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V Week 4: Capital Structure with Taxes and Costs of Financial Distress
V 第四周：带税的资本结构与财务困境成本

Mark as done 标记为完成

This week we will introduce two frictions, (taxes and costs of financial distress) and we will consider their implications on the firms’ decisions regarding their capital structure. You will learn that when companies are subject to corporate taxes, and because interest payments to debt-holders and dividends paid to equity-holders are treated differently by the tax code, using debt instead of equity to finance investments creates value. We will discuss how this value is reflected in share prices. You will also learn that increasing the level of debt in the firm’s capital structure comes with an increase in the expected costs of financial distress.
本周我们将介绍两种摩擦（税收和财务困境成本），并考虑它们对公司资本结构决策的影响。您将了解到，当公司面临企业税时，由于税法对债权人支付的利息和股东支付的股息的处理方式不同，使用债务而非股权来融资投资会创造价值。我们将讨论这种价值如何反映在股价中。您还将了解到，增加公司资本结构中的债务水平会伴随预期财务困境成本的增加。
In general, the gain to investors from the tax deductibility of interest payments is referred to as the interest tax shield.
一般来说，投资者从利息支付的税收扣除中获得的收益被称为利息税盾。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确
Question 2 问题 2
The interest tax shield is the additional amount that a firm would have paid in taxes if it did not have leverage.
利息税盾是指如果公司没有杠杆，它将多支付的税款。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确
Because corporations pay taxes on their profits after interest payments are deducted, interest expenses reduce the amount of corporate tax firms must pay.
因为公司在扣除利息支付后的利润上缴税款，利息支出减少了企业必须支付的公司税额。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确

Question 4 问题 4

As Modigliani and Miller made clear in their original work, capital structure does not matter in perfect capital markets. Thus, if capital structure does matter, then it must stem from a market imperfection.
正如莫迪利安尼和米勒在他们的原始工作中所明确指出的，资本结构在完美资本市场中并不重要。因此，如果资本结构确实重要，那么它必须源于市场的不完善。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确

Question 5 问题 5

To determine the benefit of leverage for the value of the firm, we must compute the present value of the stream of future interest tax shields the firm will receive.
为了确定杠杆对公司价值的好处，我们必须计算公司将获得的未来利息税盾流的现值。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确
By increasing the amount paid to debt holders through interest payments, the amount of the pre-tax cash flows that must be paid as taxes increases.
通过增加支付给债权人的利息支付金额，必须作为税款支付的税前现金流量的金额增加。
Select one: 选择一个：
a. Correctb. Incorrect a. 正确 b. 不正确
Consider the income statement for Kroger Inc. shown below (all figures in $ million).
考虑下面显示的 Kroger Inc.的收入报表（所有数字以百万美元计）。

Income Statement for Kroger Inc.
克罗格公司收入报表

Year 年 2006 2005 2004
Total sales 总销售额 60,553 56,434 53,791

销售成本
Cost of goods
sold
Cost of goods sold| Cost of goods | | :--- | | sold |
 45,565 42,140 39,637

销售、一般及管理费用
Selling, general
& admin
expenses
Selling, general & admin expenses| Selling, general | | :--- | | & admin | | expenses |
 11,688 12,191 11,575
Depreciation 折旧 1265 1256 1209
 营业收入
Operating
income
Operating income| Operating | | :--- | | income |
 2035 847 1370
Other income 其他收入 0 847 1370
EBIT 2035 557 604
Interest expense 利息费用 510 290 766
 税前收益
Earnings before
tax
Earnings before tax| Earnings before | | :--- | | tax |
 1525
Year 2006 2005 2004 Total sales 60,553 56,434 53,791 "Cost of goods sold" 45,565 42,140 39,637 "Selling, general & admin expenses" 11,688 12,191 11,575 Depreciation 1265 1256 1209 "Operating income" 2035 847 1370 Other income 0 847 1370 EBIT 2035 557 604 Interest expense 510 290 766 "Earnings before tax" 1525 | Year | 2006 | 2005 | 2004 | | :--- | :--- | :--- | :--- | | Total sales | 60,553 | 56,434 | 53,791 | | Cost of goods <br> sold | 45,565 | 42,140 | 39,637 | | Selling, general <br> & admin <br> expenses | 11,688 | 12,191 | 11,575 | | Depreciation | 1265 | 1256 | 1209 | | Operating <br> income | 2035 | 847 | 1370 | | Other income | 0 | 847 | 1370 | | EBIT | 2035 | 557 | 604 | | Interest expense | 510 | 290 | 766 | | Earnings before <br> tax | 1525 | | |
Taxes (35%) 税收 (35%) 534 102 268
Net income 净收入 991 189 498
Taxes (35%) 534 102 268 Net income 991 189 498| Taxes (35%) | 534 | 102 | 268 | | :--- | :--- | :--- | :--- | | Net income | 991 | 189 | 498 |
The interest rate tax shield for Kroger in 2006 is closest to:
2006 年克罗格的利息税盾最接近：
Select one: 选择一个：
a. $187 million 1.87 亿美元
b. $332 millionc. $ 534 $ 534 $534\$ 534 million
b. 3.32 亿美元 c. $ 534 $ 534 $534\$ 534 百万
d. $179 million 1.79 亿美元
Question 1
问题1
    Correct 正确马克 1.00 分(满分 1.00 『 Flag question 『 旗帜问题
In general, the gain to investors from the tax deductibility of interest payments is referred to as the interest tax shield.
一般来说，投资者从利息支付的税收可扣除性中获得的收益被称为利息税盾。
一般来说，投资者从利息支出的税前扣除中获得的收益被称为利息税盾。
Select one: 选择一个： 选择一个：
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确

Question 2 问题 2

问题 2
Mark 1.00 out of 1.00 Correct 正确马克 1.00 分（满分 1.00 『 Flag question 『 旗帜问题  Mark  1.00  out of  1.00  Correct 正确马克  1.00  分（满分  1.00  『 Flag question  『  旗帜问题  {:[" Mark "1.00" out of "1.00],[" Correct 正确马克 "1.00" 分（满分 "1.00" 『 Flag question "『" 旗帜问题 "]:}\begin{aligned} & \text { Mark } 1.00 \text { out of } 1.00 \\ & \text { Correct 正确马克 } 1.00 \text { 分（满分 } 1.00 \text { 『 Flag question } 『 \text { 旗帜问题 } \end{aligned}正确马克分（满分『『旗帜问题
The interest tax shield is the additional amount that a firm would have paid in taxes if it did not have leverage.
利息税盾是指如果公司没有杠杆，它将多支付的税款。
利息税盾是指公司在没有杠杆的情况下本应支付的额外税款。
Select one: 选择一个: 选择一个:
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确
Because corporations pay taxes on their profits after interest payments are deducted, interest expenses reduce the amount of corporate tax firms must pay.由于公司在扣除利息支出后才按利润纳税，因此利息支出减少了公司必须缴纳的公司税额。
由于公司在扣除利息支出后才按利润纳税，因此利息支出减少了公司必须缴纳的公司税额。
Select one: 选择一个: 选择一个:
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确

