Understanding Capital Asset Pricing Model (CAPM) And Its Applications

Assumptions underlying the theory

Questions :

1. A Critical Assessment of The Capital Asset Pricing Model (CAPM) You are required to-

(a) Describe the Capital Asset Pricing Model, including the assumptions underlying the theory.

(b) Explain the relationship between the Security Market Line and the Capital Market Line, using diagrams and examples to illustrate your explanation.

(c) Briefly set out arguments in favour of – and against – the theory, outline its uses and make a critique of its underlying assumptions.

(d) dentify any alternatives which have been suggested in place of CAPM.

(e) Conclude with an overall assessment of the theory and state any recommendations you may have from your study.

(f) Conclusion a brief overall assessment of the CAPM theory.

2. You are required to work  the following problem, using a discounted cash flow (NPV) analysis.

“Gordon Hall is considering replacing an old machine with a new one from Li Ho. The old machine (bought 5 years ago from Tom Lee) cost $340,000, while the new one will cost $280,000, fully financed by a 5 year 9% per annum interest only loan.

“The new machine will be depreciated prime cost to $50,000 over its 5 year life. Gordon estimates that it will be worth $40,000 (salvage value) after 5 years. The old machine is being depreciated at prime cost to zero over its original expected life of 10 years. However, George can sell the old machine today for $86,000.

“The new machine will save Gordon $70,000 a year in cooling costs. Other costs are that, one year ago, a feasibility study on the new machine conducted for Gordon by an external firm of consultants, cost Gordon $20,000. With the new machine, Gordon will also lose $10,000 of sales of another product to Tom Lee.  

“With the new machine, a one-off amount of cleaning supplies (current assets) at a cost of $9,000 will be required, and Henry estimates that accounts receivable   (also current assets) will increase by $14,000. Both of these increases in working capital will be recouped at the end of the new machine’s life in five years time.

“Gordon’s cost of capital is 9%. The tax rate is 30%. Tax is paid in the year in which earnings are received.

(a) Calculate the net present value of the proposed change, that is, the net benefit or net loss in present value terms of the proposed changeover.

(b) Should Henry purchase the new machine? State clearly why.”

Capital Asset pricing Model (CAPM) has been on the most important theories related to financial management and modern financial economics that has applications in project financing and securities market with respect to estimation of cost of capital of the firms and evaluation of the performance of the portfolios respectively. It is one of the most widely used models although has been challenged several times with respect to its applications and accuracy. This essay provides the basic understanding of the CAPM by highlighting the assumptions underlying the theory. Further the relationship between the Security Market Line and the Capital Market Line is studied.  The essay also discussed the applications, benefits and limitations of CAPM. Lastly the recommendations have been made for the alternative of CAPM or what adjustments can be made to CAPM to reduce the effect of limitations.

Relationship between Security Market Line and Capital Market Line

CAPM provides the relationship between risk and expected return. This relationship is given by the mathematical formula

Here

is expected return

is the risk free return

is sensitivity of the asset to the changes in return on market

is the expected return of the market

The relationship that is given by the CAPM is useful in two ways. Firstly it provides benchmark rate of return that has to be expected from the given investment opportunities. Secondly it is employed for forecasting the returns to a certain extent.  

There are certain assumptions based on which CAPM has been developed. These are as mentioned below

Risk Return interest of investors: The investors are risk averse and desire more return on investment. The risk will be avoided if the return is same on two investment options.

Diversified portfolio is held by the investors: This assumptions is based on the fact that it has been assumed that there is no unsystematic risk and that

Borrowing at risk free rate: Another assumption is that the investors can invest in high return investments by borrowing at risk free rate.

Short Selling: There is no restriction on short selling in the market and all the investors can trade in all the available options. The buying or selling of the stock will not have any impact on the prices.

Perfectly efficient market: It is assumed that the market is perfectly efficient and that same information is available to all the investors. There is no transaction cost or any other tax that is applicable.

Based on these assumptions the CAPM model has been developed. The other aspects with respect to CAPM have been discussed below.

Capital Market Line (CML) is used in CAPM for illustrating the return from efficient portfolio which is dependent on the risk free rate and the level of risk associated with the portfolio. CML is the relation of return with risk measured in terms of standard deviation. On the other hand Security market Line (SML) shows the relationship between the beta of the stock and the return associated with it.

