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Adding Value by Post-loss
Financing- I
Lecture 7
Dr. Tahir Khan DurraniCEngr, MCIT, ACII, MSc, MPhil, CMBA, PhD
Meditation for the week:
“When looked at with proper perspective, difficult
situations always yield valuable lessons.”
“Believing in yourself and your abilities is the first step to
overcoming adversity.”
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Topic Objectives
We examine the implications of
recapitalising the firm after it suffers a
sudden risky event. We examine the use of equity or debt to fund
post-loss investments.
We discuss the post-loss capital structure of
the firm.
We also look at the fundability of post-loss
investment using debt or equity.
Dr. Tahir Khan Durrani 2
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Post-loss Decisions
Should the firm reinvest in productive assets?
Should it undertake new investment activity?
Can these investments add value?
Can they be financed?
If they add value, how should the firm raise money?
Dr. Tahir Khan Durrani 3
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Generic Sources of Funds
Hedging Cost of risky event borne by counter party, firm retains
internal funds and its excess to external funds
Contingent financing
Line of credit with interest rate fixed in advance, hedging risk
in future cost of capital
Put options issued on firm’s own stock
Convertible debt
Post-loss financing
Withholding of dividends
Raising new debt or equity
Dr. Tahir Khan Durrani 4
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Financial Structure Puzzle Modigliani-Miller hypothesis (1958) :
Capital structure is irrelevant under certain conditions: no taxes
all investors are asymmetrically informed
no transaction costs
investment policy of the firm already determined. No advantage for a firm to manipulate its debt-to-equity ratio,
since the effect of any leverage choice on investors can bereplicated by the investors themselves in the management of their portfolios.
Capital structure matters, because of taxes, information cost,transaction costs, or interdependence between the firm’sfinancing and investment policies.
Optimal capital structure is a compromise between costs andbenefits of different sources of finance.
Dr. Tahir Khan Durrani 5
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Corporate and Personal Taxes
Interest income is deductible income, but dividends are not. This creates advantage fordebt financing.
The cost of debt is partly paid by the InlandRevenue
Value of levered firm = value of all-equity firm+ PV (tax shield)
PV (tax shield) =
Dr. Tahir Khan Durrani 6
Dt k
Dk t
c D
E c
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Corporate and Personal Taxes Deductibility of interest thereby increases the
value of disbursement that can be made to thecompany’s security holders.
The size of the pie has been increased by using
debt. But are investors necessarily better off? This depends on personal tax rates.
The slices of the bigger pie still have to be taxed at the personal rate.
It should be immediately apparent that if personaltaxes on equity income are sufficiently smallerthan on debt, investors could be better off without corporate borrowing.
Dr. Tahir Khan Durrani 7
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Corporate and Personal Taxes
The personal rate on equity income iscomplicated by the fact that this income can be in
the form of capital gains or dividend income.
If all equity income were in the form of dividends,
investors would pay the same tax rate on interest
and dividends and corporate borrowing would be
attractive.
But equity income can be in the form of capitalgains, which are taxed at a different rate from
other income and can be deferred until realized.
Dr. Tahir Khan Durrani 8
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Cost of financial Distress
If the risk of the cash flows is fixed, then the higher theleverage, the higher the probability of bankruptcy, andthe higher the expected value of bankruptcy costs.
Indirect costs of bankruptcy, share holders may fail toundertake positive NPV projects that simply shore up thevalue of debt
Value of levered firm = value of all-equity firm
+PV (tax shield)
-
PV (cost of financial distress)
Dr. Tahir Khan Durrani 9
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Recapturing Value through Post-Loss Reinvestment
Does post-loss financing to fundreconstruction or new investment, add valueto existing shareholders?
Do the terms on which new money is raisedpermit value to be created for existingshareholders?
After a big loss, will investors have theconfidence to buy newly issued securities andcan the firm raise enough money for itsinvestment needs?
Dr. Tahir Khan Durrani 10
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Recapturing Value through Post-Loss Reinvestment
Suppose a firm has a loss of value from somerisky event that is not hedged and nocontingent financing available.
