The Structural Agency Solution to
Determine
Going Concern Status
黃佳婷
黃怡嘉
2009/05/22
1
Outline
•
•
•
•
•
•
Introduction
Structural Agency Problem
The Agency Cost
The Going Concern Decision
Case Study: Lucent Technologies Inc.
Conclusion
2
Introduction
• This paper presents a positive theory to
determine a firm’s going-concern for auditing
• Structural agency problem
– the different maturity structure of the debt and
– insufficient asset value (=‘negative equity value’)
• Using an option-theoretic approach
– in a multi-period setting
3
Outline
•
•
•
•
•
•
Introduction
Structural Agency Problem
The Agency Cost
The Going Concern Decision
Case Study: Lucent Technologies Inc.
Conclusion
4
Structural Agency Problem
Assets < Debts
Default
1. 無法發新股票
2. 無法發新債
An agency problem occurs
Share holders
1. 有能力支付下期的
debt payment
2. 繼續控制公司
3. 逃避default
Debt holders
1. 沒有權力去查帳
2. 無法限制股東賣資產
5
Structural Agency Problem
• 償債方式：發新股票、發新債、賣資產….
• Geske (1977)
– 假設沒有structural agency problem
– a multi-period capital structure model under the BlackScholes assumptions
– 償債方式：發新股票
– 無法發新股票等同於default
• 這篇論文
– 假設有structural agency problem
– 從兩種不同的假設計算agency cost
6
Structural Agency Problem
• A simple numerical example
– Two zero coupon debts
• one and two years to maturity
• both are $100 face value
–t=0
– the risk free rate
is about 10%
230
7
Structural Agency Problem
• t=1
• the asset
grows to $450
raise equity
• Geske (1977)
the firm should
raise equity to
pay for the first
debt
8
Structural Agency Problem
• t=1
• the asset
drops to
$150
raise equity
• the second debt is priced at $75
– due to higher risk
• the new equity owner pays $100 in cash but
in return receives a portion of $75
9
Structural Agency Problem
• t=1
• the asset
drops to
$150
raise equity
• the second debt is priced at $75
– due to higher risk
• the new equity owner pays $100 in cash but
in return receives a portion of $75
10
Structural Agency Problem
• t=1
• The (breakeven) asset
value is falls to
$186.01
raise equity
• The second
debt is worth
$86
• The default
point is $186
11
Structural Agency Problem
The relationships between the market value of debt (twoyear debt at year 1) and market value of asset in previous
examples.
raise equity
12
Structural Agency Problem
• t=1
• The default point
is $186
sell assets
• Selling assets
cause the second
debt to drop
• the equity
immediately has
an option value
at the cost of the
remaining debt
13
Structural Agency Problem
• t=1
• The default point is
$186
new debt
• The principal of the
new debt can be
extremely high
• It should not matter if
the funds come from
new equity or new
debt at just over
break-even point
14
Structural Agency Problem
• Companies will receive a going concern opinion
• at $186
– breakeven point using the Geske Model (1977)
– The firm cannot raise equity
• at $150
–
–
–
–
the firm cannot raise equity
sell assets to pay the senior debt
the junior debt will be worth less than $50
The transferring of wealth from debt owner to equity
owner is what we define as the agency problem
15
Structural Agency Problem
Figure 2 gives a plot of the equity value versus asset value
for the example of 186 breakeven point at time 1 of $186
using the Geske Model (1977).
16
Structural Agency Problem
Figure 3: Default Difference and the Cause of Agency Problem
Using the Geske
Model (1977)
100 150
186
17
Structural Agency Problem
• Geske (1977) model
– at the due date of the first debt, the company faces a
decision whether to pay the coupon
– if the company decides to pay, the company continues
to survive much like exercising the compound option
to keep the option alive
– The company’s survival criterion
• whether the company can raise new equity capital
• the market value of the assets must stay above the market
value of the liabilities at the moment of the coupon.
18
Outline
•
•
•
•
•
•
Introduction
Structural Agency Problem
The Agency Cost
The Going Concern Decision
Case Study: Lucent Technologies Inc.
Conclusion
19
The Agency Cost
• A model of the structural agency problem in a
two-period Geske framework
– The way that immediate debt payments can be
paid:
• Excess liquidity
• Selling assets
– Ki : coupon at t=i
– Ai : the total asset value at t=I
The Agency Cost
• At t=1
– Asset value
dAt
 rdt  dWt
At
r : risk free rate, σ : volatility, Wt : the Wiener process
– Equity value
E1  C ( A1 , K 2 , r ,  , h)
 e rh E1[max{ A2  K 2 ,0}]
 A1 N (d   h )  e rh K 2 N (d )
1
ln A1  ln K 2  (r   2 )h
2
where d 
 h
The Agency Cost
• At t=1
– Debt value
D1  A1  E1
 A1[1  N (d   h )]  e  rh K 2 N (d )
– Balance table
Before Coupon
Equity
Debt
Total Asset
After Coupon
E1  K1
E1
D1  K1  A1  E1  K1
D1  A1  E1
A1
A1
The Agency Cost
• At t=1
– Default condition
 E1  K1  0

