This Document Contains Chapters 16 to 17 Chapter 16 capital structure: limits to the use of debt 1. Direct costs are potential legal and administrative costs. These are the costs associated with the litigation arising from a liquidation or bankruptcy. These costs include lawyer’s fees, courtroom costs, and expert witness fees. Indirect costs include the following: 1) Impaired ability to conduct business. Firms may suffer a loss of sales due to a decrease in consumer confidence and loss of reliable supplies due to a lack of confidence by suppliers. 2) Incentive to take large risks. When faced with projects of different risk levels, managers acting in the shareholders’ interest have an incentive to undertake high-risk projects. Imagine a firm with only one project, which pays €100 in an expansion and €60 in a recession. If debt payments are €60, the shareholders receive €40 (= €100 – 60) in the expansion but nothing in the recession. The bondholders receive €60 for certain. Now, alternatively imagine that the project pays €110 in an expansion but €50 in a recession. Here, the shareholders receive €50 (= €110 – 60) in the expansion but nothing in the recession. The bondholders receive only €50 in the recession because there is no more money in the firm. That is, the firm simply declares bankruptcy, leaving the bondholders “holding the bag”. Thus, an increase in risk can benefit the shareholders. The key here is that the bondholders are hurt by risk, since the shareholders have limited liability. If the firm declares bankruptcy, the shareholders are not responsible for the bondholders’ shortfall. 3) Incentive to under-invest. If a company is near bankruptcy, shareholders may well be hurt if they contribute equity to a new project, even if the project has a positive NPV. The reason is that some (or all) of the cash flows will go to the bondholders. Suppose a property developer owns a building that is likely to go bankrupt, with the bondholders receiving the property and the developer receiving nothing. Should the developer take €1 million out of his own pocket to add a new wing to a building? Perhaps not, even if the new wing will generate cash flows with a present value greater than €1 million. Since the bondholders are likely to end up with the property anyway, the developer will pay the additional €1 million and likely end up with nothing to show for it. 4) Milking the property. In the event of bankruptcy, bondholders have the first claim to the assets of the firm. When faced with a possible bankruptcy, the shareholders have strong incentives to vote for increased dividends or other distributions. This will ensure them of getting some of the assets of the firm before the bondholders can lay claim to them. 2. In sum, managers will act in their own interests and that of shareholders when the firm is in financial distress. With respect to their own jobs, they will opt for projects that minimize risk, possibly to the detriment of maximizing value. If a firm is very likely to fail, they may decide to go for an exceptionally risky project that has a low probability of very high returns. If the project fails, the firm will become insolvent (which was going to happen anyway) and if the project succeeds, they have staved off a job loss. Managers will also concern themselves with decisions that increase the wealth of shareholders to the detriment of bondholders, especially if they themselves are shareholders. Examples of such activity include issuing extraordinary dividends, choosing risky projects that may pay off, and other selfish strategies. 3. Shareholders can undertake the following measures in order to minimize the costs of debt: 1) Use protective covenants. Firms can enter into agreements with the bondholders that are designed to decrease the cost of debt. There are two types of protective covenants. This Document Contains Chapters 16 to 17 Negative covenants prohibit the company from taking actions that would expose the bondholders to potential losses. An example would be prohibiting the payment of dividends in excess of earnings. Positive covenants specify an action that the company agrees to take or a condition the company must abide by. An example would be agreeing to maintain its working capital at a minimum level. 2) Repurchase debt. A firm can eliminate the costs of bankruptcy by eliminating debt from its capital structure. 3) Consolidate debt. If a firm decreases the number of debt holders, it may be able to decrease the direct costs of bankruptcy should the firm become insolvent. 4. Modigliani and Miller’s theory with corporate taxes indicates that, since there is a positive tax advantage of debt, the firm should maximize the amount of debt in its capital structure. In reality, however, no firm adopts an all-debt financing strategy. MM’s theory ignores both the financial distress and agency costs of debt. The marginal costs of debt continue to increase with the amount of debt in the firm’s capital structure so that, at some point, the marginal costs of additional debt will outweigh its marginal tax benefits. Therefore, there is an optimal level of debt for every firm at the point where the marginal tax benefits of the debt equal the marginal increase in financial distress and agency costs. 5. Firms can signal future growth opportunities to the market by issuing debt instead of equity. If a firm is unlikely to generate strong cash flows in the future, they would want to avoid debt because the interest burden may result in financial distress and possible insolvency. Thus, a debt issue is likely to signal good news. Managers should not try to fool the market by issuing debt when they do not have strong future cash flow generating power because the market may be fooled for a short while, but once it understands the true prospects of the firm, investors will flock to sell the shares of the company possibly putting it in a worse position than if it had issued equity. 6. There are two major sources of the agency costs of equity: 1) Shirking. Managers with small equity holdings have a tendency to reduce their work effort, thereby hurting both the debt holders and outside equity holders. 