**By Samuel K. Kiranga **

The task of investment capital budgeting and project appraisal can be a complex and challenging management issue. Many modern methods have been invented and developed to aid investment managers and analysts in finding the right mix of assets in any portfolio or project to which the company intends to make investment return on its excess cash flow. The concept of time value for money has been crucial in the development of these appraisal models and techniques and some of the models that make use of this idea are Discounted cash flow techniques, Accounting rate of return, Profitability index, Internal rate of return and Real options. When using discount rates for establishing the net present value of an investment model such as the Capital Asset Pricing Model, mean variance portfolio analysis and weighted average cost of capital are useful in today’s business environment. We shall take an intrinsic analysis of the Capital Asset Pricing Model, and explore its application to the investment strategy of the multinational telecommunications firm Vodafone Group.

**The Capital Asset Pricing Model**

**Introduction**

The Capital Asset Pricing Model concept was developed by Sharpe (1964) and this work on the subject of portfolio management won him the 1990 Nobel Prize in economics. The model was founded upon earlier works on investment portfolio analysis. A portfolio is a set of different assets that are held for investment purposes. In his paper on modern portfolio theory, Markowitz’s (1952) puts forward the idea that the risk accompanied by investing in such a portfolio of assets in a particular ratio outlay is lower than that of investing in each asset separately using the same level of capital funding. This idea is referred to amongst investors as portfolio diversification. In investment analysis though, Sharpe recognizes two types of risk to the prospect of an asset’s returns i.e systematic and non systematic risk. Systematic risk is risk that cannot be reduced by diversification and may come as result of factors such as interest rates and inflation trends on the entire market while non-systematic risks can be reduced by diversification as shown by Markowitz and includes risks for specific assets in a stock market. (Wang, 2003)

**Credibility of Risk Valuation within the Investment Model**

The backbone of the CAPM decision making strategy is Harry Marcowitz’s (1952) Mean variance portfolio theory which basically states that for a given market the optimal market line on which to base your asset selection is that which minimizes standard deviation and for any given expected return upon investment of the asset. The standard deviation in this case represents the individual asset’s risk. Typically this market line is known as the efficient frontier. This line represents the most economic points in terms of capital investment value at which investors are willing to trade off expected return for minimal risk. In a market that combines risk free investment options (e.g loans and treasury bonds) and risky assets such as stocks, the graph of expected return against risk (standard deviation) will have a tangent line that runs through the risk free return rate on the y-axis while touching the efficient frontier at a point where minimal risk is absorbed if the maximum expected returns are to be brought from including the risk free options into the portfolio. The resultant equation for calculating the expected return of such a portfolio is known as the Capital Asset Pricing Model and appears as follows,

E[˜*r*_{i}] = E(* r*_{F }) * + β*_{iM}(E[˜*r*_{M}] *− r*_{F})

Where ˜*r*_{i }is the return on asset portfolio i , *r*_{F }is the rate on the risk free asset, ˜*r*_{M }is the return on the risky market asset and *β*_{iM }(beta) is the systematic risk * βiM *= *σiM/σ*2*M*

The first term on the right-hand side of the equation,* r*_{F,,}is the expected return on risk free assets that have market betas equal to zero, which means their returns are uncorrelated with the market return. The second term is a risk premium, i.e the systematic risk function beta of asset i, β_{iM}, multiplied by the premium per unit, which is the expected market return, E(R_{M}) less E(R_{f}). (Farma & French)

Hamilton (2004, p4) stated that the different between a 15% discount rate and a 14% discount rate can mean a difference in value conclusion of hundreds of thousands of dollars. How could that be? Take an example of the following scenario;

Suppose that a market’s expected return (discount rate) on a stock is 14% and the treasury bills are repaid at a rate of 5% then with a beta value of 0.75 on the stock, what would the expected return on one unit of stock be?

By simply applying the above formula we will have:

E(˜*r*_{i}) = 0.05 + 0.75(0.14 – 0.05) = 0.1175

Now take an example of an altered risk premium that comes from a discount rate of 15 %.

The calculation then shifts to

E(˜*r*_{i}) = 0.05 + 0.75(0.15 – 0.05) = 0.125

Evidently we can already see that the non-systematic element in each of the answers remains constant and so does the expected return on risk free assets. Thus we use a standard capitalization to see the difference in using either discount rate. Suppose a company such as Vodafone which makes billions in net profits annually invests Kshs. 10 Billions in the above CAPM portfolio with the funds going the a risky market asset. The expected return under the 15 % rate will be 0.125(10,000,000,000) = 1,250,000,000 while under the 14% rate it will be 0.1175(10,000,000,000) = 1,175,000,000 which is an entire difference of Kshs. 75,000,000. Economically speaking, βiM is proportional to the risk each unit currency investment in asset i adds to the market portfolio (Farma & French, 2004) while the risk premium signifies the value added by investing in the risky asset over risk free options. These combination of factors thus add credibility to the model by incorporating an asset specific risk factor for consideration during the investment appraisal process.

APPRECIATION: I am grateful to Sam Kiranga for this insightful post. You can find more of his work here