T

  • WACCT - weighted average cost of capital in year T

  • g - expected growth rate of the free cash flows

  • Note that TVT is in year T dollars. It must be discounted back to year 0 before it is used in equation [1].

Valuation techniques
Valuation Techniques

The WACC formula can be written as

The APV formula can be written as

Valuation techniques1
Valuation Techniques

  • The techniques are equivalent if you assume the following

    • The project has risk equivalent to the average risk of the firm’s existing assets

    • The firm maintains a constant debt-equity ratio

    • Corporate taxes are the only market imperfections

Wacc valuation example
WACC Valuation Example

  • Assume Avco is considering introducing a new line of packaging, the RFX Series.

    • Avco expects the technology used in these products to become obsolete after four years. However, the marketing group expects annual sales of $60 million per year over the next four years for this product line.

    • Manufacturing costs and operating expenses are expected to be $25 million and $9 million, respectively, per year.

Wacc valuation example cont
WACC Valuation Example (cont.)

  • Developing the product will require upfront R&D and marketing expenses of $6.67 million, together with a $24 million investment in equipment.

    • The equipment will be obsolete in four years and will be depreciated via the straight-line method over that period.

  • Avco expects no net working capital requirements for the project.

  • Avco pays a corporate tax rate of 40%.

  • Forecast the expected free cash flow (FCF).

  • FCF = Unlevered Net Income plus Depreciation less Capital Expenditures less additions to Net Working Capital

Wacc valuation example cont1
WACC Valuation Example (cont.)

Note that no interest expense is included in the cash flow forecasts.

Hence the terminology unlevered net income.

Wacc valuation example cont2
WACC Valuation Example (cont.)

Avco's Current Market Value Balance Sheet ($millions) and Cost of Capital without the RFX Project

Note that Net Debt = Debt – Cash = 320 - 20 = 300

And Enterprise Value = Debt + Equity – Cash = 320 + 300 – 20 = 600

In general net out “excess” cash to determine net debt.

Wacc valuation example cont3
WACC Valuation Example (cont.)

  • Avco intends to maintain a similar (net) debt-equity ratio for the foreseeable future, including any financing related to the RFX project. Thus, Avco’s WACC is

Wacc valuation example cont4
WACC Valuation Example (cont.)

  • The value of the project, including the tax shield from debt, is calculated as the present value of its future free cash flows.

Continuation value or terminal value
Continuation Value or Terminal Value

  • We have forecast the cash flows out to year 4.

  • However, for most projects and in most valuations the cash flows continue into the future.

  • We need to estimate the value of all of the cash flows to be received after year 4.

  • We could continue to forecast pro-forma statements, but this would be difficult.

  • Instead, we forecast cash flows explicitly up to the point we believe the business will reach a steady state of growth and then summarize the remaining cash flows in what is called the continuation (or terminal) value.

The discounted cash flow approach to continuation value
The Discounted Cash Flow Approach to Continuation Value

  • The continuation value in year T, using the WACC valuation method, is calculated as:

  • Free cash flow in year T + 1 is computed as:

The discounted cash flow approach to continuation value cont d
The Discounted Cash Flow Approach to Continuation Value (cont'd)

  • If the firm’s sales are expected to grow at a nominal rate g and the firm’s operating expenses remain a fixed percentage of sales, then its unlevered net income will also grow at rate g.

    • Similarly, the firm’s receivables, payables, and other elements of net working capital will grow at rate g.

  • The simplest assumption is that free cash flow grows at rate g:

Avco s continuation value dcf approach
AVCO’s continuation value (DCF approach)

  • Assume that you believe the business can grow at 2% per year indefinitely after year 4.

  • The average growth rate in GDP is a good starting point.

  • The free cash flow in year 5 is:

    • FCF4*(1+g) = $18*(1.02) = $18.36 million

  • Continuation value in year 4 is:

  • TV4 = 18.36/(0.068-0.02) = $382.5

  • Continuation value in year 0 is:

  • TV0 = 382.5/(1+0.068)4 = $294

  • Add to PV of other cash flows.

  • Enterprise Value (without initial investment of $28) = $61.25 + $294 = $355.25M

Continuation value or terminal value1
Continuation Value or Terminal Value

  • The Multiples Approach

    • Practitioners often estimate a firm’s continuation value (also called the terminal value) at the end of the forecast horizon using a valuation multiple, with the EBITDA multiple being the multiple most often used in practice.

    • For AVCO, EBITDA in year 4 is $26 million.

    • Suppose comparable firms have enterprise value to EBITDA multiples of 12x

Continuation value or terminal value2
Continuation Value or Terminal Value

  • Therefore, the continuation value for AVCO at year 4 is 12x26 = $312 million

  • Need to discount this back to year zero to get the present value of the continuation value and add it to the present value of the other cash flows.

  • PV(continuation value) = 312/(1.068)4 = $239.81

  • Plus the value of cash flows years 1-4 = $ 61.25

  • Enterprise (Firm) Value = $301.6

The adjusted present value method another valuation method
The Adjusted Present Value Method:Another Valuation Method

  • Adjusted Present Value (APV)

    • A valuation method to determine the levered value of an investment by first calculating its unlevered value and then adding the value of the interest tax shield and deducting any costs that arise from other market imperfections.

    • APV is useful for understanding where the value of the investment is coming from.

The unlevered value of the project
The Unlevered Value of the Project

  • The first step in the APV method is to calculate the value of the free cash flows using the project’s cost of capital if it were financed without leverage.

