Looking at the regressions of publicly traded firms that yield the
bottom-up beta should provide an answer.
The average R-squared across the high-end retailer regressions is 25%.
Since betas are based on standard deviations (rather than variances), we
will take the correlation coefficient (the square root of the R-squared) as
our measure of the proportion of the risk that is market risk.
Total Unlevered Beta
= Market Beta/ Correlation
with the market
= 1.18 / 0.5 = 2.36
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The final step in the beta computation: Estimate a
Debt to equity ratio and cost of equity
With publicly traded firms, we re-lever the beta using the market D/E
ratio for the firm. With private firms, this option is not feasible. We have
two alternatives:
Assume that the debt to equity ratio for the firm is similar to the average market
debt to equity ratio for publicly traded firms in the sector.
Use your estimates of the value of debt and equity as the weights in the
computation. (There will be a circular reasoning problem: you need the cost of
capital to get the values and the values to get the cost of capital.)
We will assume that this privately owned restaurant will have a debt to
equity ratio (14.33%) similar to the average publicly traded restaurant
(even though we used retailers to the unlevered beta).
Levered beta = 2.36 (1 + (1-.4) (.1433)) = 2.56
Cost of equity =4.25% + 2.56 (4%) = 14.50%
(T Bond rate was 4.25% at the time; 4% is the equity risk premium)
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Estimating
a cost of debt and capital
While the firm does not have a rating or any recent bank
loans to use as reference, it does have a reported operating
income and lease expenses (treated as interest expenses)
Coverage Ratio = Operating Income/ Interest (Lease) Expense
= 400,000/ 120,000 = 3.33
Rating based on coverage ratio = BB+
Default spread = 3.25%
After-tax Cost of debt = (Riskfree rate + Default spread) (1 – tax rate)
= (4.25% + 3.25%) (1 - .40) = 4.50%
To compute the cost of capital, we will use the same industry
average debt ratio that we used to lever the betas.
Cost of capital = 14.50% (100/114.33) + 4.50% (14.33/114.33) = 13.25%
(The debt to equity ratio is 14.33%; the cost of capital is based on the
debt to capital ratio)
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Step 2: Clean up the financial statements
Stated
Adjusted
Revenues
$1,200
$1,200
- Operating lease expenses
$120
Leases are financial expenses
- Wages
$200
$350
! Hire a chef for $150,000/year
- Material
$300
$300
- Other operating expenses
$180
$180
Operating income
$400
$370
- Interest expnses
$0
$69.62
7.5% of $928.23 (see below)
Taxable income
$400
$300.38
- Taxes
$160
$120.15
Net Income
$240
$180.23
Debt
0
$928.23
! PV of $120 million for 12 years @7.5%
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Step 3: Assess the impact of the “key” person
Part of the draw of the restaurant comes from the
current chef. It is possible (and probable) that if he sells
and moves on, there will be a drop off in revenues. If you
are buying the restaurant, you should consider this drop
off when valuing the restaurant. Thus, if 20% of the
patrons are drawn to the restaurant because of the chef’s
reputation, the expected operating income will be lower
if the chef leaves.

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