To undertake post-loss investment it must useinternal funds available after loss or raise newmoney.
Definitionally, it must use post-loss financing
to fund reconstruction of the destroyed assets,or to fund new investment, add value forexisting shareholders?
Dr. Tahir Khan Durrani 11
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Recapturing Value through Post-Loss Reinvestment
The question can be asked with a different emphasis.
Do the terms on which new money is raised
permit value to be created for existingshareholders?
More pointedly, if a firm has just suffered amajor setback, say a major liability suit, willinvestors have the confidence to buy newlyissued securities and can the firm raise enoughmoney for its investment needs?
Dr. Tahir Khan Durrani 12
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Value of Equity Before a Loss
From previous lecture we derived this equation onthe value of equity:
V(E) = V0 + L - Kt + Vt - D -T
V(E) = Value of equity before a loss
V0 = PV of earnings from existing operations
L = liquid assets
- Kt + Vt = the value added by new investment
D = the existing debt
T = transaction costs of any new issues
Dr. Tahir Khan Durrani 13
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Value of Equity Before a Loss
Firm refinances using debt / equity raises amount denoted by
S. The PV of dividends / interest payment is denoted by R.
Cost of new investment is Kt
V(E) = V0 + L + (S - R - Kt ) + Vt - D -T
Term R represents a set of future payments expressed as thevalue raised S, times the expected rate of return “r”.
R = rS/r = S
R and S cancel out, as these are competitively priced
If existing share holders can attract capital in a competitivecapital market, they only offer a competitive rate of return oncapital raised. They need not share added value with newinvestors. All NPV of new investment is captured by existingshare holders.
Dr. Tahir Khan Durrani 14
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Value of Equity After a Loss
Will investors be willing to pay enough forthese new security issues after a loss to fund
reconstruction of old assets and possibly new
investments? V'(E) = - C + V0' + L - Kt ' + Vt ' - D -T
The primes denotes post-loss values
C is the direct cost of the risky event
Dr. Tahir Khan Durrani 15
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Value of Equity After a Loss
Rewriting the previous equation showingamount new investors pay for a post-loss
security as S.
The PV of expected payments to shareholdersis rS/r, if the new issue is competitively
priced
The bracket in the equation below simplifies to-C,
V'(E) = (S - rS/r - C) + V0' + L - Kt ' + Vt ' - D -T
Dr. Tahir Khan Durrani 16
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Fundability with Post-loss Equity Financing
Is the amount investors are willing to pay,S, sufficient to pay for the capitalinvestment of C?
Existing shareholders hold a total of m
shares & new shares n sold to new investors(n + m), who receive a proportion n/(n+m)of total value of equity ET.
ET
= V0' + L - Kt ' + Vt ' - D -T’ The aggregate sum paid in a competitive
market for new shares is nET/(m + n).
Dr. Tahir Khan Durrani 17
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Fundability with Post-loss Equity Financing
This will be sufficient to raise enough money to pay forrequired post-loss capital needs, C, if.
(ET)n/(m + n) C
which requires n mC/(ET - C), if ET>C
If ET were exactly equal to C, then mathematically Nwould have to be infinite to satisfy the inequality.
There is no value added from continuing to run thefirm, as firm is on the verge of insolvency.
Principle: As long as the cost of post-loss investment is less than the
post-reinvestment value of total equity, it is alwayspossible to finance the investment from a new equityissue.
Dr. Tahir Khan Durrani 18
F d bili i h P l E i
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Fundability with Post-loss Equity Financing
If post-loss investment is fundable, it does not followthat it should be undertaken.
Example:
Chair and Wares makes furniture and expects an earningsstream of £1,000 (after deduction of costs of renewing
plant) indefinitely from its current operations. The firm canreinvest two-year earnings in some product improvement,and expect earnings stream to grow by 2%. Cash at hand is£1,000, with the existing plant and other productive assetshave a replacement cost of £8,000 with a salvage value of £5,000.
The firm has existing debt of £5,000; the cost of debt is 0.05,The firm’s WACC is 0.1. The owners hold 1,000 shares of stock.
