* Basic Framework

- Philosphical basis and general principles

- Basic Approaches to Valuation

- Estimating inputs

- Discount Rates

- Cash Flows

- Growth Rates

* Wide range of models in use

* Classified into broader categories

- easier to understand where models fit into the big picture

- commonalities among the models

- differences between models

- spot fundamental errors in logic

* Discounted cashflow valuation, relates the value of an asset to the present value of expected future cashflows on that asset.

* Relative valuation, estimates the value of an asset by looking at the pricing of 'comparable' assets relative to a common variable like earnings, cashflows, book value or sales.

* Contingent claim valuation, uses option pricing models to measure the value of assets that share option characteristics.

Basis for Approach



where,

n = Life of the asset

CFt = Cashflow in period t

r = Discount rate reflecting the riskiness of the estimated cashflows

Two basic sub-approaches --

* value just the equity stake in the business

* value the entire firm, which includes, besides equity, the other claimholders in the firm

The value of equity is obtained by discounting expected cashflows to equity, i.e., the residual cashflows after meeting all expenses, tax obligations and interest and principal payments, at the cost of equity, i.e., the rate of return required by equity investors in the firm.



where,

CF to Equityt = Expected Cashflow to Equity in period t

ke = Cost of Equity

The dividend discount model is a specialized case of equity valuation, and the value of a stock is the present value of expected future dividends.

The value of the firm is obtained by discounting expected cashflows to the firm, i.e., the residual cashflows after meeting all operating expenses and taxes, but prior to debt payments, at the weighted average cost of capital, which is the cost of the different components of financing used by the firm, weighted by their market value proportions.



where,

CF to Firmt = Expected Cashflow to Firm in period t

WACC = Weighted Average Cost of Capital

Never mix and match cash flows and discount rates. The key error to avoid is mismatching cashflows and discount rates, since discounting cashflows to equity at the weighted average cost of capital will lead to an upwardly biased estimate of the value of equity, while discounting cashflows to the firm at the cost of equity will yield a downward biased estimate of the value of the firm.

Illustration 1: Effects of mismatching cashflows and discount rates

Assume that you are analyzing a company with the following cashflows for the next five years. Assume also that the cost of equity is 13.625% and the firm can borrow long term at 10%. (The tax rate for the firm is 50%.) The current market value of equity is $1,073 and the value of debt outstanding is $800.

Year CF to Equity Interest(1-t) CF to Firm

Year	Cash Flow to Equity	Interest(1-t)	Cashflow to Firm
1	$ 50	$ 40	$ 90
2	$ 60	$ 40	$ 100
3	$ 68	$ 40	$ 108
4	$ 76.2	$ 40	$ 116.2
5	$ 83.49	$ 40	$ 123.49
Terminal Value	$ 1603.008		$ 2363.008

Cost of Equity = 13.625%

Cost of Debt = Pre-tax rate (1- tax rate) = 10% (1-.5) = 5%

Value of Equity = $1073 Value of Debt = 800

WACC = Cost of Equity (Equity / (Debt + Equity)) + Cost of Debt (Debt/(Debt+Equity))

= 13.625% (1073/1873) + 5% (800/1873) = 9.94%

Method 1: Discount CF to Equity at Cost of Equity to get value of equity

PV of Equity = 50/1.13625 + 60/1.13625² + 68/1.13625³ + 76.2/1.13625⁴

+ (83.49+1603)/1.13625⁵ = $1073

Method 2: Discount CF to Firm at Cost of Capital to get value of firm

PV of Firm = 90/1.0994 + 100/1.0994² + 108/1.0994³ + 116.2/1.0994⁴

+ (123.49+2363)/1.0994⁵ = $1873

PV of Equity = PV of Firm - Market Value of Debt

= $ 1873 - $ 800 = $1073

X Method 1: Discount CF to Equity at Cost of Capital to get too high a value for equity

PV of Equity = 50/1.0994 + 60/1.0994² + 68/1.0994³ + 76.2/1.0994⁴

+ (83.49+1603)/1.0994⁵ = $1248

X Method 2: Discount CF to Firm at Cost of Equity to get too low a value for the firm

PV of Firm = 90/1.1362⁵ + 100/1.13625² + 108/1.13625³ + 116.2/1.13625⁴

+ (123.49+2363)/1.13625⁵ = $1613

PV of Equity = PV of Firm - Market Value of Debt

= $1612.86 - $800 = $813

This approach is easiest to use for assets (firms) whose cashflows are currently positive and can be estimated with some reliability for future periods, and where a proxy for risk that can be used to obtain discount rates is available.