The unlevered value of the project cont d
The Unlevered Value of the Project (cont'd)

  • Unlevered Cost of Capital

    • The cost of capital of a firm, were it unlevered: for a firm that maintains a target leverage ratio, it can be estimated as the weighted average cost of capital computed without taking into account taxes (pre-tax WACC).

    • Can also compute this as the cost of equity capital based on the unlevered beta of the firm.

The unlevered value of the project cont d1
The Unlevered Value of the Project (cont'd)

  • For Avco, its unlevered cost of capital is calculated as:

    RA = 0.50 × 10% + 0.50 × 6% = 8%

  • The project’s value without leverage is calculated as:

Valuing the interest tax shield
Valuing the Interest Tax Shield

  • The value of $59.62 million is the value of the unlevered project and does not include the value of the tax shield provided by the interest payments on debt.

  • The interest tax shield is equal to the interest paid multiplied by the corporate tax rate.

Apv with known debt schedule
APV with known debt schedule

  • Suppose that instead of maintaining a constant leverage ratio, AVCO will initially borrow 20 million and will pay off 5 million per year for each of the next four years.

  • Cost of unlevered equity is 8%

  • Cost of debt is 6%

  • The tax shields are:

The unlevered value of the project cont d2
The Unlevered Value of the Project (cont'd)

  • Recall, the project’s value without leverage is calculated as:

  • The value of the tax shields with the fixed debt schedule is:

  • Project value = $59.62 + $1.03 = $60.63 million

Summary of the apv method cont d
Summary of the APV Method (cont'd)

  • The APV method has some advantages.

    • It can be easier to apply than the WACC method when the firm does not maintain a constant debt-equity ratio.

    • The APV approach also explicitly values market imperfections and therefore allows managers to measure their contribution to value.

      • In the example, the interest tax shield increase the value of the project by $1.03 Million over and above the value of the project value without leverage.

      • Note that we have not directly valued any costs (e.g., financial distress costs) associated with the debt level chosen by Avco.

Summary of the apv method cont d1
Summary of the APV Method (cont'd)

  • If you assume that the firm maintaines a constant leverage ratio, the risk of the tax shields is the same as the risk of unlevered equity.

  • We valued the firm in two steps.

    • Value the unlevered firm.

    • Value the tax shields.

  • We used the same discount rate for both because both had the same risk.

Continuation value cont d
Continuation Value (cont'd)

  • The Multiples Approach to Continuation (Terminal) Value

    • One difficulty with relying on comparables when forecasting a continuation value is that future multiples of the firm are being compared with current multiples of its competitors.

    • This is especially problematic if the industry is presently in a phase of either rapid growth or decline.

Market Approaches: Valuation using Multiples

  • Two general approaches

    • Comparable Multiples Analysis

    • Comparable Transactions Analysis

  • Identify publicly-traded companies engaged in similar business activities with risk/return characteristics similar to those at the subject company

  • Infer value from the prices of the securities at these publicly-traded firms

Comparable Multiples Analysis

  • Infers value from the prices of publicly-traded securities at comparable firms

  • The most commonly used multiple is Price-Earnings (P/E)

  • It is simple by construction and does reflect a market valuation

  • However it does require us to find comparable firms and assume that the characteristics of the firms are similiar enough to use the ratio

Multiples analysis
Multiples Analysis

  • Part of the problem with P/E ratios is that earnings reflect accounting performance

  • There are numerous issues with earnings measurement and different accounting conventions and choices can create comparison problems

  • Ratios that avoid some of these issues include

    • P/EBITA, P/Sales, Price/Cash Flow

    • Market/Book

    • EV/Sales, EV/FCF [EV (Enterprise Value) = MV Debt + MV Equity – Cash]

  • Multiples analysis also requires extensive analysis of

    • Products, Markets, Sales growth, Profit margins

    • Geographic scope of operations, Financial structure, Financial and Operating Trends, Quality of Management

  • We do not assume a specific model but conjecture the ratios reflect a market view of the growth and value of the firm

Comparable Multiples Analysis

  • Use contemporaneous data

  • Adjust the comparable company data for depreciation methods, off-balance sheet transactions, extraordinary income or expense items, non-operating assets etc.

  • Achieve consistency between numerator and denominator

Choosing the level of the multiplier
Choosing the Level of the Multiplier

  • Examine historic multiples for the company. Pay special attention to trends.

  • Examine the multiples and trends for several comparable companies.

  • Determine if the company has historically traded at a premium, at the same level, or a discount to its competitors. If at a premium, can it maintain that premium? Why? If a discount, can it move to the industry level? How?

  • Repeat above relative to the S&P index (easiest if the multiple is a P/E).


  • We want to value an unlisted company in the automobile manufacturing sector.

  • Our pro forma estimates suggest earnings next year of $25 million.

  • Data on four comparables are given on the next slide (the comparables are chosen from the same industry and are about the same size as our company)

Example data
Example Data

Comparable P/E

Arvin Industries 12.75

Detroit Diesel 15.72

Donnely 16.86

Excel 10.76

Lear Corp. 6.16

Average 14.45

P e example
P/E Example

We believe our company has better growth prospects than the typical firm in the industry.

Therefore we assign it a P/E multiple of 17

Using this gives the following valuation:

Value = $25m x 17 = $425m

Target and wal mart
Target And Wal-Mart

Computing Profitability and Valuation Ratios for Wal-Mart and Target

Following data from 2004 for both firms

Let’s compare operating margin, net profit margin, P/E ratio and ratio of enterprise value to operating income and sales

Walmart and target
Walmart and Target

Despite the difference in size, Walmart and Target’s P/E ratio, and enterprise value to operating income ratios are very similar. Target profitability was somewhat higher than Walmart’s explaining the difference in enterprise value to sales.