Using CAPM (Capital Asset Pricing Model)

In addition to Gordon Model, another way to find the cost of common stock is by using Capital Asset Pricing Model (CAPM). CAPM allows us to ascertain the relationship between required return and non-diversifiable risk, which is measured by the beta coefficient (b).

Beta coefficient (b) refers to the index that measures non-diversifiable risk (risk which a company cannot eliminate through diversification). It indicates how an asset’s return will react to the changes in the market return, which in turn shows the return on a portfolio of all securities in the market.

Capital Asset Pricing Model (CAPM) is simple, as long as you know the formula and have the information necessary for the formula. The formula is as follows:

rs= Rf+(b*(rm-Rf))

Where:

rs – required return (return on a portfolio or a security)

Rf – risk free rate (e.g. rate on the U.S. Treasury bill)

b – beta coefficient

rm – market return

EXAMPLE:

If Rf (risk free rate) is 5%, beta is 2 and market return (rm) is 12%, the rs (required return or cost of common stock) can be found as follows:

Rs=5%+(2*(12%-5%)

Rs=19%

Test yourself

Assuming we know that beta (company’s market risk coefficient) is 2, market return is 13%, risk free rate of return is 7%, current dividend is $4 and dividend growth over the past 5 years is 5% and the same growth is expected in the future. With CAPM, find the price of the ordinary share.

SOLUTION:

First, using CAPM, we find rs:

rs= Rf+(b*(rm-Rf))

rs=7+(2*(13-7))

rs=19%

Next, we use the Gordon model (P0=D1/(rs-g)) to find the price of the ordinary share:

Po=(4*(1+.05))/(.19-.05)

Po=4.2/0.14

Po=$30

Test yourself:

ABC’s financial manager prepared the following information. The dividend which were paid in the current year was $5. The growth of dividends over the last 5 years were 7% and the same growth of dividends is expected to be in the future. Risk free rate is 8%, market rate is 14% and beta coefficient is 2.

Required: What is the market price of ABC’s ordinary shares?

Solution:

Firstly we need to find required return (rs) with the help of the capital asset pricing model (CAPM).

rs= Rf+(b*(rm-Rf))

rs=8+(2*(14-8))

rs=20

Next, we need to use Gordon model:

Po=D1/(rs-g)

Po=5*(1+0.07)/(0.20-0.07)

Po=5.35/0.13

Po=41.15

The price of the ABC’s ordinary share is $41.15. Note that we determined D1 (dividend within the next period) by taking known D0 (last dividend) and multiplying it by (1+ growth rate).

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Risk Adjusted Discount Rate: Dealing with Risk in Capital Budgeting

Breakeven cash inflow analyses, risk adjusted discount rate (RADR) and scenario analyses are tools that facilitate better insight into managing risk in capital budgeting.

Risk in capital budgeting especially refers to variability of the returns (variability of cash inflows), because the initial investment is more or less known with some level of confidence. Therefore, we need to ensure that present value (PV) of cash inflows will be large enough to ensure that project is acceptable.

To adjust the present value of future cash inflows for risk embodied in particular project, we can either adjust cash inflow directly or we can adjust the discount rate. Because adjusting cash inflow is highly subjective, we will rather adjust discount rate. This is when risk adjusted discount rate technique comes into play.

RADR is a discount rate that must be earned to compensate an investor for the risk undertaken. Under RADR the value of the firm must be at least maintained or must increase. Risk adjusted discount rate is the most popular risk adjustment technique that utilize NPV.

The higher is the risk of specific project, the higher RADR will be.

The deployment of RADR is best illustrated by the use of an example:

EXAMPLE

Amanda can invest in two shares, A and B. Both shares presently cost $50 and Amanda wants to hold shares for 4 years. Annual dividends from share A expected to be $7. Annual dividends from share B are expected to be $12. However, shares B are more risky. In 4 years time Amanda expects to be able to sale shares A for $55 each and shares B for $70 each. Amanda’s required return is 8%. However, for shares B she adjusts her return so that her risk adjusted discount rate becomes 12%. Calculate risk adjusted net present values (NPVs) of shares A and B and recommend which shares should Amanda purchase.

Solution:

We will use financial calculator to find risk adjusted net present values (NPVs) of shares A and B.

Risk adjusted NPV of shares A:

Clear calculator: second function, C ALL

CFo: -50

CF1: 7

CF2: 7

CF3: 7

CF4: 62 (7+55)

I: 8

Second function, NPV: $15.38

Risk adjusted NPV of shares B:

Clear calculator: second function, C ALL

CFo: -50

CF1: 12

CF2: 12

CF3: 12

CF4: 82 (12+70)

I: 12

Second function, NPV: $30.94

Since investment in shares B offers higher risk adjusted NPV, Amanda should choose to invest in shares B.

The main difficulty in using risk adjusted discount rate (RADR) technique is in determining level of risk and approximating an appropriate risk adjusted discount rate (RADR). There is currently no systematic way to adjust required return to risk adjusted discount rate (RADR). Management usually determines risk adjusted discount rate (RADR) subjectively.

Sometimes risk index is determined which reflects risk adjusted discount rate (RADR) for every subsequent level of risk. For example, risk can be categorized into below average, average, above average and very high. Past experience and CAPM can be used to subjectively determine the risk adjusted discount rate (RADR) appropriate for each subsequent level (category) of risk.

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