Dr. Tahir Khan Durrani 19
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Value of Equity Without New Investment
E = e/(k-g) - D + L
= £1,000/(0.1 - 0) - £5,000 + £1,000
= £6,000
Where:
e = c/f from current operations
g = growth of this cash flow
k = cost of capital
Dr. Tahir Khan Durrani 20
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Value of Equity With New Investment
E = 0/(1 + 0.1) + 0/(1 + 0.1)2 + [1/(1+0.1)2][1,000/(0.1-0.02) -5,000 + 1,000 = £6,331
The new investment adds value (6331 is more than 6000) andshould be undertaken.
Suppose the existing plant suffers an explosion and is uninsured.The plant can still partly operate, and earnings are reduced to£300, but this figure is not expected to grow. However, an
investment of £3,000 will fully restore the plant, and earnings willreturn to the pre-loss level of £1,000.
The firm must raise new money for this reconstruction, but stillplans to pay for the new investment in two years from retainedearnings.
Does the reinvestment add value to equity? What opportunities exist for raising new money by an equity
issue after the loss?
The transaction cost of new issue is £200.
Dr. Tahir Khan Durrani 21
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No Reinvestment
The firm has insufficient funds toundertake the new investments, thevalue is as follows:
V'(E) = 300/(0.1 - 0) - 5000 + 1000
= 0 (limited liability)
The value of equity should be -1000,however because of limited liability,the equity is worthless.
Dr. Tahir Khan Durrani 22
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With Reinvestment They can raise £3,200, with the £200 covering transaction
costs.
V'(E) = - 3,200 + [1/(1+0.1)2][1,000/(0.1-0.02)]
- 5,000 + 1,000 = 3,131
Notice reinvestment is necessary for survival and raises levelof owner’s equity from zero to 3,131.
How many shares must be issued to fund thereconstruction?
The firm needs enough shares to raise 3200 (3000 forreconstruction and 200 for transaction costs. Total value of
equity is 6331 (firm raises 3200 in new equity and existingshares are worth 3131).
The firm need to issue 1,022 new shares. This ensures totalequity of 6331 is divided into a total of 2022 shares, eachworth 3.131.
Dr. Tahir Khan Durrani 23
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No Future Risk It would seem that because the value of equity is
positive after reinvestment, the firm hadsufficient value to pay off all debt (senior debt of 5000 and junior debt of 3200) and still have aresidual value of 3131.
Suppose that the story was as follows. The firm takes the reinvestment and is then is
immediately obligated to sell off the firm anddischarge all claims to existing credits.
The firm would receive the full firm value, 11,331(the earnings stream is worth 10,331 and there iscash of 1000), in a competitive market, and pay5000 to senior creditors and 3200 to juniorcreditors, leaving 3131 to shareholders.
Dr. Tahir Khan Durrani 24
N F Ri k
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No Future Risk Then investors would be willing to pay at par for debt
with a face value of 3200.
But now suppose there is no such obligation to sell thefirm in this way. Can junior bondholders always be surethat they will paid in full in the future?
If the earnings stream of 1000, growing at 2%, wereentirely risk- free, there would be no problem and theanalysis of this paragraph would still apply; the juniordebt would still be worth its face of 3200.
Since there is no future risk, the simply fundabilitycondition for news investors to subscribe fully to new
debt is fulfilled. The condition was V’(F) – D – C > 0, where V’(F) is post -
loss firm value after reinvestment, D is preexisting debt,and C is the capital cost.
The condition fills out as 11,331 – 5000 – 3200 > 0.Dr. Tahir Khan Durrani 25
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Fundability with Post-loss DebtFinancing
Whether debt or equity is used, investors will be
willing to subscribe a sufficient amount to fund the
new investment if the post-loss value of the firm,
minus any pre-existing debt, exceeds the direct cost,
C.
Even if the expected value of E(V'(F)) - C > D, thefirm is still exposed to future risk.
Dr. Tahir Khan Durrani 26
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Fundability with Post-loss DebtFinancing
To see whether investor in a new debt issuewould be willing to pay a sufficient amount forthe firm’s debt to pay for the direct cost, C, wewill simply the default assumption.