Question 4
问题4 问题 4

As Modigliani and Miller made clear in their original work, capital structure does not matter in perfect capital markets. Thus, if capital structure does matter, then it must stem from a market imperfection.
正如莫迪利安尼和米勒在他们的原始工作中所明确指出的，资本结构在完美资本市场中并不重要。因此，如果资本结构确实重要，那么它必须源于市场的不完善。
莫迪利亚尼和米勒在他们的原著中明确指出，在完美的资本市场中，资本结构并不重要。因此，如果资本结构确实重要，那么它一定源于市场的不完善。
Select one: 选择一个: 选择一个:
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确
To determine the benefit of leverage for the value of the firm, we must compute the present value of the stream of future interest tax shields the firm will receive.要确定杠杆对公司价值的益处，我们必须计算公司未来获得的利息税盾流的现值。
要确定杠杆对公司价值的益处，我们必须计算公司未来获得的利息税盾流的现值。
Select one: 选择一个: 选择一个:
a. Correct 正确 ✓ ✓ ✓\checkmark
a. 正确 ✓ ✓ ✓\checkmark
b. Incorrect 不正确 b. 不正确
Question 6 问题 6
问题 6
Incorrect 不正 Mark 0.00 out of 1.00
不正 标记 0.00 / 1.00
By increasing the amount paid to debt holders through interest payments, the amount of the pre-tax cash flows that must be paid as taxes increases.
通过增加支付给债权人的利息支付金额，必须作为税款支付的税前现金流量的金额增加。
通过利息支出向债务人支付的金额增加，税前现金流中必须作为税收支付的金额也随之增加。
Select one: 选择一个: 选择一个:
a. Correct 正确 × × xx\times
a. 正确 × × xx\times
b. Incorrect 不正确 b. 不正确
The interest rate tax shield for Kroger in 2006 is closest to:
2006 年克罗格的利息税盾最接近：
克罗格公司 2006 年的利率税盾最接近于
Select one: 选择一个: 选择一个:
a. $187 million 1.87 亿美元
1.87 亿美元
b. $332 million 3.32 亿美元
3.32 亿美元
c. $ 534 $ 534 $534\$ 534 million 5.34 亿美元
c. $ 534 $ 534 $534\$ 534 百万 5.34 亿美元
d. $179 million 1.79 亿 ✓ ✓ ✓\checkmark Explanation 说明
1.79 亿
美元
Tax rate × × xx\times Interest expense = 510 × 0.35 = = 510 × 0.35 = =510 xx0.35==510 \times 0.35= $178.5 million.
税率 × × xx\times 利息支出 = 510 × 0.35 = = 510 × 0.35 = =510 xx0.35==510 \times 0.35= 1.785 亿美元。
税率 x 利息支出 = 510 × 0.35 = 1.785 = 510 × 0.35 = 1.785 =510 xx0.35=1.785=510 \times 0.35=1.785 亿美元。
Once investors know the recapitalisation will occur, the share price will rise immediately to a level that reflects the value of the interest tax shield that the firm will receive from its recapitalisation.
一旦投资者知道资本重组将会发生，股价将立即上涨至一个反映公司从资本重组中获得的利息税盾价值的水平。
Select one: 选择一个：
a. Correctb. Incorrect a. 正确 b. 不正确
When securities are fairly priced, the original shareholders of a firm capture the full benefit of the interest tax shield from an increase in leverage.
当证券价格合理时，公司的原始股东能够充分享受由于杠杆增加而带来的利息税盾的全部好处。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确
In the presence of corporate taxes, we do not include the interest tax shield as one of the firm’s assets on its market value balance sheet.
在公司税存在的情况下，我们不将利息税盾视为公司市场价值资产负债表上的一项资产。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确
We can analyse the recapitalisation using the market value balance sheet; it states that the total market value of a firm’s securities must equal the total market value of the firm’s assets.
我们可以使用市场价值资产负债表分析资本重组；它表明公司的证券总市场价值必须等于公司资产的总市场价值。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确
Once investors know the recapitalisation will occur, the share price will rise immediately to a level that reflects the value of the interest tax shield that the firm will receive from its recapitalisation.
一旦投资者知道资本重组将会发生，股价将立即上涨至一个反映公司从资本重组中获得的利息税盾价值的水平。
一旦投资者知道将进行资本结构调整，股价就会立即上涨，达到反映公司从资本结构调整中获得的利息税保护价值的水平。
Select one: 选择一个: 选择一个:
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确
Question 2 问题 2
问题 2
When securities are fairly priced, the original shareholders of a firm capture the full benefit of the interest tax shield from an increase in leverage.
当证券价格合理时，公司的原始股东能够充分享受由于杠杆增加而带来的利息税盾的全部好处。
当证券定价公允时，公司的原始股东就能从杠杆率的增加中获得利息税保护的全部好处。
Select one: 选择一个: 选择一个:
a. Correct 正确 ✓ ✓ ✓\checkmark
a. 正确 ✓ ✓ ✓\checkmark
b. Incorrect 不正确 b. 不正确
Question 3 问题 3
问题 3
Correct 正确卫 Mark 1.00 out of 1.00
正确卫 标记 1.00 / 1.00
In the presence of corporate taxes, we do not include the interest tax shield as one of the firm’s assets on its market value balance sheet.
在公司税存在的情况下，我们不将利息税盾视为公司市场价值资产负债表上的一项资产。
在存在公司税的情况下，我们不将利息税盾作为公司资产的市值资产负债表中的资产之一。
Select one: 选择一个: 选择一个:
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确
Question 4 问题 4
问题 4
Mark 1.00 out of 1.00 Correct 正确马克 1.00 分（满分 1.00 『 Flag question 『 旗帜问题  Mark  1.00  out of  1.00  Correct 正确马克  1.00  分（满分  1.00  『 Flag question  『  旗帜问题  {:[" Mark "1.00" out of "1.00],[" Correct 正确马克 "1.00" 分（满分 "1.00" 『 Flag question "『" 旗帜问题 "]:}\begin{aligned} & \text { Mark } 1.00 \text { out of } 1.00 \\ & \text { Correct 正确马克 } 1.00 \text { 分（满分 } 1.00 \text { 『 Flag question } 『 \text { 旗帜问题 } \end{aligned}正确马克分（满分『『旗帜问题
We can analyse the recapitalisation using the market value balance sheet; it states that the total market value of a firm’s securities must equal the total market value of the firm’s assets.
我们可以使用市场价值资产负债表分析资本重组；它表明公司的证券总市场价值必须等于公司资产的总市场价值。
我们可以用市值资产负债表来分析资本结构调整；该表规定，公司证券的总市值必须等于公司资产的总市值。
Select one: 选择一个： 选择一个：
  • a. Correct 正确 a. 正确
    b. Incorrect 不正确 b. 不正确
Because the assets of the firm might be more valuable if kept together, creditors seizing assets in a piecemeal fashion might destroy much of the remaining value of the firm
由于公司的资产如果保持在一起可能更有价值，债权人以零散的方式扣押资产可能会摧毁公司剩余价值的很大一部分
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确
Debt holders can then take legal action against the firm to collect payment by seizing the firm’s assets.
债权人可以对公司采取法律行动，通过扣押公司的资产来收回款项。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确
When a corporation becomes financially distressed, outside professionals, such as legal and accounting experts, consultants, appraisers, auctioneers, and others who are experienced in selling distressed assets, are generally hired.
当公司面临财务困境时，通常会聘请外部专业人士，如法律和会计专家、顾问、评估师、拍卖师以及其他在出售困境资产方面经验丰富的人士。

Select one: 选择一个：

a. Correctb. Incorrect
To receive the full tax benefits of leverage, a firm needs to use 100% debt financing.
为了获得杠杆的全部税收优惠，企业需要使用 100%的债务融资。
Select one: 选择一个：
a. Correct 正确
b. Incorrect b. 错误

If bankruptcy is costly, these costs might offset the tax advantages of debt
如果破产成本高，这些成本可能会抵消债务的税收优势

