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Capital Structure in Banks 227
critical threshold at which a bank goes into default). Hence, we also extract
the following two percentages from annual reports:
ST% = Customer and short-term liabilities as percent of total assets
Other% = Other (long-term) liabilities as percentage of total assets
Additionally, we assume that all off-balance sheet liabilities will become
due immediately if the bank approaches default. Since we use annual financial
statement figures and apply the information from publicly available
ratings, we set the horizon for our analysis to T = 1.
Therefore, as a first proxy, we estimate the default point DP′ as:
⎛
⎞
DP′= ⎜ ST + Other BVA
BV
⎝
% 1
2
%⎟ ⎠
× +
where ′ = indicates a first proxy.
OBS
(5.50) 441
Contrary to the value of bank debt, the market value of equity (V E
) is
fairly easy to observe. We can derive V E
either by calculating (share value)
× (number of shares outstanding) or by directly taking sanitized market values
from sources such as Datastream.
Therefore, we are able to calculate as a starting point for our estimations
the market value of assets V A
′ as:
V A
′ = DP′ + V E
(5.51) 442
As we saw in the Merton approach, we can view the (market) value of
equity as a call option on the underlying assets of the firm. Using the Black-
Scholes option-pricing formula for European call options, we can therefore
write: 443 −⋅ rT
VE
= VA′ ⋅N( d1) − DP′⋅e ⋅N( d2 )
(5.52)
where:
d
1
2
⎛ VA′
⎞ ⎛ σ ⎞
A
ln⎜
⎟ + r + T
⎝ DP′
⎜
⎠ ⎝ 2
⎟
⎠
⋅
=
σ ⋅ T
A
441 Basically following Ong (1999), pp. 83–84.
442 This approach is also used by other authors. For example, Mian (1996), p. 420,
and Tufano (1996), p. 1108, use as a proxy for firm size, book value of assets minus
book value of common equity plus market value of common equity = firm value.
443 See Hull (1997), p. 241.