Marriott Corporation: The Cost of Capital
The risk premium will differ across all divisions, because this is the market (all assets) return versus the respective risk free rates for each division. In computing the risk premium, we should use the arithmetic returns for both the T-bills and market return for the period of 1927-1987. We are using the arithmetic average because the geometric average tends to underestimate the expected return. A reason for favouring the arithmetic mean is given in Kolbe et. al. (1984):
Note that the arithmetic mean, not the geometric mean, is the relevant value for this purpose. The quantity desired is the rate of return that investors expect over the next year for the random annual rate of return on the market. The arithmetic mean, or simple average, is the unbiased measure of the expected value of repeated observations of a random variable, not the geometric mean…the geometric mean underestimates the expected annual rate of return.
Lodging
We use a long period to calculate returns because we want to capture the effects of economic expansion and contraction. We select long term US Government Bond returns because we are focusing on a long term investment:
Rf = 4.58% (page 10, Long-Term US Government Bond Returns, arithmetic average)
Rm = 12.01% (page 10, S&P 500 Composite Stock Index Returns, arithmetic average)
Risk premium: Rm - Rf = 12.01% - 4.58% = 7.43%
As explained above, given that it is a long term project, the risk premium is 7.43%. For our beta calculations, we will take the average of our comparables:
Company Unlevered Beta
Hilton BL: 0.88 - BU: 0.81
Holiday BL: 1.46 - BU: 0.48
La Quinta BL: 0.38 - BU: 0.17
Ramada BL: 0.95 - BU: 0.47
AVERAGE BU: 0.48
To unlever beta, we used the following formula: BU = BL / [1+ (D/E) (1-T)]. For the tax rate, we calculated the effective tax rate of Marriot for the years