financing. 融资。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确
Although indirect costs of bankruptcy are difficult to measure accurately, they are typically much lower than the direct costs of bankruptcy.
尽管破产的间接成本难以准确衡量，但通常远低于破产的直接成本。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确
Because many aspects of the bankruptcy process are independent of the size of the firm, the costs are typically higher, in percentage terms, for smaller firms.
由于破产过程的许多方面与公司的规模无关，因此小型公司的成本通常在百分比上更高。
Select one: 选择一个：
a. Correctb. Incorrect a. 正确 b. 不正确
Question 8 问题 8
Suppliers may be unwilling to provide a firm with inventory if they fear they will not be paid.
供应商可能不愿意向公司提供库存，如果他们担心不会得到付款。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确
The loss of customers is likely to be large for producers of raw materials (such as sugar or aluminium), as the value of these goods, once delivered, depends on the seller’s continued success.
客户流失对原材料生产商（如糖或铝）的影响可能会很大，因为这些商品一旦交付，其价值取决于卖方的持续成功。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确
The loss of key employees is negligible during periods of financial distress, as they expect to get a large compensation in case the company goes bankrupt.
在财务困境期间，关键员工的流失几乎可以忽略不计，因为他们预计在公司破产的情况下会获得丰厚的赔偿。
Select one: 选择一个：
a. Correctb. Incorrect a. 正确 b. 不正确
The indirect costs of financial distress are higher for companies with relatively more intangible assets, as these tend to lose more value in fire sales.
财务困境的间接成本对于拥有相对更多无形资产的公司来说更高，因为这些资产在火灾销售中往往会损失更多价值。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确
The tradeoff theory weighs the costs of debt that result from shielding cash flows from taxes against the benefits from the effects of financial distress associated with leverage.
权衡理论权衡了由于保护现金流免受税收影响而产生的债务成本与与杠杆相关的财务困境所带来的好处。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确
According to the tradeoff theory, the total value of a levered firm equals the value of the firm without leverage plus the present value of the tax savings from debt, less the present value of financial distress costs.
根据权衡理论，杠杆公司的总价值等于无杠杆公司的价值加上债务带来的税收节省的现值，减去财务困境成本的现值。
Select one:a. Correctb. Incorrect
选择一个：a. 正确 b. 不正确
Because the assets of the firm might be more valuable if kept together, creditors seizing assets in a piecemeal fashion might destroy much of the remaining value of the firm
由于公司的资产如果保持在一起可能更有价值，债权人以零散的方式扣押资产可能会摧毁公司剩余价值的很大一部分
由于公司的资产如果保持在一起可能更有价值，债权人以零散的方式扣押资产可能会摧毁公司剩余价值的很大一部分
Select one: 选择一个: 选择一个:
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确
Question 2 问题2 Correct 正确评分 1.00 / 1.00 1.00 / 1.00 1.00//1.00quad1.00 / 1.00 \quad Flag question ↾ ↾ ↾\upharpoonright 标记问题
问题 2 正确评分 1.00 / 1.00 1.00 / 1.00 1.00//1.00quad1.00 / 1.00 \quad 标记问题 ↾ ↾ ↾\upharpoonright
Debt holders can then take legal action against the firm to collect payment by seizing the firm’s assets.
债权人可以对公司采取法律行动，通过扣押公司的资产来收回款项。
债权人可以对公司采取法律行动，通过扣押公司的资产来收取付款。
Select one: 选择一个: 选择一个:
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确
When a corporation becomes financially distressed, outside professionals, such as legal and accounting experts, consultants, appraisers, auctioneers, and others who are experienced in selling distressed assets, are generally hired.
当公司面临财务困境时，通常会聘请外部专业人士，如法律和会计专家、顾问、评估师、拍卖师以及其他在出售困境资产方面经验丰富的人士。
当公司面临财务困境时，通常会聘请外部专业人士，如法律和会计专家、顾问、评估师、拍卖师以及其他在出售困境资产方面经验丰富的人士。
Select one: 选择一个: 选择一个:
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确
Question 4 问题 4 4 4quad4 \quad Correct 正确评分 1.00 / 1.00 1.00 / 1.00 1.00//1.00quad1.00 / 1.00 \quad Flag question ∇ ∇ grad\nabla 标记问题
问题 4 4 4 4quad4 \quad 正确评分 1.00 / 1.00 1.00 / 1.00 1.00//1.00quad1.00 / 1.00 \quad 标记问题 ∇ ∇ grad\nabla
To receive the full tax benefits of leverage, a firm needs to use 100% debt financing.
为了获得杠杆的全部税收优惠，企业需要使用 100%的债务融资。
为了获得杠杆的全部税收优惠，企业需要使用 100 % 100 % 100%100 \% 的债务融资。
Select one: 选择一个： 选择一个：
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确
Correct 正确评分 1.00 / 1.00 ∣ 1.00 / 1.00 ∣ 1.00//1.00quad∣1.00 / 1.00 \quad \mid Flag question ↾ ↾ ↾\upharpoonright 标记问题
正确评分 1.00 / 1.00 ∣ 1.00 / 1.00 ∣ 1.00//1.00quad∣1.00 / 1.00 \quad \mid 标记问题 ↾ ↾ ↾\upharpoonright
If bankruptcy is costly, these costs might offset the tax advantages of debt financing.
如果破产成本高，这些成本可能会抵消债务融资的税收优势。

如果破产成本高，这些成本可能会抵消债务融资的税收优势。

Select one: 选择一个： 选择一个：
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确
Question 6 问题6 Correct 正确评分 1.00 / 1.00 1.00 / 1.00 1.00//1.00quad1.00 / 1.00 \quad Fark 1.00 out of 1.00
问题 6 正确评分 1.00 / 1.00 1.00 / 1.00 1.00//1.00quad1.00 / 1.00 \quad Fark 1.00 满分 1.00
Although indirect costs of bankruptcy are difficult to measure accurately, they are typically much lower than the direct costs of bankruptcy.
尽管破产的间接成本难以准确衡量，但通常远低于破产的直接成本。
尽管破产的间接成本难以准确衡量，但通常远低于破产的直接成本。
Select one: 选择一个: 选择一个:
a. Correct 正确 a. 正确
）b. Incorrect 不正确 不正确
Question 7 问题 7
问题 7
Because many aspects of the bankruptcy process are independent of the size of the firm, the costs are typically higher, in percentage terms, for smaller firms.
由于破产过程的许多方面与公司的规模无关，因此小型公司的成本通常在百分比上更高。
由于破产过程的许多方面与公司的规模无关，因此小型公司的成本通常在百分比上更高。
Select one: 选择一个： 选择一个：
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确
Question 8 问题 8 问题 8
Correct 正确评分 1.00 / 1.00 ⊩ 1.00 / 1.00 ⊩ 1.00//1.00quad⊩1.00 / 1.00 \quad \Vdash Flag question ↾ ↾ ↾\upharpoonright 标记问题
正确评分 1.00 / 1.00 ⊩ 1.00 / 1.00 ⊩ 1.00//1.00quad⊩1.00 / 1.00 \quad \Vdash 标记问题 ↾ ↾ ↾\upharpoonright
Suppliers may be unwilling to provide a firm with inventory if they fear they will not be paid.
供应商可能不愿意向公司提供库存，如果他们担心不会得到付款。
供应商可能不愿意向公司提供库存, 如果他们担心不会得到付款。
供应商可能不愿意向公司提供库存，如果他们担心不会得到付款。
Select one: 选择一个: 选择一个:
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确
The loss of customers is likely to be large for producers of raw materials (such as sugar or aluminium), as the value of these goods, once delivered, depends on the seller’s continued success.
客户流失对原材料生产商（如糖或铝）的影响可能会很大，因为这些商品一旦交付，其价值取决于卖方的持续成功。
客户流失对原材料生产商（如糖或铝）的影响可能会很大，因为这些商品一旦交付，其价值取决于卖方的持续成功。
Select one: 选择一个： 选择一个：
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确
Question 10 问题 10
问题 10
Correct 正确评分 1.00 / 1.00 Fark question ↾ 标记问题  Correct 正确评分  1.00 / 1.00  Fark question  ↾  标记问题  " Correct 正确评分 "1.00//1.00quad" Fark question "↾" 标记问题 "\text { Correct 正确评分 } 1.00 / 1.00 \quad \text { Fark question } \upharpoonright \text { 标记问题 }正确评分标记问题
The loss of key employees is negligible during periods of financial distress, as they expect to get a large compensation in case the company goes bankrupt.
在财务困境期间，关键员工的流失几乎可以忽略不计，因为他们预计在公司破产的情况下会获得丰厚的赔偿。
在财务困境期间，关键员工的流失几乎可以忽略不计，因为他们预计在公司破产的情况下会获得丰厚的赔偿。
Select one: 选择一个: 选择一个:
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确
According to the tradeoff theory, the total value of a levered firm equals the value of the firm without leverage plus the present value of the tax savings from debt, less the present value of financial distress costs.
根据权衡理论，杠杆公司的总价值等于无杠杆公司的价值加上债务带来的税收节省的现值，减去财务困境成本的现值。
根据权衡理论，杜杆公司的总价值等于无杠杆公司的价值加上债务带来的税收节省的现值，减去财务困境成本的现值。
Select one: 选择一个: 选择一个:
a. Correct 正确 a. 正确
b. Incorrect 不正确 b. 不正确