2) Perquisites. Since management receives all the benefits of increased perquisites but only shoulder a fraction of the cost, managers have an incentive to overspend on luxury items at the expense of debt holders and outside equity holders. 7. The pecking order theory states that firms will use internal financing for new investments as a first choice. If this has been exhausted, the firm will go for external financing with safer financing options, such as debt, preferred to other riskier sources such as equity. A deeply discounting rights offering is an equity issue at a significantly lower issue price. Therefore, managers would choose a public issue before a deep discount issue, if possible. 8. Growth opportunities reduce the optimal level of debt in a firm. The trade-off theory argues that the optimal debt level should be close to 100 percent, but this does not occur in practice. In addition the pecking order theory argues that firms will use debt if possible to a company’s maximum level. Again, this does not occur in many companies. Incorporating growth opportunities into the issue may explain differences in capital structure across companies. 9. Market timing theory argues that managers issue debt when debt is selling at a premium and issue equity when equity is selling at a premium. Thus, capital structure is path dependant and has nothing to do with bankruptcy costs, tax shield, or asymmetric information. 10. No theory explains every aspect of practice. There are likely to be elements of all theories in firm financial decision making but no firm is likely to follow any theory blindly. The static trade-off theory, pecking order theory, and market timing theory attempt to explain corporate practice. Each theory was not developed to predict what will happen although they may have some predictive power. In addition, different corporate environments are likely to lead to different decision making patterns. This is discussed in more detail in chapter 2 on Corporate Governance. 11. The statement is incorrect. If a firm has debt, it might be advantageous to shareholders for the firm to undertake risky projects, even those with negative net present values. This incentive results from the fact that most of the risk of failure is borne by bondholders. Therefore, value is transferred from the bondholders to the shareholders by undertaking risky projects, even if the projects have negative NPVs. This incentive is even stronger when the probability and costs of bankruptcy are high. 12. The question is in error. Debt does not increase the risk of the firm; it increases the risk of the equity. A manager may be able to diversify bankruptcy risk if the risk relates to macroeconomic factors. For example, if a firm’s cost base is hugely dependent on the cost of oil, the firm can hedge this risk by buying derivatives in oil. Alternatively, if the revenue of a firm is dependent on oil, it can go short on oil derivatives. 13. The choice of debt and equity depends upon the tax system operating within a country and the maturity of the financing. In this case, the tax lost carry-forward lasts for only three years. Funding is normally required over a longer period and so the benefit of the tax-loss carry forward is not great unless more losses are incurred in the meantime. Obviously, this question relates to the tax effect on financing choices. However, there is still no consensus on what really drives the choice between debt and equity. Students should be given free rein to develop their ideas and discuss them in class. 14. The more capital intensive industries, such as airlines, telecommunication, and utilities, tend to use greater financial leverage. Also, industries with less predictable future earnings, such as technology firms, tend to use less financial leverage. Such industries also have a higher concentration of growth and start-up firms. Overall, the general tendency is for firms with identifiable, tangible assets and relatively more predictable future earnings to use more debt financing. These are typically the firms with the greatest need for external financing and the greatest likelihood of benefiting from the interest tax shelter. Notice that financial firms have very high debt levels. This was more a reflection of the nature of the finance sector between 1998 and 2007 than a general reflection of the finance industry. 15. It could be argued that using bankruptcy laws as a sword may simply be the best use of the asset. Creditors are aware at the time a loan is made of the possibility of bankruptcy, and the interest charged incorporates it. 16. If the firm was going to go bankrupt because its costs made it uncompetitive, this could be an argument for going into administration. Bankruptcy could allow a firm to restructure its cost base and continue operations. However, the other side of the argument is that a firm could abuse the bankruptcy code. Rather than renegotiate labour agreements, a firm can use bankruptcy to trample on the rights of employees. A strong argument can always be made that making the best use of bankruptcy law is no different from, for example, minimizing taxes by making best use of tax laws. Indeed, a strong case can be made that it is the financial manager’s duty to do so. 17. a. Using M&M Proposition I with taxes, the value of a levered firm is: VL = [EBIT(1 – tC)/R0] + tCB VL = [£750,000(1 – .28)/.15] + .28(£1,500,000) VL = £4,020,000 b. The CFO may be correct. The value calculated in part a does not include the costs of any non-marketed claims, such as bankruptcy or agency costs. 