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Session 8: Weights and Cost of Capital
Dynamics
Aswath Damodaran
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Weights for Cost of Capital Calculation
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The weights used in the cost of capital computation should be market
values.
There are three specious arguments used against market value
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Book value is more reliable than market value because it is not as volatile: While it
is true that book value does not change as much as market value, this is more a
reflection of weakness than strength
Using book value rather than market value is a more conservative approach to
estimating debt ratios: For most companies, using book values will yield a lower
cost of capital than using market value weights.
Since accounting returns are computed based upon book value, consistency
requires the use of book value in computing cost of capital: While it may seem
consistent to use book values for both accounting return and cost of capital
calculations, it does not make economic sense.
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Disney: From book value to market value for debt…
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In Disney’s 2008 financial statements, the debt due over time was
footnoted.
No maturity was given for debt
due after 5 years. I assumed 10
years.
Disney’s total debt due, in book value terms, on the balance sheet is
$16,003 million and the total interest expense for the year was $728
million. Assuming that the maturity that we computed above still holds
and using 6% as the pre-tax cost of debt:
Estimated MV of Disney Debt =
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é
1
ê (1 (1.06)5.38
728ê
.06
ê
êë
ù
ú 16,003
ú+
= $14,962 million
5.38
(1.06)
ú
úû
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And operating leases…
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The pre-tax cost of debt at Disney is 6%.
Year
1
2
3
4
5
Commitment
$392.00
$351.00
$305.00
$265.00
$198.00
Present Value
$369.81
$312.39
$256.08
$209.90
$147.96
6&7
Debt Value of
leases =
$309.50
$424.02
Disney reported $619 million in
commitments after year 5. Given
that their average commitment
over the first 5 years of $302
million, we assumed two years @
$309.5 million each.
$1,720.17
Debt outstanding at Disney
= MV of Interest bearing Debt + PV of Operating Leases
= $14,962 + $ 1,720= $16,682 million
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Aswath Damodaran
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Current Cost of Capital: Disney
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Equity
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Debt
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Cost of Equity = Riskfree rate + Beta * Risk Premium
= 3.5% + 0.9011 (6%) = 8.91%
Market Value of Equity =
$45.193 Billion
Equity/(Debt+Equity ) =
73.04%
After-tax Cost of debt =(Riskfree rate + Default Spread) (1-t)
= (3.5%+2.5%) (1-.38) =
3.72%
Market Value of Debt =
$ 16.682 Billion
Debt/(Debt +Equity) =
26.96%
Cost of Capital = 8.91%(.7304)+3.72%(.2696) = 7.51%
45.193/ (45.193+16.682)
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Dealing with Hybrids and Preferred Stock
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When dealing with hybrids (convertible bonds, for instance), break the
security down into debt and equity and allocate the amounts
accordingly. Thus, if a firm has $ 125 million in convertible debt
outstanding, break the $125 million into straight debt and conversion
option components. The conversion option is equity.
When dealing with preferred stock, it is better to keep it as a separate
component. The cost of preferred stock is the preferred dividend yield.
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Decomposing a convertible bond…
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Assume that the firm that you are analyzing has $125 million in face value of
convertible debt with a stated interest rate of 4%, a 10 year maturity and a
market value of $140 million. If the firm has a bond rating of A and the
interest rate on A-rated straight bond is 8%, you can break down the value of
the convertible bond into straight debt and equity portions.
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Aswath Damodaran
Straight debt = (4% of $125 million) (PV of annuity, 10 years, 8%) + 125
million/1.0810 = $91.45 million
Equity portion = $140 million - $91.45 million = $48.55 million
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Debt ratios for private businesses
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While the temptation is to go with book values for debt and equity,
you should steer away from them. There are three alternatives you can
employ.
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Use the industry average market debt ratio, obtained by looking at publicly traded
companies in the sector, to estimate the cost of equity and capital.
Use an estimated market value of equity, based upon applying a multiple (say a PE
ratio) to your private company’s earnings to arrive at a debt to equity ratio.
Use your DCF estimates of equity and debt value to compute your cost of capital.
Since you will need the cost of capital to arrive at these estimates, this will create
circularity in your valuation. If you are willing to use the iteration function in
Excel, you should be still able to work with the circularity.
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Target versus Actual Debt Ratios
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The actual debt ratio for a firm reflects what the current management
of the firm has chosen as the appropriate debt ratio. To the extent that
the managers have either been too conservative or too extreme in the
use of debt, the “right” debt ratio for the firm may be different from
the actual.
To estimate this “right’ or “target” debt ratio, analysts use one of three
choices:
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An arbitrary number, based upon gut feeling and experience
An industry average for the industry in which your company operates
An “optimal” debt ratio that minimizes your cost of capital
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Computing an optimal debt ratio
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Should you value your business using the target or optimal?
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If you are valuing a business for a sale or acquisition, it does make
sense to use the target debt ratio, since the acquirer can reset the debt
ratio at the time of the acquisition.
If you are valuing a business as a passive investor or observer, you
may be better off using the actual debt ratio, since the existing
managers will continue to run the firm (and presumably keep intact
their views of debt).
If you are uncertain about who will be running the business in the
future (existing managers or a new owner), you can either
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Change the debt ratio gradually over time from the actual to the optimal
Do two valuations, one with the actual and one with the optimal, and take an
expected value.
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Changing risk profiles & changing costs of capital
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When valuing young, growth firms, the cost of capital at the start of
your valuation should reflect the high risk of the firms (high costs of
equity) and their inability to borrow money (low or no debt). As a
result, your cost of capital will be high.
As you bring down the growth rate of the firm over time and make it a
more mature business (with higher revenues & profits), you should
expect
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The cost of equity to change over time, as your risk moves towards the average for
the sector or the market.
The debt ratio to rise, as earnings and cash flows go up
The cost of capital to drift down towards the average for the market (or the sector).
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Back to the beginning…
Assets
Value of investments already
made by the company over it's
history. The value is updated to
reflect their current cash flow
potential.
Value of investments the
company is expected to take into
the future. This value rests on
perceptions of growth
opportunities.
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Liabilities
Assets in Place
Debt
Lenders, both short and long
term, get first claim whatever
cash flow is generated by the
firm.
Growth Assets
Equity
Equity investors get whatever is
left over, after meeting the debt
obligations.
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