ECOM144 Principles of Corporate Finance Problem Set 4
ECOM144 公司财务原理 习题集 4

  1. Pelamed Pharmaceuticals has EBIT of $ 325 $ 325 $325\$ 325 million in 2006. In addition, Pelamed has interest expenses of $ 125 $ 125 $125\$ 125 million and a corporate tax rate of 40%.
    Pelamed 制药在 2006 年的息税前利润（EBIT）为 $ 325 $ 325 $325\$ 325 百万。此外，Pelamed 的利息支出为 $ 125 $ 125 $125\$ 125 百万，企业税率为 40%。
    a) What is Pelamed’s 2006 net income?
    Pelamed 2006 年的净收入是多少？
    b) What is the total of Pelamed’s 2006 net income and interest payments?
    b) Pelamed 2006 年的净收入和利息支付总额是多少？
    c) If Pelamed had no interest expenses, what would its 2006 net income be?
    c) 如果 Pelamed 没有利息支出，那么它 2006 年的净收入将是多少？
How does it compare to your answer in part b?
它与您在 b 部分的答案相比如何？
d) What is the amount of Pelamed’s interest tax shield in 2006?
d) Pelamed 在 2006 年的利息税盾金额是多少？
2. Suppose the corporate tax rate is 40 % 40 % 40%40 \%. Consider a firm that earns $ 1000 $ 1000 $1000\$ 1000 before interest and taxes each year with no risk. The firm’s capital expenditures equal its depreciation expenses each year, and it will have no changes to its net working capital. The risk-free interest rate is 5 % 5 % 5%5 \%.
2. 假设企业税率为 40 % 40 % 40%40 \% 。考虑一家每年在无风险情况下赚取 $ 1000 $ 1000 $1000\$ 1000 的公司，税前利润。该公司的资本支出等于每年的折旧费用，并且其净营运资本不会发生变化。无风险利率为 5 % 5 % 5%5 \% 。
a) Suppose the firm has no debt and pays out its net income as a dividend each year. What is the value of the firm’s equity?
假设公司没有债务，每年将净收入作为股息支付。公司的股权价值是多少？
b) Suppose instead the firm makes interest payments of $ 500 $ 500 $500\$ 500 per year. What is the value of equity? What is the value of debt?
b) 假设公司每年支付利息 $ 500 $ 500 $500\$ 500 。股权的价值是多少？债务的价值是多少？
c) What is the difference between the total value of the firm with leverage and without leverage?
c) 带杠杆和不带杠杆的公司的总价值有什么区别？
d) The difference in part © is equal to what percentage of the value of the debt?
d) 部分©的差额占债务价值的百分比是多少？
3. Rally, Inc., is an all-equity firm with assets worth $ 25 $ 25 $25\$ 25 billion and 10 billion shares outstanding. Rally plans to borrow $ 10 $ 10 $10\$ 10 billion and use these funds to repurchase shares. The firm’s corporate tax rate is 35 % 35 % 35%35 \%, and Rally plans to keep its outstanding debt equal to $ 10 $ 10 $10\$ 10 billion permanently.
3. Rally, Inc. 是一家全股权公司，资产价值 $ 25 $ 25 $25\$ 25 亿，流通股为 100 亿股。Rally 计划借款 $ 10 $ 10 $10\$ 10 亿，并将这些资金用于回购股票。公司的企业税率为 35 % 35 % 35%35 \% ，Rally 计划将其流动债务永久保持在 $ 10 $ 10 $10\$ 10 亿。
a) Without the increase in leverage, what would Rally’s share price be?
a) 如果没有杠杆的增加，Rally 的股价会是多少？
b) What is the lowest price Rally can offer and have shareholders tender their shares? What will its stock price be after the share repurchase in that case?
b) Rally 可以提供的最低价格是多少，以便股东愿意出让他们的股份？在这种情况下，回购股份后其股票价格将是多少？
c) Suppose Rally offers $ 3.00 $ 3.00 $3.00\$ 3.00 per share, and shareholders tender their shares at this price. What will Rally’s share price be after the repurchase?
c) 假设 Rally 以每股 $ 3.00 $ 3.00 $3.00\$ 3.00 的价格报价，股东以此价格出售他们的股份。那么 Rally 的股价在回购后将是多少？
4. Markum Enterprises is considering permanently adding $ 100 $ 100 $100\$ 100 million of debt to its capital structure. Markum’s corporate tax rate is 35 % 35 % 35%35 \%.
4. Markum Enterprises 正在考虑将 $ 100 $ 100 $100\$ 100 百万美元的债务永久性地添加到其资本结构中。Markum 的公司税率为 35 % 35 % 35%35 \% 。
a) Absent personal taxes, what is the value of the interest tax shield from the new debt?
a) 在没有个人税的情况下，新债务的利息税盾的价值是多少？
b) If investors pay a tax rate of 40 % 40 % 40%40 \% on interest income, and a tax rate of 20 % 20 % 20%20 \% on income from dividends and capital gains, what is the value of the interest tax shield from the new debt?
b) 如果投资者对利息收入的税率为 40 % 40 % 40%40 \% ，对股息和资本利得的收入税率为 20 % 20 % 20%20 \% ，那么新债务的利息税盾的价值是多少？
5. Rogot Instruments makes fine violins and cellos. It has $ 1 $ 1 $1\$ 1 million in debt outstanding, equity valued at $ 2 $ 2 $2\$ 2 million, and pays corporate income tax at a rate of 21 % 21 % 21%21 \%. Its cost of equity is 12 % 12 % 12%12 \% and its cost of debt is 7 % 7 % 7%7 \%.
5. Rogot Instruments 制造精美的小提琴和大提琴。它有 $ 1 $ 1 $1\$ 1 百万的未偿债务，股权价值为 $ 2 $ 2 $2\$ 2 百万，企业所得税税率为 21 % 21 % 21%21 \% 。其股本成本为 12 % 12 % 12%12 \% ，债务成本为 7 % 7 % 7%7 \% 。
a) What is Rogot’s pre-tax WACC?
罗戈特的税前加权平均资本成本（WACC）是多少？
b) What is Rogot’s (effective after-tax) WACC?
b) Rogot 的（税后有效）加权平均资本成本（WACC）是多少？

