Case 1: Marriott Corporation
Submitted on October 7, 2019
1. Estimate asset betas for the lodging, restaurant, and contract
service divisions.
We estimate asset betas of Lodging and Restaurant division by using the
asset beta of comparable company. Since there is some extreme value in
the betas of comparable company, we choose to use median of their beta
instead of the average.
The table below shows the value of each factor and their source
Factor
Source
Value
𝜷𝒂𝒔𝒔𝒆𝒕(𝑳𝒐𝒅𝒈𝒊𝒏𝒈 𝒅𝒊𝒗𝒊𝒔𝒊𝒐𝒏)
Comparable company’s asset beta
0.32
𝜷𝒂𝒔𝒔𝒆𝒕(𝑹𝒆𝒔𝒕𝒂𝒖𝒓𝒂𝒏𝒕 𝒅𝒊𝒗𝒊𝒔𝒊𝒐𝒏)
Comparable company’s asset beta
0.68
Since the asset beta for the company is the weighted average of each
division’s beta. We can derive the asset beta for contract division.
The formula to calculate asset beta by equity beta is below:
𝛽45567 =
𝐸
𝐷
× 𝛽6<=>7? + × 𝛽B6C7
𝑉
𝑉
And we assume that 𝛽B6C7 = 0.
Factor
𝛽45567(EFGH4I?)
Asset proportion of
lodging division
Asset proportion of
Source
Derived from 𝛽6<=>7?(EFGH4I?) provided by
the case
Derived from the proportion of
identifiable asset (Exhibit 2)
Derived from the proportion of
1
Value
0.39
61%
12%
restaurant division
identifiable asset (Exhibit 2)
Asset proportion of
Derived from the proportion of
contract division
identifiable asset (Exhibit 2)
𝜷𝒂𝒔𝒔𝒆𝒕(𝑪𝒐𝒏𝒕𝒓𝒂𝒄𝒕)
Calculated by method mentioned before
27 %
0.41
2. Calculate equity betas for each of the three divisions using their
respective target leverage ratios.
As we already have the asset beta, we can calculate equity beat by the
formula below, as we assume 𝛽B6C7 = 0
𝛽6<=>7? = 𝛽45567 ∗
𝑉
𝐸
Factor
Source
Lodging
Restaurant
Contract
Debt percentage
Table A of Case
74%
42%
40%
Equity percentage
Table A of Case
26%
58%
60%
𝜷𝒆𝒒𝒖𝒊𝒕𝒚
Calculate by formula above
1.23
1.13
0.71
3. Using the asset betas and equity betas in Questions 1 and 2,
calculate the all equity opportunity cost of capital (ra ) for each of
the divisions as well as the cost of equity (re ) for each of the
divisions at their respective target leverage ratios. For each
division, compare the ra and the re . Why are the re’s larger than
the ra’s ?
Marriott used the Capital Asset Pricing Model (CAPM) to estimate the
cost of equity:
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Expected return = Risk-free rate + equity beta*[Risk premium]
As stated in the case, lodging assets like hotels, had long useful lives, so
we choose the 30-year government bond rate of 8.95% (see in Table B)as
the riskfree rate for lodging division; as for the restaurant and contract
services divisions, we use shorterterm government bond of 6.90% as the
riskfree rate, because those assets had shorter useful lives.
Market risk premium can be obtained from Exhibit 5: We prefer the
arithmetic average, because CAPM is a single-period model and
arithmetic mean is better at estimating the average risk premium for the
next year. So the Spread between S&P 500 Composite Returns and LongTerm U.S. Government Bond Returns from 1926 to 1987(which is 7.43%)
can be used as the risk premium of the lodging division, while Spread
between S&P 500 Composite Returns and Short-Term Treasury Bill
Returns from 1926 to 1987(which is 8.47%) can be used as the risk
premium of the restaurant and contract divisions.
Factor
Lodging
Restaurant
Contract
rf
8.95%
6.90%
6.90%
β(equity)
1.23
1.13
0.71
rm-rf
7.43%
8.47%
8.47%
re
18.08%
16.45%
12.88%
Marriott measured the opportunity cost of capital using the weighted
average cost of capital (WACC):
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Ra=WACC = (1-t)rd (D/V) + re (E/V)
The tax rate can be calculated by (income tax)/ (income before tax) in 1987,
the data is given in Exhibit 1:
Period
Income before income tax
Income tax
Tax rate
1987
398.90
175.90
0.44
Target D/V and E/V and the cost of debt, which is calculated by adding
specific risk premium to the riskfree rate are shown in the Table A:
Rd= riskfree rate + Debt Rate Premium above Government
Calculation for all equity opportunity cost of capital (ra)
Factor
Lodging
Restaurant
Contract
1-t
0.56
0.56
0.56
D/V
0.74
0.42
0.40
E/V
0.26
0.58
0.60
rf
8.95%
6.90%
6.90%
Credit Spread
1.10%
1.80%
1.40%
rd
10.05%
8.70%
8.30%
ra
8.86%
11.59%
9.58%
The reason why re’ are larger than the ra’s is that the equity holder often
takes more risk than the creditors, so re is usually higher than rd.
Mathematically, according to the formula of WACC:
ra=(1-t)*rd*(D/V) + re*(E/V) ≤ (1-t)*re*(D/V)+re*(E/V)=re-t*re*D/V ≤ re
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4.If Marriott used a single cost of capital for evaluating investment
projects for all lines of business, what would happen to the company
over time.
We use the formula mentioned in the case to calculate Marriott’s WACC.
(The tax rate is been calculated by income tax/ income before tax):
WACC = (1 − t)r (D/V) + r (E/V).
As stated in the case, Marriott used the cost of long-term debt for its
Lodging cost-of-capital calculation and short-term one for the other two
divisions.Therefore, we choose corresponding rates to do the evaluation.
Marriott’s three divisions are from different business area and have
totally different leverage ratios. If Marriott used a single cost of
capital(𝑊𝐴𝐶𝐶RFGH4I? = 9.9%) for evaluating all its divisions, proper
investment opportunities could be rejected while improper ones be
accepted. An investment opportunity which will yield a positive NPV for
Lodging division(𝑊𝐴𝐶𝐶VFBW>IW = 8.86%) could be rejected. While at the
same time, projects resulting in a negative NPV and reduced cash flow in
restaurant division (𝑊𝐴𝐶𝐶Z6574=[4I7 = 11.59%)could be accepted. Over
time, Lodging and Contract Service divisions would have to take
improperly high risk, while restaurant division would suffer a loss. This will
terribly harm Marriott’s performance and destroy the interest of
shareholders.
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