(1) Firms in trouble: Negative earnings, cash flows, book value.... possibility of bankruptcy

(2) Cyclical Firms: Earnings are function of economic cycle. Likely to be biased at peak and trough.

(3) Firms with unutilized assets: Cash flows from these assets will not be counted in value.

(4) Firms with patents or product options: If patents not expected to pay off during time horizon, they may not be counted.

(5) Firms in the process of restructuring: Inputs have to be adjusted to reflect the effects of restructuring.

(6) Firms involved in acquisitions: Effects of synergy and control changes have to be factored int.

(7) Private Firms: Inputs relating to risk are difficult to estimate; Short histories.

In relative valuation, the value of an asset is derived from the pricing of 'comparable' assets, standardized using a common variable such as earnings, cashflows, book value or revenues. Examples include --

* Price/Earnings (P/E) ratios

and variants (EBIT multiples, EBITDA multiples, Cash Flow multiples)

* Price/Book (P/BV) ratios

and variants (Tobin's Q)

* Price/Sales ratios

1. Using Fundamentals

* Relates multiples to fundamentals.

* Primary advantage is that it shows the relationship between multiples and firm characteristics, and allows us to explore how multiples change as these characteristics change.

2. Using Comparables

* The second approach estimates multiples for a firm by looking at comparable firms.

* Key issue in this approach is the definition of a comparable firm.

* The allure of multiples is that they are simple and easy to relate to. They can be used to obtain estimates of value quickly for firms and assets, and are particularly useful when there are a large number of comparable firms being traded on financial markets, and the market is, on average, pricing these firms correctly.

* By the same token, they are also easy to misuse and manipulate, especially when comparable firms are used. Given that no two firms are exactly similar in terms of risk and growth, the definition of 'comparable' firms is a subjective one.

* Market errors in valuation get built into new valuations.

Illustration 2: The potential for misuse with comparable firms

Assume that an analyst is valuing an initial public offering of a firm that manufactures computer software. At the same time, the price-earnings multiples of other publicly traded firms manufacturing software are as follows:

Firm	PE Ratio
Adobe Systems	23.2
Autodesk	20.4
Brodebund	32.8
Computer Associates	18.0
Lotus Development	24.1
Microsoft	27.4
Novell	30.0
Oracle	37.8
Software Publishing	10.6
System Software	15.7

* Average PE ratio = 24

* Average PE ratio (without Software Publishing and System Software)= 27.

* Average PE ratio (without Broderbund and Oracle) = 21.

A contingent claim or option is an asset which pays off only under certain contingencies - if the value of the underlying asset exceeds a pre-specified value for a call option, or is less than a pre-specified value for a put option. Much work has been done in the last twenty years in developing models that value options, and these option pricing models can be used to value any assets that have option-like features.

An option can be valued as a function of the following variables -

* the current value

* the variance in value of the underlying asset

* the strike price

* the time to expiration of the option

* the riskless interest rate.

The basic models in use are the -

* Black and Scholes Model

* Binomial Model

* Direct examples of securities that are options

(1) primes and scores, traded on the American Stock Exchange, primes entitling investors to dividends and scores providing price appreciation

(2) contingent value rights, which provide protection to stockholders in companies against stock price declines

(3) warrants, which are long term call options issued by firms.

* Indirect examples of securities with option characteristics

(a) Equity, for instance, can be viewed as a call option on the value of the underlying firm, with the face value of debt representing the strike price and term of the debt measuring the life of the option

(b) A patent can be analyzed as a call option on a product, with the investment outlay needed to get the project going considered the strike price and the patent life becoming the time to expiration of the option.

* assumptions made about constant variance and dividend yields, which are not seriously contested for short term options, are much more difficult to defend when options have long lifetimes.

* When the underlying asset is not traded, the inputs for the value of the underlying asset and the variance in that value cannot be extracted from financial markets and have to be estimated.