Solution 解决方案

  1. Pelamed Pharmaceuticals has EBIT of $ 325 $ 325 $325\$ 325 million in 2006. In addition, Pelamed has interest expenses of $ 125 $ 125 $125\$ 125 million and a corporate tax rate of 40%.
    Pelamed 制药在 2006 年的息税前利润（EBIT）为 $ 325 $ 325 $325\$ 325 百万。此外，Pelamed 的利息支出为 $ 125 $ 125 $125\$ 125 百万，企业税率为 40%。
    a) What is Pelamed’s 2006 net income?
    Pelamed 2006 年的净收入是多少？
N I = ( 325 − 125 ) ( 1 − 0.4 ) = $ 120 m N I = ( 325 − 125 ) ( 1 − 0.4 ) = $ 120 m NI=(325-125)(1-0.4)=$120 mN I=(325-125)(1-0.4)=\$ 120 m
b) What is the total of Pelamed’s 2006 net income and interest payments?
b) Pelamed 2006 年的净收入和利息支付总额是多少？
N I + Interest = 120 m + $ 125 m = $ 245 m N I +  Interest  = 120 m + $ 125 m = $ 245 m NI+" Interest "=120 m+$125 m=$245 mN I+\text { Interest }=120 m+\$ 125 m=\$ 245 m
c) If Pelamed had no interest expenses, what would its 2006 net income be? How does it compare to your answer in part b?
c) 如果 Pelamed 没有利息支出，那么它 2006 年的净收入将是多少？这与你在 b 部分的答案相比如何？
N I = 325 ( 1 − 0.4 ) = $ 195 m N I = 325 ( 1 − 0.4 ) = $ 195 m NI=325(1-0.4)=$195 mN I=325(1-0.4)=\$ 195 m
This is $ 50 m $ 50 m $50m\$ 50 \mathrm{~m} lower than in part b).
这比部分 b)低 $ 50 m $ 50 m $50m\$ 50 \mathrm{~m} 。
d) What is the amount of Pelamed’s interest tax shield in 2006?
d) Pelamed 在 2006 年的利息税盾金额是多少？
Taxshild = 0.4 × $ 125 m = $ 50 m  Taxshild  = 0.4 × $ 125 m = $ 50 m " Taxshild "=0.4 xx$125 m=$50 m\text { Taxshild }=0.4 \times \$ 125 m=\$ 50 m
  1. Suppose the corporate tax rate is 40 % 40 % 40%40 \%. Consider a firm that earns $ 1000 $ 1000 $1000\$ 1000 before interest and taxes each year with no risk. The firm’s capital expenditures equal its depreciation expenses each year, and it will have no changes to its net working capital. The risk-free interest rate is 5 % 5 % 5%5 \%.
    假设企业税率为 40 % 40 % 40%40 \% 。考虑一家每年在无风险情况下赚取 $ 1000 $ 1000 $1000\$ 1000 的公司，税前利润和利息。该公司的资本支出等于每年的折旧费用，并且其净营运资本不会发生变化。无风险利率为 5 % 5 % 5%5 \% 。
    a) Suppose the firm has no debt and pays out its net income as a dividend each year. What is the value of the firm’s equity?
    假设公司没有债务，每年将净收入作为股息支付。公司的股权价值是多少？
N I = ( 1 − 0.4 ) 1000 = 600 N I = ( 1 − 0.4 ) 1000 = 600 NI=(1-0.4)1000=600N I=(1-0.4) 1000=600
Thus, equity holders receive dividends of $ 600 $ 600 $600\$ 600 per year with no risk.
因此，股东每年获得 $ 600 $ 600 $600\$ 600 的股息，且没有风险。
E = $ 600 0.05 = $ 12 , 000 E = $ 600 0.05 = $ 12 , 000 E=($600)/(0.05)=$12,000E=\frac{\$ 600}{0.05}=\$ 12,000
b) Suppose instead the firm makes interest payments of $ 500 $ 500 $500\$ 500 per year. What is the value of equity? What is the value of debt?
b) 假设公司每年支付利息 $ 500 $ 500 $500\$ 500 。股权的价值是多少？债务的价值是多少？
D = 500 0.05 = 10 , 000 N I = ( 1 − 0.4 ) ( 1000 − 500 ) = 300 E = $ 300 0.05 = $ 6 , 000 D = 500 0.05 = 10 , 000 N I = ( 1 − 0.4 ) ( 1000 − 500 ) = 300 E = $ 300 0.05 = $ 6 , 000 {:[D=(500)/(0.05)=10","000],[NI=(1-0.4)(1000-500)=300],[E=($300)/(0.05)=$6","000]:}\begin{gathered} D=\frac{500}{0.05}=10,000 \\ N I=(1-0.4)(1000-500)=300 \\ E=\frac{\$ 300}{0.05}=\$ 6,000 \end{gathered}
c) What is the difference between the total value of the firm with leverage and without leverage?
c) 带杠杆和不带杠杆的公司的总价值有什么区别？
Without leverage the firm value is: $ 12 , 000 $ 12 , 000 $12,000\$ 12,000
没有杠杆的公司价值为： $ 12 , 000 $ 12 , 000 $12,000\$ 12,000
With leverage: $ 10 , 000 + $ 6 , 000 = $ 16 , 000 $ 10 , 000 + $ 6 , 000 = $ 16 , 000 $10,000+$6,000=$16,000\$ 10,000+\$ 6,000=\$ 16,000 带杠杆： $ 10 , 000 + $ 6 , 000 = $ 16 , 000 $ 10 , 000 + $ 6 , 000 = $ 16 , 000 $10,000+$6,000=$16,000\$ 10,000+\$ 6,000=\$ 16,000
The difference is $ 4 , 000 $ 4 , 000 $4,000\$ 4,000
差异是 $ 4 , 000 $ 4 , 000 $4,000\$ 4,000
d) The difference in part © is equal to what percentage of the value of the debt?
d) 部分©的差额占债务价值的百分比是多少？
4 , 000 10 , 000 = 0.4 = corporate tax rate 4 , 000 10 , 000 = 0.4 =  corporate tax rate  (4,000)/(10,000)=0.4=" corporate tax rate "\frac{4,000}{10,000}=0.4=\text { corporate tax rate }
Did you expect that? 你期待吗？
3. Rally, Inc., is an all-equity firm with assets worth $ 25 $ 25 $25\$ 25 billion and 10 billion shares outstanding. Rally plans to borrow $ 10 $ 10 $10\$ 10 billion and use these funds to repurchase shares. The firm’s corporate tax rate is 35 % 35 % 35%35 \%, and Rally plans to keep its outstanding debt equal to $ 10 $ 10 $10\$ 10 billion permanently.
3. Rally, Inc. 是一家全股权公司，资产价值 $ 25 $ 25 $25\$ 25 亿，流通股为 100 亿股。Rally 计划借款 $ 10 $ 10 $10\$ 10 亿，并将这些资金用于回购股票。公司的企业税率为 35 % 35 % 35%35 \% ，Rally 计划将其流动债务永久保持在 $ 10 $ 10 $10\$ 10 亿。
a) Without the increase in leverage, what would Rally’s share price be?
a) 如果没有杠杆的增加，Rally 的股价会是多少？
Share price = $ 25 b 10 b = $ 2.5  Share price  = $ 25 b 10 b = $ 2.5 " Share price "=($25 b)/(10 b)=$2.5\text { Share price }=\frac{\$ 25 b}{10 b}=\$ 2.5
b) What is the lowest price Rally can offer and have shareholders tender their shares? What will its stock price be after the share repurchase in that case?
b) Rally 能够提供的最低价格是什么，以便股东愿意出让他们的股份？在这种情况下，回购股份后其股票价格将是多少？
V L = $ 25 + 0.35 × $ 10 = $ 28.5 V L = $ 25 + 0.35 × $ 10 = $ 28.5 V_(L)=$25+0.35 xx$10=$28.5V_{L}=\$ 25+0.35 \times \$ 10=\$ 28.5
The value of levered equity is E L = $ 28.5 − $ 10 = $ 18.5 E L = $ 28.5 − $ 10 = $ 18.5 E_(L)=$28.5-$10=$18.5E_{L}=\$ 28.5-\$ 10=\$ 18.5
杠杆股权的价值为 E L = $ 28.5 − $ 10 = $ 18.5 E L = $ 28.5 − $ 10 = $ 18.5 E_(L)=$28.5-$10=$18.5E_{L}=\$ 28.5-\$ 10=\$ 18.5
Let n n nn (in billions) be the number of shares to be repurchased and p p pp the lowest repurchase price. We solve the two equation below:
让 n n nn （以十亿为单位）为要回购的股份数量， p p pp 为最低回购价格。我们解下面的两个方程：
n × p = $ 10 ( 10 − n ) × p = $ 18.5 n × p = $ 10 ( 10 − n ) × p = $ 18.5 {:[n xx p=$10],[(10-n)xx p=$18.5]:}\begin{gathered} n \times p=\$ 10 \\ (10-n) \times p=\$ 18.5 \end{gathered}
The lowest repurchase price is 2.85 . The number of shares repurchased is 10 b 2.85 = 3.51 b 10 b 2.85 = 3.51 b (10 b)/(2.85)=3.51 b\frac{10 b}{2.85}=3.51 b, the number of shares outstanding is 6.49 b 6.49 b 6.49 b6.49 b.
最低回购价格为 2.85 。回购的股份数量为 10 b 2.85 = 3.51 b 10 b 2.85 = 3.51 b (10 b)/(2.85)=3.51 b\frac{10 b}{2.85}=3.51 b ，流通在外的股份数量为 6.49 b 6.49 b 6.49 b6.49 b 。
c) Suppose Rally offers $ 3.00 $ 3.00 $3.00\$ 3.00 per share, and shareholders tender their shares at this price. What will Rally’s share price be after the repurchase?
c) 假设 Rally 以每股 $ 3.00 $ 3.00 $3.00\$ 3.00 的价格报价，股东以此价格出售他们的股份。那么 Rally 的股价在回购后将是多少？
The number of shares repurchased is 10 b 3 = 3.33 b 10 b 3 = 3.33 b (10 b)/(3)=3.33 b\frac{10 b}{3}=3.33 b, the number of shares outstanding is 6.67 b 6.67 b 6.67 b6.67 b. The post repurchase share price is:
回购的股份数量为 10 b 3 = 3.33 b 10 b 3 = 3.33 b (10 b)/(3)=3.33 b\frac{10 b}{3}=3.33 b ，流通在外的股份数量为 6.67 b 6.67 b 6.67 b6.67 b 。回购后的股价为：
18.5 b 6.67 b = $ 2.77 18.5 b 6.67 b = $ 2.77 (18.5 b)/(6.67 b)=$2.77\frac{18.5 b}{6.67 b}=\$ 2.77
  1. Markum Enterprises is considering permanently adding $ 100 $ 100 $100\$ 100 million of debt to its capital structure. Markum’s corporate tax rate is 35 % 35 % 35%35 \%.
    Markum Enterprises 正在考虑永久性地将 $ 100 $ 100 $100\$ 100 百万美元的债务添加到其资本结构中。Markum 的公司税率为 35 % 35 % 35%35 \% 。
    a) Absent personal taxes, what is the value of the interest tax shield from the new debt?
    a) 在没有个人税的情况下，新债务的利息税盾的价值是多少？
Tax shield = 0.35 × 100 m = $ 35 m = 0.35 × 100 m = $ 35 m =0.35 xx100 m=$35 m=0.35 \times 100 m=\$ 35 m 税盾 = 0.35 × 100 m = $ 35 m = 0.35 × 100 m = $ 35 m =0.35 xx100 m=$35 m=0.35 \times 100 m=\$ 35 m
b) If investors pay a tax rate of 40 % 40 % 40%40 \% on interest income, and a tax rate of 20 % 20 % 20%20 \% on income from dividends and capital gains, what is the value of the interest tax shield from the new debt?
b) 如果投资者对利息收入的税率为 40 % 40 % 40%40 \% ，对股息和资本利得的收入税率为 20 % 20 % 20%20 \% ，那么新债务的利息税盾的价值是多少？
T ⋆ = 1 − ( 1 − 0.2 ) ( 1 − 0.35 ) 1 − 0.4 = 0.1333 T ⋆ = 1 − ( 1 − 0.2 ) ( 1 − 0.35 ) 1 − 0.4 = 0.1333 T^(***)=1-((1-0.2)(1-0.35))/(1-0.4)=0.1333T^{\star}=1-\frac{(1-0.2)(1-0.35)}{1-0.4}=0.1333
Tax shield = 0.1333 × 100 m = $ 13.33 m = 0.1333 × 100 m = $ 13.33 m =0.1333 xx100m=$13.33m=0.1333 \times 100 \mathrm{~m}=\$ 13.33 \mathrm{~m} 税盾 = 0.1333 × 100 m = $ 13.33 m = 0.1333 × 100 m = $ 13.33 m =0.1333 xx100m=$13.33m=0.1333 \times 100 \mathrm{~m}=\$ 13.33 \mathrm{~m}
5. Rogot Instruments makes fine violins and cellos. It has $ 1 $ 1 $1\$ 1 million in debt outstanding, equity valued at $ 2 $ 2 $2\$ 2 million, and pays corporate income tax at a rate of 21 % 21 % 21%21 \%. Its cost of equity is 12 % 12 % 12%12 \% and its cost of debt is 7 % 7 % 7%7 \%. 
a) What is Rogot’s pre-tax WACC?
罗戈特的税前加权平均资本成本（WACC）是多少？
The pre-tax WACC is:
税前加权平均资本成本（WACC）为：
r w a c c = D D + E r D + E D + E r E r w a c c = 1 3 × 0.07 + 2 3 × 0.12 = 0.1033 r w a c c = D D + E r D + E D + E r E r w a c c = 1 3 × 0.07 + 2 3 × 0.12 = 0.1033 {:[r_(wacc)=(D)/(D+E)r_(D)+(E)/(D+E)r_(E)],[r_(wacc)=(1)/(3)xx0.07+(2)/(3)xx0.12=0.1033]:}\begin{gathered} r_{w a c c}=\frac{D}{D+E} r_{D}+\frac{E}{D+E} r_{E} \\ r_{w a c c}=\frac{1}{3} \times 0.07+\frac{2}{3} \times 0.12=0.1033 \end{gathered}
b) What is Rogot’s (effective after-tax) WACC?
b) Rogot 的（有效税后）加权平均资本成本（WACC）是多少？
r w a c c = D D + E r D ( 1 − T C ) + E D + E r E r w a c c = 1 3 × 0.07 ( 1 − 0.21 ) + 2 3 × 0.12 = 0.0984 r w a c c = D D + E r D 1 − T C + E D + E r E r w a c c = 1 3 × 0.07 ( 1 − 0.21 ) + 2 3 × 0.12 = 0.0984 {:[r_(wacc)=(D)/(D+E)r_(D)(1-T_(C))+(E)/(D+E)r_(E)],[r_(wacc)=(1)/(3)xx0.07(1-0.21)+(2)/(3)xx0.12=0.0984]:}\begin{gathered} r_{w a c c}=\frac{D}{D+E} r_{D}\left(1-T_{C}\right)+\frac{E}{D+E} r_{E} \\ r_{w a c c}=\frac{1}{3} \times 0.07(1-0.21)+\frac{2}{3} \times 0.12=0.0984 \end{gathered}

