RETURN AND RISK RELATIONSHIP: CAPITAL ASSET PRICING MODEL

The CFO of Bunyan Lumber Corporation, Anita Rai has decided to invest some money in the financial market to diversify the risks of business operations and increase rate of return. She has been reading corporate finance books and journal articles to enhance her knowledge on risk/return relationships, capital asset pricing model (CAPM), cost of capital and stock valuation. On risk/return relationship, Anita has learnt that there is apositiverelationship between risk and return. This implies that the higher the risk, the greater the expected return on an investment. This relationship is clearly explained by thecapital asset pricing modelin this equation:

R_E=R_F+x (R_M R_F)

whereR_E=expected return on the security,R_F= the risk-free rate,= Beta of the security,R_M= the expected return on the market, and (R_M R_F) represents the difference between the expected return on the market and the risk-free rate, also known as the market risk premium.

According to the CAPM, the expected return of any security depends on its risk measured by its beta.Anita found out that the betais a measure of the risk of a security arising from exposure to general economic and market movements i.e.,systematic riskas opposed to business specific risks or factors (i.e.,unsystematic risk). The higher the beta, the greater the systematic risk and vice versa. The market portfolio of all investable assets has a beta of 1. Anita learnt that If = 0, then the asset has no risk of financial loss. Therefore, the expected return of the security should be equal to the risk-free rate. If = 1, that asset has same risk as the market and the expected return should equal the expected return on the market such as the S&P 500 market index. To Anita this makes sense because the beta of the market portfolio is exactly 1. However, if a securitys = 2, then that security is twice riskier than the market and the expected return should be higher than the return of the market portfolio.

Anita understands that the risk-free rate used in the CAPM is the government-issued treasury bill rate.Since thetreasury billhas norisk, any other investment having someriskwill have to have a higherrateof return than the risk-free rate in order to induce any investor to invest in that security.Anita is considering the stock ofAardvark Enterprisesand Zebra Enterprises. Aardvark Enterprises has a beta of 1.6 and Zebra Enterprises has a beta of 2.5. The risk-free rate is 3.5%, and the difference between the expected return on the market and the risk free is 9.0%.

The board of directors of Bunyan Lumber Inc. is hiring you as a financial consultant to work with Anita to analyze the investment options.

1. Based on the beta of Aardvark Enterprises and Zebra Enterprises, which one of the two companies has a higher market risk? Explain.

2. Assuming the stock market is expected to do very well because of recent positive economic news and announcement of higher GDP figures, which company, Aardvark Enterprises or Zebra Enterprises, is expected to do better, and why?

3. Using thecapital asset pricing model,calculate the expected return for Aardvark Enterprises and Zebra Enterprises stocks if the return on the stock market is 12.5%.

4. You want to calculate the average return of Aardvark Enterprises to see how the stock has performed over the past five years:

Exhibit 1: Historical Returns of Aardvark Enterprises.

Year	Return
2016	13.50%
2017	22.25%
2018	34.12%
2019	12.90%
2020	-6.15%

a. Using the historical returns above, what is theaverage returnfor Aardvark Enterprises stock?

5. You notice that stock returns fluctuate daily in the financial market making it risky to invest in stocks. You want to usestandard deviation, to assess the volatility of Aardvark Enterprise stock if mean return is 15.30% and standard deviation is 12%. What is the possible return of this stock one standard deviation from the mean if the return is normally distributed? (Note: expected return = mean return 1).

6. You want to use total market return approach to estimate the rate of return on another stock which Anita wants to consider for the investment portfolio. The stock is selling for $25 and pays a dividend of $2 per share during the year. You think that because of profitable capital investment that the company is undertaken, its stock price will appreciate to $35 per share by the end of next year.

a. Calculate thedividend yield.

b. Calculatethe percentagecapital gainof this stock.

c. Calculate the expected total return of this stock.

7. You are looking at sources of risk for the investment portfolio and came acrosssystematic risk and unsystematic riskin a financial journal. The systematic risk is defined as any risk that affects the whole economy or large number of assets to a greater or lesser degree. And unsystematic risk is a risk that affects specific assets or small group of assets.

a. List two examples each ofsystematic riskandunsystematic risk.

8. Anita believes that diversification reduces portfolio risk. She believes that some of the riskiness associated with individual assets can be eliminated by diversification; that is spreading the investment across many assets. She states that the principle of diversification of spreading investment across many assets will eliminate both systematic risk and unsystematic risk. Explain if Anitas statement is correct or incorrect.

9. The board of directors wants to know how the following events might cause stocks in general to change price, and whether they might cause Bunyan Lumber stock to change price.

a. the government announces that inflation unexpectedly jumped by 2% last month

b. the government reports that economic growth rate increases this year by 3% as expected

c. congress approves a surprise reduction in corporate tax rate from 25% to 22%

d. The CEO of Bunyan Lumber dies in a plane crash

Explain to the board the effect of these events on the stock market in general and Bunyans stock.

10. Anita wants you to estimate theweighted average cost of capital (WACC) for Verizon LLC. The IRR computed on a capital project for Verizon is 12%. The board wants to see if it will be a good investment. Anita thinks that if IRR > WACC then it will be a good investment to consider. The market values for Verizons debt and equity are $40 million and $60 million respectively. The total value of the firm is $100 million, implying that the weight of debt is 40% ($40 million /$100 million) whereas the weight of equity is 60% ($60 million /$100 million).

a. Estimate WACC for Verizon if the cost of equity is 14.40% and after-tax cost of debt is 3.95%. (Note: WACC = Before-tax cost of debt (1 tax rate) (weight_Debt) + cost of equity (weight_Equity).