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The capital Asset Pricing Model (CAPM) is one of the most widely used methods used to estimate the cost of equity. Specifically, this important tool asserts that the risk premium of a risky asset is determined by its systematic risks. It provides a methodology to analyze the value of risky securities and emphasizes the importance of portfolio diversification to determine the risk premium (Elton et al. 288). The Capital Asset Pricing Model (CAPM) for Krispy Kreme Doughnuts will be an estimation of the minimum rate of return that its investors demand or expect on their investment.

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The expected rate of return demanded by investors depends on the compensation for the time value of money invested, and the systematic risk premium which depends on the market risk premium and the beta (Brealey ET al.115; Schroeder et al. 214).  

The CAPM estimate or the rate of return is calculated using the formula:

Rj = RF + %u03B2j [RM - RF]

Where Rj is the expected return on the capital asset; %u03B2j is the company’s systematic risk coefficient or beta; RF is the risk-free rate of interest, and RM is the expected return of the market.

Calculating the cost of equity for Krispy Kreme

Krispy Kreme estimated 'beta' = 1.78

The risk-free rate of interest = 6.62%

Assuming a difference of about 7.0% between the expected rate of return and the risk-free rate of return on the 'market portfolio’, the CARP of Krispy is calculated as;

            Rj = 6.62 + 1.78(13.32- 6.62)

                = 19.08

Discussion: The basic idea behind the capital asset pricing model is that investors expect a reward for both waiting and worrying (Brealey 121). The greater the worry, the greater the expected return.

Krispy Krème is a fast-growing top snack shop and doughnuts chain of stores, which is predicted to have sustained growth in the foreseeable future. However, the CARP model estimates show that the Company’s expected rate of return on the capital asset, which stands at 19.08, is far above the average cost of capital for a firm in the S&P 500, which stands at 10.2 percent. This shows that Investing in Krispy Krème is riskier than investing in an S&P 500 average firm.

Comparing Krispy Krème, Dunkin Doughnuts, and Einstein Brothers Bagel

Calculating Dunkin Doughnuts Expected rate of return

Dunkin Doughnuts estimated 'beta' = 1.39

Rj = 6.62 + 1.39 (13.32- 6.62)

    = 16.35

Krispy Krème is seeking to overthrowDunkin Doughnuts as the leading snack food chain in the United States. However, going by the CARP estimates above, Krispy Krème is having a higher Expected rate of return, meaning that investors still find it riskier to invest in this company and therefore will demand more returns from their investments in Krispy Krème as compared with those investing in Dunkin Doughnuts.

Calculating Einstein Brothers Bagel expected rate of return

Einstein Brothers Bagel estimated 'beta' = 2.13

Rj = 6.62 + 2.13 (13.32- 6.62)

    = 21.53

Einstein Brothers Bagel has a higher Estimated Rate of Return compared to Krispy Kreme and Dunkin Doughnuts. This is because it has a higher beta (the sole measure of risk), which means that investors will demand or expect more for their investments in this firm as compared to either Krispy Kreme or Dunkin Doughnuts.

Estimating the cost of equity using the arbitrage pricing theory

The Arbitrage Theory of capital asset pricing is an alternative to the mean-variance CAPM, whose main conclusion is that the market portfolio is mean-variance efficient. The arbitrage pricing theory (APT) postulates that an asset’s expected return is influenced by a variety of risk factors, as opposed to just market risk as assumed by the CAPM (Gray 92).

The Model describes how returns should be defined and hypothesizes that any departure from the model will be wiped out by the arbitrage. The APT model states that the return on a security is largely related to the systematic risk factors. However, the APT model does not specify what the systematic risk factors are, but it is assumed that the relationship between asset returns and the risk factors is linear (Gray 92). 

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