University of London 伦敦大学

Capital Structure with Taxes and Bankruptcy Costs
带税和破产成本的资本结构

Debt and Taxes 债务与税收
Lecturer: Radoslawa Nikolowa
讲师：拉多斯瓦娃·尼科洛娃
School of Economics and Finance
经济与金融学院

Capital Structure and Corporate Taxes
资本结构与公司税务

In a less than perfect world, capital structure matters because it affects a firm’s tax bill.
在一个不完美的世界里，资本结构很重要，因为它会影响公司的税务负担。
Different financial transactions are taxed differently.
不同的金融交易税率不同。
For a corporation (typically):
对于一家企业（通常）：
  • Taxes are paid on their profits after interest payments are deducted and are tax exempt for the firm.
    税款是在扣除利息支付后的利润上支付的，并且对公司是免税的。
  • Dividends are taxed. 股息需纳税。

MM with Taxes: Intuition
带税的 MM：直觉

Define the “size of the pie” = Value of before-tax cash flows.
定义“蛋糕的大小” = 税前现金流的价值。
MM say: The size of the pie is unaffected by capital structure.
MM 说：饼的大小不受资本结构的影响。
But, with taxation, the government gets a slice too. The firm’s choice of capital structure affects the size of that slice.
但是，随着税收，政府也会得到一部分。公司的资本结构选择会影响这一部分的大小。
Interest payments being tax deductible, the value of the government’s slice can be reduced by using debt rather than equity.
利息支付可抵税，政府份额的价值可以通过使用债务而非股权来降低。

Pie Analogy 饼图类比

Example 示例

Consider our previous example (EPS fallacy) of an all-equity financed firm. Assume now corporate taxes are 40%.
考虑我们之前的例子（每股收益谬论）一个全股权融资的公司。现在假设企业税为 40%。
High 高
 中等（预期）
Medium
(expected)
Medium (expected)| Medium | | :---: | | (expected) |
 Low 低
EBIT 20 M 20 百万 15 M 10 M
Interest payments 利息支付 0 0 0
Taxes 税收 8 M 8 百万 6 M 6 个月 4 M 4 百万
Net income 净收入 12 M 12 个月 9 M 9 百万 6 M 6 个月
Number of shares 股份数量 10 M 10 M 10 M
EPS 1.2 0.9 0.6
High "Medium (expected)" Low EBIT 20 M 15 M 10 M Interest payments 0 0 0 Taxes 8 M 6 M 4 M Net income 12 M 9 M 6 M Number of shares 10 M 10 M 10 M EPS 1.2 0.9 0.6 | | High | Medium <br> (expected) | Low | | :--- | :---: | :---: | :---: | | EBIT | 20 M | 15 M | 10 M | | Interest payments | 0 | 0 | 0 | | Taxes | 8 M | 6 M | 4 M | | Net income | 12 M | 9 M | 6 M | | Number of shares | 10 M | 10 M | 10 M | | EPS | 1.2 | 0.9 | 0.6 | | | | | | | | | | |

Example: Levered Firm 杠杆公司

Suppose the firm announces the issue £ 50 M £ 50 M £50M£ 50 \mathrm{M} of perpetual debt, at a 8% coupon, and uses the proceeds to repurchase shares.
假设公司宣布发行 £ 50 M £ 50 M £50M£ 50 \mathrm{M} 的永久债务，票息为 8%，并利用所得资金回购股票。
(in millions of £ £ ££ )
（以百万 £ £ ££ 计）		 High 高 Medium (expected) 中等（预期） Low 低
EBIT 20 15 10
Interest payments 利息支付 4 4 4
Pretax income 税前收入 16 11 6
Taxes 税收 6.4 4.4 2.4
Net income 净收入 9.6 6.6 3.6
U C F = ( 1 − T c ) ∗ E B I T U C F = ( 1 − T c ) ∗ E B I T UCF=(1-Tc)**EBITU C F=(1-T c) * E B I T Unlevered cash flow 无杠杆现金流 12 9 6
TS = = == Tc ∗ ∗ *** Interest
TS = = == Tc ∗ ∗ *** 利息		 Tax shield 税盾 1.6 1.6 1.6
T C F = U C F + T S T C F = U C F + T S TCF=UCF+TST C F=U C F+T S Total cash flow 总现金流 13.6 10.6 7.6
(in millions of £ ) High Medium (expected) Low EBIT 20 15 10 Interest payments 4 4 4 Pretax income 16 11 6 Taxes 6.4 4.4 2.4 Net income 9.6 6.6 3.6 UCF=(1-Tc)**EBIT Unlevered cash flow 12 9 6 TS = Tc ** Interest Tax shield 1.6 1.6 1.6 TCF=UCF+TS Total cash flow 13.6 10.6 7.6| | (in millions of $£$ ) | High | Medium (expected) | Low | | :---: | :---: | :---: | :---: | :---: | | | EBIT | 20 | 15 | 10 | | | Interest payments | 4 | 4 | 4 | | | Pretax income | 16 | 11 | 6 | | | Taxes | 6.4 | 4.4 | 2.4 | | | Net income | 9.6 | 6.6 | 3.6 | | $U C F=(1-T c) * E B I T$ | Unlevered cash flow | 12 | 9 | 6 | | TS $=$ Tc $*$ Interest | Tax shield | 1.6 | 1.6 | 1.6 | | $T C F=U C F+T S$ | Total cash flow | 13.6 | 10.6 | 7.6 |
TCF = = == Interest + N I + N I +NI+N I TCF = = == 利息 + N I + N I +NI+N I

