1FIN 534B
Advanced Corporate Finance 2 ‐ Financing
Practice Problems (Comprehensive)
Professor Yaron Leitner
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Explain under which conditions an increase in the dividend payment can be interpreted
as a signal of the following:
a. Good news
Signals that managers believe that future earnings will be high enough to maintain the
new dividend payment.
b. Bad news
Signals that the firm does not have any positive NPV investment opportunities..
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Why an announcement of a share repurchase is considered a
positive signal?
Management credibly signals that they believe the stock is
undervalued.
Problem 4 from Group Assignment 2
(With Some Added Numbers)
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3Dynron’s assets currently have a market value of $150 million.
The firm is exploring the possibility of raising $50 million by selling part of its
pipeline network and investing the $50 million in a fiber‐optic network to generate
revenues by selling high‐speed network bandwidth.
While this new investment is expected to increase profits, it will also substantially
increase Dynron’s risk.
If Dynron is levered, would this investment be more or less attractive to equity
holders than if Dynron had no debt?
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Existing New Investment
Bad Good Bad Good Expected
Current Assets 150 150 100 100 100
New Asset 0 140 70
Total Asset Value 150 150 100 240 170
Debt
Equity
Table shows market values next year.
Bad and good state are equally likely
All risk is idiosyncratic and = 0%
NPV(new investment)
= .ହ ሺሻା.ହሺଵସሻଵା% ‐ 50 = 20
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Existing New Investment
Bad Good Bad Good Expected
Current Assets 150 150 100 100 100
New Asset 0 140 70
Total Asset Value 150 150 100 240 170
Debt (face value 120) 120 120 100 120 110
Equity
Table shows market values next year.
Bad and good state are equally likely
All risk is idiosyncratic and = 0%
NPV(new investment) = 20
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Existing New Investment
Bad Good Bad Good Expected
Current Assets 150 150 100 100 100
New Asset 0 140 70
Total Asset Value 150 150 100 240 170
Debt (face value 120) 120 120 100 120 110
Equity 30 30 0 120 60
Table shows market values next year.
Bad and good state are equally likely
All risk is idiosyncratic and = 0%
NPV(new investment) = 20
Equity value increased by 30.
Why? Because debt value fell by 10.
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Existing New Investment
Bad Good Bad Good Expected
Current Assets 150 150 100 100 100
New Asset 0 140 70
Total Asset Value 150 150 100 240 170
Debt (face value 80) 80 80 80 80 80
Equity 70 70 20 160 90
Table shows market values next year.
Bad and good state are equally likely
All risk is idiosyncratic and = 0%
NPV(new investment) = 20
Now equity value increased by 20.
The new investment did not affect the market value of debt…
Bottom line:
In a highly levered firm, equity holders decide based on
Project’s NPV + Gain from increased risk
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Everything else equal, increased risk reduces
the market value of existing debt, and hence
increases the market value of equity.
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6Practice Problem 1
Agency Cost of Debt
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• ABC, Inc. is about to launch a new product (the new product is their only asset).
The firm can use either a proven technology or a new (experimental) method.
• The proven technology will produce a certain (after‐tax) cash flow of $24.
• But the cash flows from the new technology are uncertain. If the new
technology works, it will produce an (after‐tax) cash flow of $28 next year. If
it is unsuccessful, it will produce a zero cash flow next year. The probability of
success is 0.8, and whether the new technology succeeds represents
idiosyncratic (diversifiable) risk.
• Both methods require a $20 investment today, and there are no cash flows after
next year. The risk‐free rate is 10%.
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7• Which technology has the highest NPV?
NPV (old) = ‐20 + ଶସଵ.ଵ = 1.82
NPV (new) = ‐20 + .଼ ଶ଼ ା.ଶ ଵ.ଵ = 0.36
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The cashflow to the old technology is risk free. So we use the risk‐free rate.
The cashflows to the new technology are risky, but the risk is diversifiable. So
we also use the risk‐free rate.
• ABC decided to raise the $20 by issuing zero‐coupon debt due next
year. What should be the face value (x) of the debt?
• If bondholders expect ABC to choose the old technology:20 ൌ ௫ଵ.ଵ x = 22
But will ABC choose the old technology?
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Old
Technology
New
Technology
Success Failure
Cash Flow 24 28 0
Debt 22
Equity 2
If managers act on behalf of shareholders, they will choose the new technology. ସ.଼ଵ.ଵ ଶଵ.ଵ
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If face value = 22
4.80
022
6 0.8(6)+0.2(0)
Expected
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New
Technology
Success Failure
Cash Flow 28 0
Debt
Equity
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• What if bondholders expect ABC to use the new technology?