The efficient frontier that has been shown in the above diagram is the set of all optimal portfolios that offer highest expected return for a given risk level or the lowest risk. The portfolios that lie below the efficient portfolio are over-valued as optimum expected return isn’t there whereas the portfolio that are above the CML have higher risk. The equation of CML is shown below.

The securities, asset or portfolio that are above the SML are underpriced whereas that below the SML are overvalued.

One of the most important differences between the CML and SML is that CML is applicable to the portfolio whereas the SML is applicable for security, asset or portfolio. Further the other difference between the SML and CML is that SML identifies risk in terms of beta whereas in CML standard deviation is the measure of risk.

CAPM has its applications in different segments. These have been discussed below

Applications of CAPM

Portfolio analysis: CAPM has its application in portfolio analysis. Based on the CML that has been discussed above it can be estimated whether the portfolio is under-valued or over-valued. Efficient portfolios lie on the CML. Further the assets that are above the SML are underpriced relative to as expected based on CAPM whereas the assets that lie below the SML are overpriced in relation to as signified by CAPM.

Investment Decisions: the investment decisions with respect to the value of the project and the return it can generate may be estimated based on the CAPM.

Applications to capital Budgeting: CAPM is employed for establishing the hurdle rate for the projects. Thus based on the CAPM WACC can be estimated which can further be used for the estimation of the Net Present value (NPV) or Internal Rate of Return (IRR).

The above applications suggest that decision making has been simplified based on the CAPM model and the consideration may be given to other factors rather than the cost of capital or the estimation of returns at the primary level.

CAPM has been one of the most important and has been implemented vastly in various studies. There are certain benefits which support CAPM in contrast to other theories and models that have been developed.

Systematic Risk Estimation: the linear relationship that has been mentioned above is represented by the Security market Line highlighting the relation between the beta, market risk and the expected return. Further the unsystematic risk is eliminated making the model quite simple and easy to understand and implement.

The empirical testing of CAPM shows that despite its inaccuracies it is much more reliable than the other models such as arbitrage pricing model etc. It is believed that CAPM can be the basis for the further study and improvement in the estimation of return in comparison to other models.

There are certain limitations of CAPM that have been discussed below

Firstly CAPM is based on certain assumptions. The assumptions that have been mentioned earlier such as no transaction cost, taxes or effect of inflation on the market are unrealistic. This effects the reliability of the CAPM. For example in the recent past the CPM has poorly explained the stock returns in USA and UK market as there has been considerable impact of these factors.

There are certain limitations with respect to the methodology that is adopted in CAPM.  The return measured by the CAPM is a function of risk. The relative volatility of the investment is the basis of estimation of return. However this is important to understand that the volatility may be higher in comparison to what is depicted by CAPM. Secondly the index that has been selected as the market proxy may not be relevant enough to measure the returns on the investment.

Lastly, as mentioned above the applications of CAPM is in estimation of weighted average cost of capital. Since CAPM uses historical data and it is expected that the same relation as depicted by the historical data will be applicable. However the impact of other factors impacting the performance in future also has to be considered. 

Limitations of CAPM

Conclusion & Recommendations

CAPM is certainly one of the most useful models that has its applications in budgeting, securities and project appraisal. The various benefits of the model show why this has been adopted across the financial sector. On the other hand the limitations highlight the need to conduct studies on the model and develop alternatives to CAPM and ways by which this can be implemented (Fletcher & Kihanda, 2005). One of the ways is to introduce the parameters such as kurtosis and skewness in the CAPM.  Certain recommendations have been discussed below to improve the reliability of the CAPM and reduce the limitations associated with the model.

Multi Beta Models: CAPM is single beta model which is for highlighting the relation of return with the market. However there can be several other factors impacting the returns and thus it may be useful to introduce several other factors related to other factors impacting the returns

Market Price Based Models: The beta calculated by the CAPM is based on the correlation of stock and the market, standard deviation of the market and the stock. The correlation factor may be highly unstable and may have huge variance over the period. The market based models estimate the relative risk and thus dispense off the correlation factors. The relative risk is estimated by the division of standard deviation of the stock by the average standard deviation of all the stocks in the market. This may be lengthy and complicated.