Cash flows of levered and unlevered firm
杠杆公司和非杠杆公司的现金流

The Value of a Levered Firm
杠杆公司的价值

…is the present value of its expected total cash flows.
…是其预期总现金流的现值。
V L = P V ( C F ) = P V ( U C F ) + P V ( T S ) V L = V U + P V ( T S ) V L = 9 r a + 1.6 r t s V L = P V ( C F ) = P V ( U C F ) + P V ( T S ) V L = V U + P V ( T S ) V L = 9 r a + 1.6 r t s {:[V_(L)=PV(CF)=PV(UCF)+PV(TS)],[V_(L)=V_(U)+PV(TS)],[V_(L)=(9)/(r_(a))+(1.6)/(r_(ts))]:}\begin{gathered} V_{L}=P V(C F)=P V(U C F)+P V(T S) \\ V_{L}=V_{U}+P \boldsymbol{V}(\boldsymbol{T S}) \\ V_{L}=\frac{9}{r_{a}}+\frac{1.6}{r_{t s}} \end{gathered}
Which rate should we use to discount the tax shields?
我们应该使用哪个利率来折现税盾？
What is the risk of the tax shields?
税盾的风险是什么？

Discounting the Tax Shield
折现税盾

For any financial policy that implies a predetermined interest payment schedule (i.e., we know with certainty the interest we will need to pay), we use the cost of debt to discount the tax shields: 
r T S = r d r T S = r d r_(TS)=r_(d)r_{T S}=r_{d}

Intuition: 直觉：

The only risk associated with tax shield is default risk. r d r d r_(d)r_{d} adjusts for default risk.
与税盾相关的唯一风险是违约风险。 r d r d r_(d)r_{d} 调整了违约风险。

The Value of the Levered Firm
杠杆公司的价值

V L = V U + V t s = P V ( U T S ) + r d × D × T r d V L = 9 0.1 + 1.6 0.08 = 90 + 20 = £ 110 M V L = V U + V t s = P V ( U T S ) + r d × D × T r d V L = 9 0.1 + 1.6 0.08 = 90 + 20 = £ 110 M {:[V_(L)=V_(U)+V_(ts)=PV(UTS)+(r_(d)xx D xx T)/(r_(d))],[V_(L)=(9)/(0.1)+(1.6)/(0.08)=90+20=£110M]:}\begin{gathered} V_{L}=V_{U}+V_{t s}=P V(U T S)+\frac{r_{d} \times D \times T}{r_{d}} \\ V_{L}=\frac{9}{0.1}+\frac{1.6}{0.08}=90+20=£ 110 \mathrm{M} \end{gathered}

Cost of Capital with Taxes
税后资本成本

Under MM, capital structure does not affect the distribution of cash flows (or their volatility)
在 MM 理论下，资本结构不影响现金流的分配（或其波动性）
✓ ✓ ✓\checkmark Company’s business risk is still unaffected by taxes
✓ ✓ ✓\checkmark 公司的商业风险仍未受到税收的影响
✓ ✓ ✓\checkmark However, the appropriate rate to discount the firm’s future cash flows (let’s call it WACC) is now lower than in a “no-tax” world, as the cost of debt to the company is lower at r d ( 1 − T c ) r d ( 1 − T c ) r_(d)(1-Tc)r_{d}(1-T c) 
In a world with taxes, the asset cost of capital r Λ r Λ r_(Lambda)r_{\Lambda} is equal to the company cost of capital r W a c c r W a c c r_(Wacc)r_{W a c c} only if the company is unlevered
在有税的世界中，资产资本成本 r Λ r Λ r_(Lambda)r_{\Lambda} 仅在公司无杠杆时等于公司资本成本 r W a c c r W a c c r_(Wacc)r_{W a c c}
r W A C C = E E + D r e + D E + D r d ( 1 − T c ) r a = E E + D r e + D E + D r d r W A C C = E E + D r e + D E + D r d ( 1 − T c ) r a = E E + D r e + D E + D r d {:[r_(WACC)=(E)/(E+D)r_(e)+(D)/(E+D)r_(d)(1-Tc)],[r_(a)=(E)/(E+D)r_(e)+(D)/(E+D)r_(d)]:}\begin{gathered} r_{W A C C}=\frac{E}{E+D} r_{e}+\frac{D}{E+D} r_{d}(1-T c) \\ r_{a}=\frac{E}{E+D} r_{e}+\frac{D}{E+D} r_{d} \end{gathered}
r W A C C r W A C C r_(WACC)r_{W A C C} decreases with leverage and r e r e r_(e)r_{e} and/or r d r d r_(d)r_{d} must change as the values of equity (E) and debt (D) change!
r W A C C r W A C C r_(WACC)r_{W A C C} 随着杠杆的增加而减少， r e r e r_(e)r_{e} 和/或 r d r d r_(d)r_{d} 必须随着股本 (E) 和债务 (D) 的变化而变化！

Modigliani and Miller Proposition 2 with Taxes
莫迪利安尼和米勒命题 2 与税收


r wacc r wacc  r_("wacc ")r_{\text {wacc }} decreases with leverage
r wacc r wacc  r_("wacc ")r_{\text {wacc }} 随着杠杆的增加而减少
The relationship is linear only if debt is safe.
只有在债务安全的情况下，关系才是线性的。
If debt is risky, its cost r D r D r_(D)r_{D} also increases in
如果债务是有风险的，其成本 r D r D r_(D)r_{D} 也会增加
D/E 负债权益比

言

University of London 伦敦大学

Capital Structure with Taxes and Bankruptcy Costs
带税和破产成本的资本结构

Tax Shield and Share Prices
税盾与股价
School of Economics and Finance
经济与金融学院

Tax shield and stock prices: Example
税盾与股票价格：示例

Now consider an all equity financed company with value £ 120 M £ 120 M £120M£ 120 \mathrm{M}, and 10 M shares outstanding.
现在考虑一家全股权融资的公司，价值 £ 120 M £ 120 M £120M£ 120 \mathrm{M} ，并且有 1000 万股流通在外。
The share price before the debt issue was £ 12 £ 12 £12£ 12 a share.
债务发行前的股价为每股 £ 12 £ 12 £12£ 12 。
The firm issues £ 60 M £ 60 M £60M£ 60 \mathrm{M} in (perpetual) debt to repurchase shares. Assume a tax rate of 40 % 40 % 40%40 \%. 
How many shares will the firm be able to repurchase with the £ 60 M £ 60 M £60M£ 60 \mathrm{M} ? Who will benefit from the change in capital structure? 

Prices Change upon Announcement 

(Semi-strong) Efficient Market Hypothesis: Stock price must change before the actual debt issue, at the moment the firm announces it will repurchase shares. 
Why? 为什么？
If not, there is an arbitrage opportunity: Buy one share today, hold it until the debt issue/share repurchase is completed, and then sell at a higher price. 

Tax shield and stock prices: Example 

The value of the unlevered firm’s equity after the announcement is: 
£ 120 M + £ 24 M = £ 144 M £ 120 M + £ 24 M = £ 144 M £120M+£24M=£144M£ 120 \mathrm{M}+£ 24 \mathrm{M}=£ 144 \mathrm{M}
Share price goes up to £ 14.4 £ 14.4 £14.4£ 14.4; existing shareholders will not sell for less. 
Firm ends up repurchasing undefined million shares. The total number of shares outstanding now is 10 − 4.17 = 5.83 10 − 4.17 = 5.83 10-4.17=5.8310-4.17=5.83 million shares. 
After the debt is issued and shares repurchased: 
D = £ 60 M E = £ 84 M D = £ 60 M E = £ 84 M D=£60 ME=£84 MD=£ 60 M E=£ 84 M

Comment 

Raising debt does not create value per se, i.e., you can’t create value by borrowing and sitting on the excess cash. 
Debt only creates value via tax shields relative to raising the same amount in equity. 
Hence, value is created by the tax shield when you: 
> > >> Finance an investment with debt rather than equity. 
> > >> Undertake a recapitalization, i.e., a financial transaction in which some equity is retired and replaced with debt. 

What does this imply in terms of optimal capital structure? 