0X =?
20 ൌ .଼ ା.ଶ ଵ.ଵ X = 27.5
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917
New
Technology
Success Failure
Cash Flow 28 0
Debt
Equity
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• What if bondholders expect ABC to use the new technology?
0
24
0.5 0 0.4 0.8(0.5)+0.2(0)
Old
Technology
27.5 24
0
ABC will indeed choose the new technology.
Expected
Conclusion:
• Bondholders should (correctly) expect ABC to use the new technology.
• The face value will be $27.5
• The new technology does not have the highest NPV.
• But once they issue debt, the new technology has the highest NPV from the
perspective of equity holders.
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• Which agency cost of debt is illustrated here?
• What’s the reduction in firm value because of this cost?
• If debt holders are rational, who ends up paying the cost?
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NPV(old) – NPV(new) = 1.82 – 0.36 = 1.46
Equity holders end up with
0.4/1.1=0.36 instead of 1.82
a) Risk shifting
b) Debt overhang
c) Free cash flow problem
a) Equity holders
b) Debt holders
c) Both equity holders and debt holders
Practice Problem 2
Mini Case
Raising Capital With Asymmetric Information
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• “We R Toys” (WRT) has a capital structure that is composed of $500M in equity
and $300M in debt (market values).
• There are 10M equity shares outstanding.
• The unlevered cost of capital is 10%
• WRT’s debt is risk free with an interest rate of 4%.
• The corporate tax rate is 25%, and there are no personal taxes.
௨ ൌ 10%
ௗ ൌ ൌ 4%
ൌ 25%
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share price = ହଵ ൌ $50
• WRT is considering expanding into new geographic markets.
• The expansion will have the same business risk as WRT’s existing assets.
• The expansion will require an initial investment of $50M and is expected to
generate perpetual EBIT of $20M per year.
• After the initial investment, future capital expenditures are expected to equal
depreciation, and no further additions to net working capital are anticipated.
NPV (new expansion) = ?
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NPV = ଵହ.ଵ – 50 = $100M
FCF = EBIT ‐ Tax + Depreciation – CapEx + Change in NWC
FCF = 20 × (1‐0.25) = $15M
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Part a
• WRT initially proposes to fund the expansion by issuing equity.
• If investors were not expecting this expansion, and if they share WRT’s view of
the expansion’s profitability, what will be the share price once the firm
announces the expansion plan?
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50 + ଵଵ ൌ $
# ℎ initial share price
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Before
Announcement
After
Announcement
Existing assets
NPV(expansion)
Total
Equity 500
Debt 300
Number of shares 10
Share price
800
800 800
900
600
300
100
10
6050
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Part b
• Suppose investors think that the EBIT from WRT’s expansion will be only $4M.
i. What will the share price be in this case?
ii. How many shares will the firm need to issue?
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FCF = 4 (1‐0.25) = $3M
NPV = 3/0.1 – 50 = ‐$20M
50 + ିଶଵ = $48
ହ
ସ଼ =1.0417M
iii. If the only way to raise money is by issuing equity, should WRT issue equity and
expand?
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The expansion has a positive NPV.
But because investors underestimate the value of expansion, issuing equity
has a negative NPV (to existing shareholders).
Management will consider: NPV (expansion) + NPV (financing)
*Assume management acts on behalf of existing shareholders
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How to calculate NPV(financing)?
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New investors give: $50M
They get: 1.0417M shares
Next slide:
What’s the value of these shares, according to management?
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Assets Liabilities
Existing assets 800 Debt 300
NPV(expansion) 100 Equity 650
cash 50
Total 950 Total 950
Market value balance sheet AFTER issuance
(management’s view)
Share price = ହଵ ା ଵ.ସଵ Value of shares to new investors:
1.0417 × ହଵ ା ଵ.ସଵ = 61.3
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How to calculate NPV(financing)?
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New investors give: $50M
They get: 1.0417M shares value $61.3M
NPV(financing) = 50 ‐ 61.3 = ‐ $11.3
NPV (expansion) + NPV (financing) = 100 ‐11.3 = $88.7
Issuing equity and financing will increase existing
shareholders' wealth by $88.7M.
