Cost of Equity
The cost of equity is comprised the cost of preferred stock and common stock. In this case, I am willing to focus on the cost of common stock because Nike did not pay any dividend after June 30, 2001(see Exhibit 4).
The cost of equity is comprised the cost of preferred stock and common stock. In this case, I am willing to focus on the cost of common stock because Nike did not pay any dividend after June 30, 2001(see Exhibit 4).
The cost of common stock is the return needed on the stock by shareholders in which investors discount the expected dividends of the firm to ascertain its share price. To perceive this definition, let me bring you an example:
Assume you want to invest on the stock of Nike, Inc. Your expected return is 12% for one year. The current share price is $42. Your benefit of the investment to purchase one share will be $5.04. If the company pay the dividend of $2.04 per share annually, the share value should increase to $45 in the next year to secure your benefit ($5.04). Therefore, the cost of equity is to cope with the risk of share price’s changes and the dividends paid by the company. There are two techniques to obtain the cost of equity as follows:
| 1) Capital Asset Pricing Model (CAPM) |
As you know, the Capital Asset Pricing Model (CAMP) establishes a rational relationship between Non-Diversifiable risk and return of all assets due to all companies can eliminate or decrease Diversifiable risk by playing on the type and return of assets.
Here is the formula of CAPM:
Rs = Rf + [ b * (Rm – Rf)]
Where:
Rs: Cost of equity
Rf: Risk – free rate of return (commonly measured by the return on a U.S. Treasury bill)
Rm: market returns (return on the market portfolio of assets)
b: beta coefficient or index of non- diversifiable risk for all assets of company
(Rm – Rf): market risk premium
Referring to above formula, we should find true data and assumptions for Rf, Rm, and beta (B).
At the first, we should consider FRICTO analysis (Flexibility, Risk, Income, Control, Timing and Others).
In this case, the timing is very important factor. We have to recognize what is NorthPoint’s timing. Would it be ok a short term investment or long term? What will be the period of investment?
Let me remind you about previous article mentioned as follows:
“ "She should use current yields on US Treasuries 3 to 12 months at 3.59% because the yield curve is upward sloping. Upward sloping yield curve means that North Point Group should rely to short-term financing instead of long term financing. In fact, by short term financing, the manager can use cheaper cost of equity. It means that North Point Group should sell the purchased shares of Nike during the period of one year.”
Therefore, my suggestion to NorthPoint is a short – term investment for the period of one year. Consequently, we should consider Rf = 3.59%
Regarding to Exhibit (4), we have Nike Historic Betas.
What is our choice for beta? Do we focus on the average (0.8)?
Let me tell you my analysis as follows:
According to the short term investment and the graph of Nike share price performance relative to S & P 500 presented in Exhibit (4), we can see the interaction between beta (B) and share price of Nike / S &P500 index. In early 2000 (Feb & Mar), Nike / S&P500 = 0.55 that it presents us more risky shares of Nike so that beta is also high (0.83). Higher beta (B) indicates that its return is more responsive to the changes of market returns. Therefore, higher beta is more risky.
But after July 2000, we can see a significant increase of Nike / S&P500 until July 2001 (the time of this case) in which it shows lesser risk of investment for Nike’s share price and we have beta (B) equal to 0.69
In the result, I assumed beta equal to 0.69 (B = 0.69) for a short term investment.
According to Exhibit (4), we have two types of Historical Equity Risk Premiums (Rm – Rf), Geometric mean and Arithmetic mean.
Which one should we consider?
In finance, we usually choose geometric mean because it is a better estimate for longer life valuation while the arithmetic mean is better for a one-year estimated expected return. For longer life valuation, we can find stable valuation. But I would like to refer you to the paper submitted by www.mit.edu that citation is as follows:
Jacquier, E., Kane, A., & Marcus, A. (2002, Dec 18). Geometric or Arithmetic Mean: A Reconsideration. Forthcoming: Financial Analysts Journal. Retrieved May 20, 2003, from http://web.mit.edu/~jacquier/www/papers/geom.faj0312.pdf
According to this paper, the proper compounding rate is in – between these two values. Therefore, I consider 6.7% as market risk premium.
(5.9% + 7.5 %) / 2 = 6.7%
Now, we can calculate the cost of equity as follows:
Rs = 3.59% + [0.69 * (6.7%)] = 8.21%
I also analyzed a long term investment (please see my spreadsheet) in which I used the adjusted beta in the reference with Blume's technique; it is assumed that all of beta in the future will reach to 1. I chose this technique because it presents us the sense of the future for beta instead of historic beta. (Adjusted Beta = 0.343 + 0.677 Bh)
In the case of long term investment, the cost of equity is equal to 10.61% where I considered Bh = 0.8
You can compare the cost of equity for long term and short term investment.
2) The Constant-Growth Valuation (Gordon) Model
We as well as know that the value of a share of stock is equal to the present value (PV) of all future dividends, which in one model were assumed to grow at a constant annual rate over an infinite time horizon (Gordon Model) in which we have below formula:
Po = D1 / (Rs – g)
Where:
Po: Value of common stock
D1: Per – share dividend expected at the end of year 1
Rs: Required return on common stock
g: Constant rate of growth in dividends
According to my spreadsheet and Exhibit (4), Rs is calculated as follows:
Rs = D1/P0 + g
= 0.24 / (42.09+0.063)
= 6.87%
Since Nike did not pay any dividend after June 30, 2001(see Exhibit 4), I rejected this model because it does not reflect the true cost of capital.
Weighted Average Cost of Capital (WACC)
CAPM was found to be more superior to other methods of calculating cost of equity, hence the cost of equity used in the WACC is one derived by CAPM. At this point, I calculated the WACC of Nike Inc. using the weights and costs of debt and equity. The formula used is as follows:
WACC = wd*kd (1-T) + we*ke
= [10.2%*8.59 ( 1-38%)] + [89.8%*8.21%]
= 0.54% + 7.38%
= 7.92%
The weighted average cost of capital for Nike Inc. is equal to 8.27 percent.
EVALUATION
Kimi Ford used a discount rate of 11 percent to find a share price of $43.22. This makes Nike Inc. share price undervalued as Nike is currently trading at $42.09. I already told you this discount rate does not reflect the true market value and solved for a discount rate that would be more accurate.
I found the weighted average cost of capital by using CAPM that presented a discount rate of 7.92 percent. This discount rate results in a share price of $75.8*, meaning that Nike Inc. is undervalued by $33.71 per share ($75.8 - $42.09).
(Refer to sensitivity analysis table in exhibit 2).
DECISION
Using this data, I found that Nike Inc. should be added to the NorthPoint Large-Cap Fund at this time because the stock is undervalued and I can say to you that the safety factor is equal to 1.8 (Fs = 75.8 / 42.09). Whereas I have still doubt on projection analysis done by Kimi Ford.
Appendix
Now, let me bring you my detail calculations to explain my spreadsheet about the cost of debt (Method (2): Based on calculating the IRR) as follows:
Calculation of cost of debt by using IRR method:
Note: “All spreadsheets and calculation notes are available. The people, who are interested in having my spreadsheets of this case analysis as a template for further practice, do not hesitate to ask me by sending an email to: soleimani_gh@hotmail.com or call me on my cellphone: +989109250225. Please be informed these spreadsheets are not free of charge.”
To be continued .......