 A1  D1  K1  0
A  K  D
1
1
 1
– Critical asset value
•
• E1-K1=0
• The default point for the firm
The Agency Cost
• Under Credit Risk
– The firm can continue to operate when
E1 < K1 < A1
– The conceptual equity value is negative
• Creates the agency problem
The Agency Cost
• Equity value
E1*  C (( A1  K1 )  , K 2 , r ,  , h)
e  rh E1[(( A1  K1 )e ( r 0.5

0
2
) h  h z
 K 2 ) ]
( A1  K1 ) N (d *   h )  e  rh K 2 N (d * )

0
where
1
ln( A1  K1 )  ln K 2  (r   2 )h
2
d* 
 h
A1 > K 1
A1 ≦ K1
A1 > K 1
A1 ≦ K1
The Agency Cost
• Agency cost
AC  E1  E1
*
The Agency Cost
• The n-period Agency Model
– Between any two coupon periods we divide the
state space into k+1 partitions
– A  A u d , u  e , d  u1 , h  Tn
– At maturity ( i  n ),
j
ij
ik  j
h
0
• Enj  max Anj  K n ,0 for all j
–
 rh k k j1

( k  j1)
E ij  max e  C j1 p (1  p)
Ei 1, j  j1  Ki ,0
j10


e rh  d
,where p  u  d
The Agency Cost
• Equity value with agency cost
– At maturity, Enj*  Enj  max Anj  Kn ,0
–
 sj
xi 0

 Ai 0
*
Eij  
Ai , j11  s j
 s j  Ai , j1 x
xi , j1
i , j11 
 Ai , j11  Ai , j1
Ai , j11  Ai , j1

,where xij  e
 rh
k
C
j10
k
j1
p j1 (1  p)( k  j1) Ei*1, j  j1
and
Ai 0  s j
Ai , j1  s j  Ai , j11
s j  max Aij  K i ,0
The Agency Cost
• The payoffs at Tn-1
– An-1 > Kn-1
– An-1 ≤ Kn-1














debt expiring at n-1=Kn-1
debt expiring at n=present value of min An , K n 
En1  present value of max An  K n ,0 K n1
debt expiring at n-1=An-1
debt expiring at t  0
En 1  0
Outline
•
•
•
•
•
•
Introduction
Structural Agency Problem
The Agency Cost
The Going Concern Decision
Case Study: Lucent Technologies Inc.
Conclusion
30
The Going Concern Decision
• Characteristic of the model
– The structural agency problem results from K1 and
– is define as “should be default point”
– E1*  Ei , and as the asset value increases, AC
approaches zero
– The max agency cost always happen at
– Default barrier
The Going Concern Decision
• The “going concern index”
E*  E
AC
GCI 

*
max( E  E ) MAC
– MAC: the max agency cost,
appears at
Outline
•
•
•
•
•
•
Introduction
Structural Agency Problem
The Agency Cost
The Going Concern Decision
Case Study: Lucent Technologies Inc.
Conclusion
33
Case Study: Lucent Technologies Inc.
• Lucent’s trouble began in late 1999 as their stock
price fell sharply and debt mounted
• The Lucent scandal coincided with the internet burst
in 2000
– These two figures show that the overall market losses
were less than Lucent’s losses after the burst of the
internet bubble
Case Study: Lucent Technologies Inc.
Case Study: Lucent Technologies Inc.
• Under pressure to meet revenue goals, Lucent in 1999 began
to give large discounts to meet projected sales numbers and
began extending more credit to service providers to win their
business
• The company could no longer
artificially inflate its earnings,
and the company started to
crumble
Case Study: Lucent Technologies Inc.
• The board took action and fired CEO
• Moreover as related to our agency costs, from 2001 to 2003
Lucent started to sell their assets and cut their work force to
avoid default
Case Study: Lucent Technologies Inc.
• The agency problems with
Lucent are not significant
from 1997 to 2000
• The agency problem starts to
grow as their financial
deteriorates sharply in 2001
• In these two years the asset
values are all below the
implied default point
making the equity E measures
all equal to 0
Outline
•
•
•
•
•
•
Introduction
Structural Agency Problem
The Agency Cost
The Going Concern Decision
Case Study: Lucent Technologies Inc.
Conclusion
39
Conclusion
• The nontraditional, structural agency
problem is the major consideration in
firms that can no longer operate as
going concerns
• A cut-off rule for those firms that we feel
should not receive a clean audit per
their going concern status
– use Geske’s rule (1977) to correctly
measure for insolvency under no agency
problem conditions
– derive a model under the existence of the
agency problem
• Take Lucent Technology as an example
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