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Do nothing Issue and
expand
Existing assets 800
NPV(expansion)
Cash
Total 800
Equity 500
Debt 300
Number of shares 10
Share price 50
Another way to see it: (management’s views):
800
100
50
950
650
300
11.0417
58.87
588.7Value to existing shareholders
(10M shares) 500
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iv. What will be the share price immediately after the equity issue?
v. Suppose that shortly after the issue, new information emerges that convinces
investors that management was, in fact, correct regarding the cash flows from
the expansion. What will the share price be now?
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$58.87
60 ‐ ଵଵ.ଷଶଵ ൌ 58.87
Fair price Cost of financing
(per share)
$48
Part c
• Suppose that instead of issuing equity, WRT finances the expansion with a
$50M issue of permanent risk‐free debt.
• What will be the new share price once the new information comes out?
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PV( ITS) = τc D = 25% (50) = $12.5M
New share price: 60 + ଵଶ.ହଵ = $61.25
Before the information comes up, price is: 48 + ଵଶ.ହଵ = $49.25
This is PV of incremental ITS
from the new debt…
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As an aside:
• After they issue the new debt, they will have $350M in debt.
• If new debt holders are willing to lend at the risk‐free rate, the total annual
interest payment will be 350 × 4% =$14M
• This means that new debt holders expect total EBIT to be at least $14M every
year…
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Comparing your answers in parts (b) and (c), what are the two
advantages of debt financing in this case?
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1. Avoiding issuing undervalued equity
2. Interest tax shields
Gain (per share): 11.32/ 10 = $1.13
Gain (per share): 12.5/ 10 = $1.25
Total gain (per share): $2.38
Share price is $61.25 instead of $58.87.
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Bigger picture:
• In this example, debt is fairly priced.
• Both management and investors think debt is risk free.
• But there could also be cases in which debt is mispriced (next slide)
• E.g., management knows new drug is likely to pass the clinical trials, so debt has low risk. But
investors don’t know that and hence, think debt has high risk….
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Practice Problem 3
Mispriced Loan
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• Gap, Inc., is considering borrowing $100 million to fund an expansion of its
stores. Given investors’ uncertainty regarding its prospects, Gap will pay a 6%
interest rate on this loan.
• The firm’s management knows, however, that the actual risk of the loan is
extremely low and that the appropriate rate on the loan is 5%.
• Suppose the loan is for five years, with all principal being repaid in the fifth year.
If Gap’s marginal corporate tax rate is 25%, what is the net effect of the loan on
the value of the expansion?
37Leitner ACF2BD: Example 18.9
If they could get a fair loan (at 5%):
• Interest (years 1‐5): 100 × 5% = 5
• Interest Tax Shields (years 1‐5): 5 × 25% = 1.25
• PV(ITS) = ଵ.ଶହଵ.ହ ଵ.ଶହሺଵ.ହሻమ ଵ.ଶହሺଵ.ହሻయ ଵ.ଶହሺଵ.ହሻర ଵ.ଶହሺଵ.ହሻఱ ൌ 5.41
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Mispriced loan (interest = 6%):
• Interest (years 1‐5): 100 × 6% = 6
• Interest Tax Shields (years 1‐5): 6 × 25% = 1.5
• PV(ITS) = ଵ.ହଵ.ହ ଵ.ହሺଵ.ହሻమ ଵ.ହሺଵ.ହሻయ ଵ.ହሺଵ.ହሻర ଵ.ହሺଵ.ହሻఱ ൌ 6.49
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When we calculate the present value, we use the correct rate (5%)
from the perspective of Gap managers
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mispriced loan:
• Debt holders give 100
• Debt holders get ଵ.ହ ଵ.ହ మ ଵ.ହ య ଵ.ହ ర ଵሺଵ.ହሻఱ = 104.33
fair loan:
• Debt holders give 100
• Debt holders get ହଵ.ହ ହଵ.ହ మ ହଵ.ହ య ହଵ.ହ ర ଵହሺଵ.ହሻఱ = 100
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*from the perspective of Gap managers….
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Fair loan
(at 5%)
Mispriced loan
(at 6%)
PV(ITS) 5.41 6.49
NPV(financing) 0 ‐4.33
NPV(taking loan) 5.41 2.16
Cost of mispricing: 5.41‐ 2.16 = $3.25 million
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100 ‐104.33
Another way to see it:
• Because the loan is mispriced, GAP pays an extra $1 in interest every year.
• After tax, they pay an extra 1*(1‐25%) = $0.75
• From the perspective of GAP, the PV of the additional interest payments is:
.ହ
ଵ.ହ .ହଵ.ହ మ .ହଵ.ହ య .ହଵ.ହ ర .ହሺଵ.ହሻఱ = $3.25
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Practice Problem 4
Capital Structure with Agency Cost
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• According to the managerial entrenchment theory, managers choose capital
structures so as to preserve their control of the firm.