The firm should issue enough debt to completely eliminate the firm’s tax liabilities. 
  • Average debt-to-value ratio during the last decade for US companies have been 35%. 
Caveats: 
  • Not all firms face full marginal tax rate 
  • There are also personal taxes 
  • High leverage may induce other costs offsetting the tax shield 

夢 Queen Mary 梦 女王玛丽

University of London 伦敦大学

Capital Structure with Taxes and Bankruptcy Costs 

Tax Shield and Personal Taxes 
School of Economics and Finance
经济与金融学院

Personal Taxes 

While corporate taxes have a direct impact on the firm’s cash flows, personal tax rates affect the required (pre-tax) return on each source of funds (debt and equity). 
Investors’ return from debt and equity are taxed differently in general. 
  • These differences might affect the decision whether to have more or less debt in the capital structure. 
  • In most countries there is a tax disadvantage of debt at the personal level. 

Personal Taxes 

How does this tax disadvantage (of debt) at the personal level affect the firm? 
  • Investors care about their after-tax income. 
  • If they pay lower taxes on equity income than on debt income then they will require a lower (pre-tax) return on equity than on debt. 
  • Thus, the firm’s cost of capital will be lower if it issues equity. 
Naturally, this will depend on the marginal investor’s tax brackets. 

Personal Taxes 

 
If paid out as
debt interest
If paid out as debt interest| If paid out as | | :--- | | debt interest |
 
Operating
income of $ 1 $ 1 $1\$ 1
Operating income of $1| Operating | | :---: | | income of $\$ 1$ |
 
If paid out
equity inc
If paid out equity inc| If paid out | | :---: | | equity inc |
Corporate tax  0 T C T C T_(C)\mathrm{~T}_{\mathrm{C}}
 
Income after
corporate tax
Income after corporate tax| Income after | | :--- | | corporate tax |
 1 1 − T C 1 − T C 1-T_(C)1-\mathrm{T}_{\mathrm{C}}
Personal tax  T D T D T_(D)\mathrm{T}_{\mathrm{D}} T E T E T_(E)\mathrm{T}_{\mathrm{E}}
 
Income after all
taxes
Income after all taxes| Income after all | | :--- | | taxes |
 1 − T D 1 − T D 1-T_(D)1-\mathrm{T}_{\mathrm{D}} ( 1 − T C ) ( 1 − T E ) 1 − T C 1 − T E (1-T_(C))(1-T_(E))\left(1-\mathrm{T}_{\mathrm{C}}\right)\left(1-\mathrm{T}_{\mathrm{E}}\right)
"If paid out as debt interest" "Operating income of $1" "If paid out equity inc" Corporate tax 0 T_(C) "Income after corporate tax" 1 1-T_(C) Personal tax T_(D) T_(E) "Income after all taxes" 1-T_(D) (1-T_(C))(1-T_(E))| If paid out as <br> debt interest | Operating <br> income of $\$ 1$ | If paid out <br> equity inc | | :--- | :--- | :---: | | Corporate tax | 0 | $\mathrm{~T}_{\mathrm{C}}$ | | Income after <br> corporate tax | 1 | $1-\mathrm{T}_{\mathrm{C}}$ | | Personal tax | $\mathrm{T}_{\mathrm{D}}$ | $\mathrm{T}_{\mathrm{E}}$ | | Income after all <br> taxes | $1-\mathrm{T}_{\mathrm{D}}$ | $\left(1-\mathrm{T}_{\mathrm{C}}\right)\left(1-\mathrm{T}_{\mathrm{E}}\right)$ |

Personal Taxes 

Corporate borrowing is better off if: ( 1 − T D ) > ( 1 − T C ) ( 1 − T E ) 1 − T D > 1 − T C 1 − T E (1-T_(D)) > (1-T_(C))(1-T_(E))\left(1-T_{D}\right)>\left(1-T_{C}\right)\left(1-T_{E}\right) 
The value of the levered firm with corporate and personal taxes: 
V L = V U + ( 1 − ( 1 − T C ) ( 1 − T E ) ( 1 − T D ) ) D V L = V U + 1 − 1 − T C 1 − T E 1 − T D D V_(L)=V_(U)+(1-((1-T_(C))(1-T_(E)))/((1-T_(D))))DV_{L}=V_{U}+\left(1-\frac{\left(1-T_{C}\right)\left(1-T_{E}\right)}{\left(1-T_{D}\right)}\right) D

The effective tax advantage with or without personal taxes 

1971-2022

University of London 伦敦大学

Capital Structure with Taxes and Bankruptcy Costs 

Costs of Financial Distress 
School of Economics and Finance
经济与金融学院

Costs of Financial Distress 

If taxes were the only issue, (most) companies would be 100% debt financed. 
Common sense suggests otherwise: If the debt burden is too high, the company will have trouble paying. 
The result is that we need to consider expected costs of financial distress. 

Financial Distress 

Financial distress: Cash flow is not sufficient to cover current obligations to creditors, which starts a process of resolving the broken contract with creditors. 
  • Private renegotiation 
  • Bankruptcy is supervised by court (In the US, Chapter 7 and Chapter 11) 
Comment: Bankruptcy does not destroy value per se. What destroys value is the costs that a company incurs when in financial distress. 

Costs of Financial Distress 

Direct costs (Bankruptcy costs): Costs that arise when a firm defaults on its debt claims. 
The average direct costs of bankruptcy are approximately 3 % 3 % 3%3 \% to 4 % 4 % 4%4 \% of the prebankruptcy market value of total assets for larger firms and 20-25% for smaller ones (observable, easier to measure). 
Indirect costs: Costs that arise when it becomes sufficiently likely that a company may default on its debt claims. 
The average indirect costs of bankruptcy are approximately 10-20% of the prebankruptcy market value of total assets (not observable, harder to measure). 

Direct Costs 

Legal expenses, court costs, advisory fees. 
Energy Future Holdings, the largest power utility in Texas, has paid its lawyers and financial advisers $600,000 a day including weekends and holidays. Since the company filed for reorganization under Chapter 11 in April 2014, lawyers and financial advisers had charged EFH close to $ 500 $ 500 $500\$ 500 million by August 2016. The bill was expected to grow up to $ 700 $ 700 $700\$ 700 million. 
Opportunity costs, for example time spent dealing with creditors 
If the firm has to liquidate assets in a fire-sale, then these assets may be sold for much less than their ‘fair value’ 

Indirect Costs 

Having to cut profitable new investments 
  • Firms cut capital expenditures and R&D investments while in financial distress 
Loss of customers and suppliers 
  • Costly when long term relationships are important 
Loss of employees 
  • Problem for firms with high-skilled employees who are (more) difficult to retain 

Indirect Costs 

It is harder to respond to competitors 
  • Empirical evidence shows that highly levered firms in a given industry lose market share to competitors with lower leverage, cannot respond to competitors price changes, close plants, etc. 

Other indirect costs 

  • Conflicts of interest between equity and debt-holders leading to under or over-investment problems. 

University of London 伦敦大学

Capital Structure with Taxes and Bankruptcy Costs 

Static Trade-off Theory of Capital Structure 
School of Economics and Finance
经济与金融学院

Value of the Firm 

The value of a levered firm is given by: 
V L = V U + P V ( T S ) − P V ( E ( C O F D ) ) V L = V U + P V ( T S ) − P V ( E ( C O F D ) ) V_(L)=V_(U)+PV(TS)-PV(E(COFD))V_{L}=V_{U}+P V(T S)-P V(E(C O F D))
Thus, there is a trade-off between: 
  • The tax advantage of leverage. 
  • The disadvantage of leverage caused by the costs of financial distress. 

Value of the Firm 

Firm's Value 

Setting a Target Capital Structure: A Checklist 

Taxes 

  • Does the company benefit from the debt tax shield? 

Expected Bankruptcy Costs and Cost of Financial Distress 

  • Cash flow volatility. 
  • Need for external funds for investment. 
  • Competitive threat if pinched for cash. 
  • Customers/Suppliers care about distress. 
  • Hard to redeploy assets. 
  • Fire sales. 

Does the checklist explain observed debt levels? 

Industry  D/V Ratio (%) 
Electric and Gas  43.2
Food Production  22.9
Paper and Plastic  30.4
Equipment  19.1
Retailers  21.7
Chemicals  17.3
Computer Software  3.5
Industry D/V Ratio (%) Electric and Gas 43.2 Food Production 22.9 Paper and Plastic 30.4 Equipment 19.1 Retailers 21.7 Chemicals 17.3 Computer Software 3.5| Industry | D/V Ratio (%) | | :--- | :---: | | Electric and Gas | 43.2 | | Food Production | 22.9 | | Paper and Plastic | 30.4 | | Equipment | 19.1 | | Retailers | 21.7 | | Chemicals | 17.3 | | Computer Software | 3.5 |
Yes at a broad level. But other factors may also matter.