cpa excel - bec - valuation of capm

7/27/2019 CPA Excel - BEC - Valuation of CAPM

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Valuation Techniques - CAPM

I. Introduction

Definition Capital Asset Pricing Model (CAPM) : An economic model that determines the relationshipbetween risk and expected return and uses that measure in valuing securities, portfolios, capitalprojects and other assets.

A. CAPM incorporates both the time value of money and the element of risk:

1. The time value of money is incorporated as the risk-free rate of return;

2. The element of risk is incorporated in a risk measure called Beta .

B. CAPM recognizes that the expected rate of return on an investment (e.g., stock, portfolio, capitalproject, etc.) must provide for (and at least be equal to) the rate on a risk-free investment plus a

premium for the risk inherent in the investment.

1. If the expected rate of return is equal to or greater than the required rate of return, theinvestment is economically feasible.

2. If the expected rate of return is less than the required rate of return, the investment is noteconomically feasible, and should not be undertaken.

II. CAPM Formula

A. The basic CAPM formula is expressed as:

RR = RFR + B(ERR - RFR)

Where:

RR = Required rate of return

RFR = Risk-free rate of return; in the U.S. generally measured by the rate (yield) on U.S. Government bonds

B = Beta of the investment; a measure of volatility, as described below

ERR= Expected rate of return for a benchmark for the asset class (type of asset) beingvalued

B. CAPM example

Example:

1. Assume the following:



Risk-free rate (RFR) = 3%

Beta ( B) = 2

Expected rate (ERR) = 10%

2. Then:

Required rate (RR) = RFR + B(ERR - RFR)

RR = .03 + 2(.10 - .03)

RR = .03 + 2(.07)

RR = .03 + .14

RR .17 (or 17%)

Thus, given the assumed facts, the required rate of return of the assumedinvestment is 17%

C. B eta described --

1. Beta is a measure of the systematic risk as reflected by the volatility of an investment.

2. Technically, it is computed as:

Beta ( B) = (Standard deviation of an asset [a]/Standard deviation of asset classbenchmark [b]) x Coefficient of correlation of a and b

3. Beta ( B) Value Significance

a. B = 1, then an investment price (value) moves in line with the asset classbenchmark for that investment; the investment has average systematic risk.

b. B > 1, then an investment price (value) moves greater than the asset classbenchmark for that investment; the investment has higher systematic risk - theinvestment is more volatile than the benchmark for the asset class.

i. 1) In the example, above, B = 2 says that the assumed asset is more volatile(more risky) than the benchmark for its asset class; therefore, the requiredrate of return (17%) is significantly more than the benchmark rate (10%).

c. B < 1, then an investment price (value) moves less than the asset class benchmarkfor that investment; the investment has lower systematic risk - the investment isless volatile than the benchmark for the asset class.

D. Additional examples:

Example:

Assume:

Risk-free rate = 3%

Benchmark rate = 7%



Excess marketreturn

= 4% (Market benchmark rate - Risk-free rate =Premium)

1. If B = 1 for an asset, the excess rate of return (premium) for the asset is 4% (1.0 x .04) and its total required rate of return is 7% (3% + 4%).

2. If B = .80 for an asset, the excess rate of return (premium) for the asset is3.2% (.80 x .04) and its total required rate of return is 6.2% (3% + 3.2%).

3. If B = 2.0 for an asset, the excess rate of return (premium) for the asset is

8% (2.0 x .04) and its total required rate of return is 11% (3% + 8%).

III. Plotting of CAPM

The following graph shows the plotted slope of Beta under three assumptions as to its value:

A. When B = 1, a percentage change in an asset class benchmark return (i.e., a market) producesthe same percentage change in an individual asset (e.g., a stock) of the same asset class.

B. When B > 1, a percentage change in an asset class benchmark return produces a greater thanequal change in an individual asset of the same asset class.

C. When B < 1, a percentage change in an asset class benchmark return produces a less than equalchange in an individual asset of the same asset class.

IV. CAPM Assumptions and Limitations

CAPM is based on a number of assumptions, some of which are more significant to the outcome thanothers. Some of the most significant assumptions and limitations of CAPM are:

A. All investors are assumed to have equal access to all investments and all investors are assumed tobe using a one period time horizon.

B. It is assumed that asset risk is measured solely by its variance from the asset class benchmark.

C. It is assumed that there are no external cost - commissions, taxes, etc.

D. It is assumed that there are no restrictions on borrowing or lending at the risk-free rate of return;all parties are assumed to be able to do so.

E. It is assumed that there is a market for all asset classes and, therefore, a market benchmark; tothe extent there is not a market or a benchmark for a particular asset class, CAPM cannot beused.

F. It uses historical data, which may not be appropriate in calculating future expected returns.

V. CAPM Uses



CAPM provides a required rate of return (discount rate) that can be used in determining the value of avariety of assets. For example, it can be used in

A. Analysis of securities -- stocks, bonds, derivatives, etc.

B. Corporate investment in capital projects -- in establishing hurdle rates (or discount rates)for capital projects.

1. In this case, the determination of a discount rate using CAPM would involve using thefollowing (with assumed values as shown for illustration purposes):

a. Company Beta or industry Beta as surrogate for the project Beta = 1.50

b. The risk-free rate of return = 8%

c. An asset class benchmark = 16%

2. Calculation of required discount rate (or hurdle rate):


RR = .08 + 1.50(.16 - .08)RR = .08 + 1.50(.08)

RR = .08 + .12 = .20 (or 20%)

3. The 20% would be used as the discount rate in the computation of the net present value(NPV) of a capital project. (Note: The net present value (NPV) method and other capitalbudgeting methods are covered in detail in the next topic.

C. Establishing fair compensation for a regulated monopoly.



FlashcardsFlashcard #1 (FC6533)

What are the major assumptions and limitations of the capital asset pricing model (CAPM)?

1. All investors have equal access to allinvestments and are using a one period timehorizon;

2. Asset risk is measured solely by its variancefrom the asset class benchmark;

3. There are no external cost - commissions,

taxes, etc.;4. There are no restrictions on borrowing or

lending at the risk-free rate of return;5. There is a market and market benchmark for all

asset classes;6. Uses historical data.

Flashcard #2 (FC6532)

Define/describe the "capital asset pricing model(CAPM)".

The capital asset pricing model (CAPM) is an economicmodel that determines the relationship between riskand expected return and uses that measure in

assigning value to securities, portfolios, capital projectsand other assets.


Give the capital asset pricing model formula anddescribe its components.


Where:RR = Required rate of return.

RFR = Risk-free rate of return.

B = Beta , a measure of volatility.

ERR = Expected rate of return for a benchmark forthe entire class of the asset being valued.


Define "Beta". Beta is a measure of the systematic risk associatedwith an investment as reflected by its volatility ascompared with the volatility of the entire class of theinvestment.


Identify and describe the three (3) possible alternativevalues of beta .

Beta (B) = 1: The individual asset being valuedchanges in the same proportion as the entire class of

the asset being valued; the asset has averagesystematic risk for the entire class.

Beta (B) > 1: The individual asset being valuedchanges greater than the entire class of the assetbeing valued; the asset is more volatile than theentire class.

Beta (B) < 1: The individual asset being valuedchanges less than the entire class of the asset beingvalued; the asset is less volatile than the entire class.

cpa excel - bec - valuation of capm

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