• On the one hand, debt is costly for managers because they risk losing control in
the event of default.
• On the other hand, if they do not take advantage of the tax shield provided by
debt, they risk losing control through a hostile takeover.
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• Suppose an all‐equity firm expects to generate free cash flows of $90M per year,
and the discount rate for these cash flows is 10%. The firm pays a tax rate of 25%.
• A raider is poised to take over the firm and finance it with $800M in permanent
debt. The raider will generate the same free cash flows, and the takeover attempt
will be successful if the raider can offer a premium of 15% over the current value
of the firm.
• According to the managerial entrenchment hypothesis, what level of permanent
debt will the firm choose?
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We will use the following formulas:
= + PV (ITS)
= PV( FCF, )
PV(ITS) = D (If debt is permanent)
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1. What is the unlevered firm value?
2. What will be the firm’s value if the raider takes it over?
3. What firm value would prevent a hostile take over?
4. What level of permanent debt should the firm choose to prevent a takeover?
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90/0.1 = $900 million
900M + 25% (800M) = $1.1 billion
$1.1billion/1.15 = $956.5 million
$900 + 25% D = $956.5 D = $226 million
Practice Problem 5
Paying Out Cash
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• ABC corp. has 7.5 billion shares outstanding, and it pays a marginal
corporate tax rate of 20%. Suppose ABC announces that it will pay out $50
billion in cash to investors as a special dividend. Investors had previously
assumed ABC would retain this excess cash permanently.
• How will ABC’s share price change upon this announcement? Assume the
only market imperfection is corporate taxes.
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a) Increase
b) Decrease
c) Stay the same
Solution
• Reducing cash is equivalent to increasing leverage.
• PV(tax savings) = 20% × 50 = 10 (billion $)
• Share price will increase by 10/ 7.5 = $1.33 (per share).
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• What will happen to the share price on the ex‐dividend date of the
special dividend.
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a) Increase
b) Decrease
c) Stay the same
will decrease by ହ.ହ ൌ $6.67
• Given these price reactions, does the decision to pay the special
dividend benefit investors?
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a) Yes
b) No, it will hurt investors.
c) It will neither hurt nor benefit investors.
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Practice Problem 6
Risk Shifting and Convertible debt
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• Managers can choose between 2 strategies that will yield the
following firm value next year:
• Risky strategy: Either 210 or 21 (equal probabilities)
• Safe strategy: 141 (for sure)
• Managers maximize shareholders value.
• The risk‐free rate is 0%, and all risk is diversifiable.
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Part 1
• Which strategy will managers choose if the firm is all equity?
Safe: ଵସଵଵା% ൌ
Risky: 0.5ሺ210ሻ 0.5ሺ21ሻଵା% ൌ 115.5
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Part 2
• Which strategy will they choose if the firm is financed with a zero‐
coupon debt with face value 100, which is due next year?
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Safe
Strategy
Risky
Strategy
Firm 141
Debt 100
Equity 41
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Value next year (will be discounted at 0%)
Success Failure Expected
210 21 115.5
100 21 60.5
110 0 55
Management will choose the risky strategy Risky strategy has a lower NPV, but it has a higher NPV from the
perspective of equity holders.
• Which agency problem is illustrated here?
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a) Risk shifting
b)Debt overhang
c) Free cash flow problem
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Part 3
• Which strategy will management choose if the debt is convertible?
• Suppose there are 100 shares outstanding initially, and the debt can
be converted to 200 shares.
• I.e., debt can be converted to 2/3 of firm value.
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Risky Strategy
Success Failure Expected
Firm value 210 21 115.5
Convertible Debt
Convert?
Don’t convert?
Equity
210*(2/3) = 140
100
70
21*(2/3) = 14
21
0 35
(will be discounted at 0%)
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Safe Strategy
Success Failure Expected
Firm value 141 141 141
Convertible debt
Convert?
Don’t convert?
Equity
il
i l
i l
141*(2/3) = 94 141*(2/3) = 94
100 100
i 41 41 41
(will be discounted at 0%)Now management will choose the safe strategy!
Intuition:
• If management chooses the risky strategy and the strategy succeeds,
debt holders will convert their debt to equity…
• So, the original equity holders will have to share some of the upside
gain with debt holders...
• This reduces the gain to equity holders from the risky strategy
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Thank you!!
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