Accounting based Models: This is the accounting based risk measurement also known as accounting beta. Under this method the detailed study of the cost structure of the company is conducted. Based on this asset beta is developed from the equation shown below

This is more realistic as the return is dependent on the profitability rather than the movement in the stock price. Another method to use accounting information based model is creation of scaled risk measurement with respect to certain accounting ratio that is important from the viewpoint of the asset.

Apart from this various other studies have been conducted and it shows that the validity of CAPM may be improved by using more data and data that isn’t too old or is based on different market conditions. This ensures that the realistic market parameters and conditions are employed.

Year	0	1	2	3	4	5
Value of Old Machine	170000
Cost of New Machine	280,000.00	230,000.00	180,000.00	130,000.00	80,000.00	30,000.00
Depreciation/ Principal Payment		50,000.00	50,000.00	50,000.00	50,000.00	50,000.00
Loan for the year		255,000.00	205,000.00	155,000.00	105,000.00	55,000.00
Interest Payment for the year		22,950.00	18,450.00	13,950.00	9,450.00	4,950.00
Salvage Value of Old Machine	86,000.00
Salvage Value of New Machine						40,000.00
Saving in Cooling Cost		70,000.00	70,000.00	70,000.00	70,000.00	70,000.00
Loss of sales		10,000.00	10,000.00	10,000.00	10,000.00	10,000.00
Working Capital Requirement	23,000.00
Working Capital Recoup						23,000.00
Cash Flow	63,000.00	(12,950.00)	(8,450.00)	(3,950.00)	550.00	38,050.00
Tax	–	–	–	–	165.00	11,415.00
Net Cash Flow	63,000.00	(12,950.00)	(8,450.00)	(3,950.00)	385.00	26,635.00
Discount Factor	1.00	0.92	0.84	0.77	0.71	0.65
PV of Cash Flow	63,000.00	(11,880.73)	(7,112.20)	(3,050.12)	272.74	17,310.92
NPV	58,540.61

  

Several assumptions have been made. These have been mentioned below    

1. No tax will be applicable on the sale of the old machine. This is because the original price of the machine is $340,000 and its life is 10 years. Since it is depreciated based on straight line method the value of the machine after five years will be $170,000. Since the machine is being sold at a price less than its actual value no tax will be applicable.  

2. The depreciation that is being calculated for the new machine is considered as the repayment amount of the loan that has been taken for the purchase of the new machine. This has been reduced from the cash flow.

3. The interest is calculated on the average of the principal amount at the start of the year and that at the end of the year.

4. All the payments, savings, losses and sale are considered to be occurred at the end of the year.

5. At the end of five years, tax is paid for the sale of new machine for the amount in excess of the salvage value. After considering the depreciation of $50,000 for the five year period the salvage value is $30,000 whereas the sale of old machine is at $40,000. There is gain of $10,000 and tax has been calculated on this amount.

6. The working capital requirement is considered at the start of the year while the recoupment of this is considered as the gain and tax is considered on this as well.

7. The cost associated with feasibility study has not been considered as this is the sunk cost for the company. This is because even if new machine is not purchased the cost cannot be recovered.

In the given situation the purchase of the new machine can be considered. This is because there is significant cash inflow and the NPV is positive. However further study with respect to the savings and the discount rate may be conducted. Even if the discount rate increase the cash flow will be positive as the inflow from the old machine is there. If this inflow from the sale of old machine is not considered, because there is loss of $84,000 in old machine, the NPV will be negative. Considering this the machine should not be purchased. However this may not be considered since only the cash flow will have to be seen. This has been shown above based on which NPV is positive.

References

Damodaran, A. (2011). Alternatives to the CAPM: Part 1: Relative Risk Measures. [online].

Fletcher, J. & Kihanda, J. (2005). An Examination of Alternative CAPM-Based Models in UK Stock Returns. Journal of Banking & Finance. volume 29. no. 12. Pp. 65-66

[online].

Knox, D.R. (2011). Examining CAPM in Today’s Markets.

Toms, S. (2012). Accounting based risk measurement: An alternative to CAPM derived discount factors. The York Management School. Working Paper No. 68. ISSN Number: 1743-4041. [online].

Machado, J.J.G. (2013). THE CAPITAL ASSET PRICING MODEL (CAPM).

Fama, E.F. & French, K.R. 92004). The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives—Volume 18, Number 3. Page 25-46. [online].