Cost of Equity:
For the risk-free rate, we decided to use the 30-year old Treasury yield, which is currently 4.6%. We believe it is important to match the time horizon when comparing financial assets. Given that stocks have essentially an endless time horizon, the 30-year Treasury seems a more reasonable asset by which to compare stocks. 1-month Treasury Bills, for instance, are comparable to safety-deposit boxes, which are completely safe, but cannot ever yield a return. It’s highly likely that no financial analyst would ever compare a stock to a deposit box; hence, it also doesn’t make sense to compare stocks with very short-term Treasury Bills. For the beta of Papa John’s equity (PZZA), we regressed the monthly return on PZZA with the monthly return on the S&P 500 index. Through doing so, we determined that PZZA had a market beta of 0.53. (Please refer to the attached spreadsheet for calculations of beta.) We also used the Ibbotson estimate for market premiums based on data from 1926-2009. Specifically, we decided that over the long run, geometric mean is more reflective of true risk premiums than arithmetic mean (since arithmetic mean fails to incorporate year-over-year returns, thus producing an overly optimistic result). According to Ibbotson, the geometric mean for returns for large-company stocks was 9.6%. The market premium is therefore 9.6%-4.6% = 5%. We decided to use the returns for large-company stocks because Papa John’s is already an established corporation with substantial market capitalization. Since the S&P 500 index is our benchmark, it makes more sense to use the market returns of large company stocks than those of small company stocks. Therefore, the cost of equity for Papa John’s is 0.046+0.53(0.05) = 7.25%.
In order to determine which companies were “comparable” to Papa John’s, we used two main criteria. First, the company would have to be in the food service industry, though not necessarily directly in pizzas. Second, the company...
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