The firm may become insolvent directly as aresult of the risky event (i.e., the post-lossvalue of equity, even with reinvestment, is
negative). But even if the post-loss equity value is
positive, future risk could lead to insolvency
and default on debt. Dr. Tahir Khan Durrani 27
d b l h l b
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Fundability with Post-loss DebtFinancing
The firm needs an amount of C to pay for the direct costs.
If debt is raised, the amount subscribed is S, but theface value of the debt is C. the amount S will be equal
to C if the value of the firm, after payment for any seniordebt, exceeds C. In equation, the firm did have pressingdebt of D, so we will call the value of the firm after lossV (F) = V0 + L – Kt +Vt - T.
Furthermore, this value is risk-free because we haveignored future risk.
If the existing debt is senior to any post loss issue, thecondition for S to equal C is that V (F) - D – C > 0.
Dr. Tahir Khan Durrani 28
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Fundability with Post-loss DebtFinancing
But notice that when discussing post-loss debt wehad defined ET= V0 + L – Kt + Vt –D –T.
So clearly, V = ET + D.
Thus, the fundability condition that V(F) – D – C ispositive the same as ET – C is positive.
This is exactly the same fundability condition wederived for post-loss equity financing.
Whether debt or equity is used, investors will bewilling to subscribe a sufficient amount to fund thenew investment if the post-loss value of the form,minus any pressing debt, exceeds the direct cost,C.
Dr. Tahir Khan Durrani 29
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Fundability with Post-loss Debt Financing
We return to Chairs and Wares, and we compute the
post-loss values as follows:No reinvestment:
V(F) = 300/(0.1-0) - 5,000 + 1,000
= 0 (Limited liability)With Reinvestment:
V(F) = -3,200 + [1/(1+0.1)2][1,000/0.1-0.02]
- 5,000 +1,000
= -3,200 + 10,331 - 5,000 + 1,000 = 3,131
Fundability condition is V'(F) - D - C > 0
Dr. Tahir Khan Durrani 30
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Debt or Equity Refinancing
Optimal capital structure after a loss must balance the tax effects, the direct and indirect cost of financial distress.
The tax effect diminishes with leverage, andthus debt is tax-preferred.
The cost of financial distress, includingunderinvestment and asset substitution costs,increase with leverage.
Dr. Tahir Khan Durrani 31
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Debt or Equity Refinancing The issue to be addressed are summarized in
the next Figure.
The solid n- shaped line at the top shows howthe value of the firm depends on the level of
leverage. The value-maximizing capital structure is
identified by the highest point on the curveand is shown as leverage A.
The position and n shape to the value curvestart with the unlevered value line shown as adashed horizontal.
Dr. Tahir Khan Durrani 32
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Debt or Equity Refinancing Taxes reduce value and are shown in the negative
quadrant. The tax effect diminishes with leverage, and thus
debt is tax- preferred.
In contrast, cost of financial distress, includingunderinvestment and asset substitution costs,increase with leverage as shown.
Combining the tax effect of leverage and costs of
distress leads to the n shape in pre-loss value. Now suppose the firm has chosen its optimal
capital structure A and then some risky lossoccurs. There are two major effects:
Dr. Tahir Khan Durrani 33
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The effect of Loss on Leverage The value curve now shifts down to the post-
loss curve.
The downward shift reflects the loss of value.
The downward shift occurs in two stages;
if no post-loss investment is undertaken (i.e.
destroyed assets are not replaced and/ or new
post-loss investment opportunities are not
undertaken), then the loss in value will be
severe.
Dr. Tahir Khan Durrani 34
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The effect of Loss on Leverage The downwards arrow shows the fall in value
curve.
However, much of this lost value can be
recaptured by post-loss investment and the
value curve shifts upwards again towards the
original curve.
As shown, not all pre-loss value is recaptured.
There can be some permanent loss of value if the event shifts demand or leads to an increase
in frictional costs.
Dr. Tahir Khan Durrani 35
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The effect of Loss on Leverage
Dr. Tahir Khan Durrani 36
Cost of Distress
Taxes
LeverageA C
Unlevered
Present
Value Pre-Loss
Post-loss
0
Eff f L f P d i A
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Effects of Loss of Productive Assets The event itself will fall disproportionate on
equity; probably increasing leverage to some
point such as B. If no post-loss investment activity is undertaken,
the firm is likely to be over levered, and positionB does not indeed shows this.
Depending on what level of post-loss investment is undertaken and how it is financed, the post-loss leverage will resettle at some point such as Con the recaptured value curve.
The post-loss optimal capital structure may not be the same as the pre-loss capital structure.
As shown, the optimal post-loss leverage, C, ishigher than pre-loss, B, but it could go the other
way. Dr. Tahir Khan Durrani 37
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Effects of Loss of Productive Assets
Dr. Tahir Khan Durrani 38
Leverage
A C
Unlevered
Present
Value Pre-Loss
AfterPost-loss
Investment
0
Before
Post-lossInvestment
B
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Debt or Equity Refinancing
After a loss the leverage
of the firm changes.
Creditors being
protected by their
priority claim, most of
the fall in value is a
dead-weight cost to
Shareholders.
Thus leverage usually
rises after a loss.
In the post-loss decision on
how to pay for newinvestment, the cost of
financial distress, plays an
important role.
From the high post-lossleverage position,
underinvestment and asset
substitution problems are
more prominent and the firmmay therefore have difficulty
in raising enough debt.
Dr. Tahir Khan Durrani 39
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Framework for Comparing Post-lossDebt and Equity Financing
The before-loss value of equity is:
V(E) = V0 + L + (S - R - Kt ) + Vt - D -T
V(E) = V0 + L - Kt + Vt - D -T
The After-loss value of the original equity is:
V'(E) = (S - rS/r - C) + V0' + L - Kt ' + Vt ' - D –T ‘
V'(E) = - C + V0' + L - Kt ' + Vt ' - D –T ‘
Dr. Tahir Khan Durrani 40
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Framework for Comparing Post-loss Debtand Equity Financing
Equity Refinancing Debt Refinancing
EBITInterestTax
123
123
Net Icome
Cost of Equity, KE
Growth RateValue of Equity, E
456
456
Value of the Firm, V 7 7
No. of Shares (m+n) 8 8
Share Price 9 9
Dr. Tahir Khan Durrani 41
F k f C i P t l D bt
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Framework for Comparing Post-loss Debtand Equity Financing
EBIT Choice of debt/equity
affects direct and
indirect costs of
bankruptcy Interest
Debt financing incurs an
additional interest and
affects the cost of debt due to increased
leverage.
Tax: Debt financing is
advantageous because
interest payment are tax
deductible. Tax benefits from debt
financing rats on both
corporate and personal
tax liabilities. Tax advantage =
(1 - t p)/(1 - t e)(1 - t c)
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Framework for Comparing Post-loss Debtand Equity Financing
Cost of Equity, KE:
Leverage affect the cost
of equity and WACC
depending on the risk
characteristics of c/f.
Growth Rate, gN:
The additional direct
and indirect bankruptcy costs from
additional debt will
affect future earnings.
Value of Equity and
No. of Shares:
There will be dilution
with new issues andthe share price will
reflect values of debt
vs. equity financing to
the firm’s originalowners.
Dr. Tahir Khan Durrani 43
Framework for Comparing Post-loss Debt
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Framework for Comparing Post-loss Debtand Equity Financing
Value of the Firm, V: The difference in
earnings and growthrates between equity
and debt financing areconsidered.
Value of levered firm =value of all-equity firm+ PV(tax shield)
- PV(cost of financialdistress)
Share Price:
provides a measure of the residual value tothe firm’s originalowners from thedifferent forms of financing.
Question:
Under what circumstances after a
loss do companieschoose to refinanceusing debt rather thanequity?
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Learning Outcomes
We learnt that: loss changes the context in which capital
budgeting decisions are made.
Losses tend to fall disproportionately on equityand consume cash.
Post-loss stresses may prevent the firm from
raising external capital.
Post-loss financing decision still needs to balance
the tax advantages of debt with various frictional
costs.