18. a. Debt issue: The company needs a cash infusion of £2 million. If the company issues debt, the annual interest payments will be: Interest = £2,000,000(.09) = £180,000 The cash flow to the owner will be the EBIT minus the interest payments, or: 40 hour week cash flow = £500,000 – £180,000 = £320,000 50 hour week cash flow = £600,000 – £180,000 = £420,000 Equity issue: If the company issues equity, the company value will increase by the amount of the issue. So, the current owner’s equity interest in the company will decrease to: Scott’s ownership percentage = £3,000,000 / (£3,000,000 + £2,000,000) = .60 So, Scott’s cash flow under an equity issue will be 60 percent of EBIT, or: 40 hour week cash flow = .60(£500,000) = £300,000 50 hour week cash flow = .60(£600,000) = £360,000 b. Scott will work harder under the debt issue since his cash flows will be higher. Scott will gain more under this form of financing since the payments to bondholders are fixed. Under an equity issue, new investors share proportionally in his hard work, which will reduce his propensity for this additional work. c. The direct cost of both issues is the payments made to new investors. The indirect costs to the debt issue include potential bankruptcy and financial distress costs. The indirect costs of an equity issue include shirking and perquisites. 19. a. The interest payments each year will be: Interest payment = .10(R980,000) = R98,000 This is exactly equal to the EBIT, so no cash is available for shareholders. Under this scenario, the value of equity will be zero since shareholders will never receive a payment. Since the market value of the company’s debt is R980,000, and there is no probability of default, the total value of the company is the market value of debt. This implies the debt to value ratio is 1 (one). b. At a 5 percent growth rate, the earnings next year will be: Earnings next year = R98,000(1.04) = R101,920 So, the cash available for shareholders is: Payment to shareholders = R101,920 – R98,000 = R3,920 Since there is no risk, the required return for shareholders is the same as the required return on the company’s debt. The payments to shareholders will increase at the growth rate of four percent (a growing perpetuity), so the value of these payments today is: Value of equity = R3,920 / (.10 – .04) = R65,333.33 And the debt to value ratio now is: Debt/Value ratio = R980,000 / (R980,000 + R65,333.33) = 0.938 c. At an 8 percent growth rate, the earnings next year will be: Earnings next year = R98,000(1.08) =R105,840 So, the cash available for shareholders is: Payment to shareholders = R105,840 – R98,000 = R7,840 Since there is no risk, the required return for shareholders is the same as the required return on the company’s debt. The payments to shareholders will increase at the growth rate of eight percent (a growing perpetuity), so the value of these payments today is: Value of equity = R7,840 / (.1 – .08) = R392,000 And the debt to value ratio now is: Debt/Value ratio = R980,000 / (R980,000 + R392,000) = .714 20. The chief executive may be correct, but he may also be incorrect. It is true the interest tax shield is valuable, and adding debt can possibly increase the value of the company. However, if the company’s debt is increased beyond some level, the value of the interest tax shield becomes less than the additional costs from financial distress. 21. a. The total value of a firm’s equity is the discounted expected cash flow to the firm’s shareholders. If the expansion continues, each firm will generate earnings before interest and taxes of £2 million. If there is a recession, each firm will generate earnings before interest and taxes of only £800,000. Since Steinberg owes its bondholders £750,000 at the end of the year, its shareholders will receive £1.25 million (= £2,000,000 – £750,000) if the expansion continues. If there is a recession, its shareholders will only receive £50,000 (= £800,000 – £750,000). So, assuming a discount rate of 15 percent, the market value of Steinberg’s equity is: SSteinberg = [.80(£1,250,000) + .20(£50,000)] / 1.15 = £878,261 Steinberg’s bondholders will receive £750,000 whether there is a recession or a continuation of the expansion. So, the market value of Steinberg’s debt is: BSteinberg = [.80(£750,000) + .20(£750,000)] / 1.15 = £652,174 Since Dietrich owes its bondholders £1 million at the end of the year, its shareholders will receive £1 million (= £2 million – £1 million) if the expansion continues. If there is a recession, its shareholders will receive nothing since the firm’s bondholders have a more senior claim on all £800,000 of the firm’s earnings. So, the market value of Dietrich’s equity is: SDietrich = [.80(£1,000,000) + .20(£0)] / 1.15 = £695,652 Dietrich’s bondholders will receive £1 million if the expansion continues and £800,000 if there is a recession. So, the market value of Dietrich’s debt is: BDietrich = [.80(£1,000,000) + .20(£800,000)] / 1.15 = £834,783 b. The value of company is the sum of the value of the firm’s debt and equity. So, the value of Steinberg is: VSteinberg = B + S VSteinberg = £652,174 + £878,261 VSteinberg = £1,530,435 And value of Dietrich is: VDietrich = B + S VDietrich = £834,783 + £695,652 VDietrich = £1,530,435 You should disagree with the CEO’s statement. The risk of bankruptcy per se does not affect a firm’s value. It is the actual costs of bankruptcy that decrease the value of a firm. Note that this problem assumes that there are no bankruptcy costs 22. a. The expected value of each project is the sum of the probability of each state of the economy times the value in that state of the economy. Since this is the only project for the company, the company value will be the same as the project value, so: Low-volatility project value = .50(CHK50,000) + .50(CHK70,000) Low-volatility project value = CHK60,000 High-volatility project value = .50(CHK10,000) + .50(CHK80,000) High-volatility project value = CHK45,000 The low-volatility project maximizes the expected value of the firm. b. The value of the equity is the residual value of the company after the bondholders are paid off. If the low-volatility project is undertaken, the firm’s equity will be worth Kc0 if the economy is bad and CHK20,000 if the economy is good. Since each of these two scenarios is equally probable, the expected value of the firm’s equity is: Expected value of equity with low-volatility project = .50(CHK0) + .50(CHK20,000) Expected value of equity with low-volatility project = CHK10,000 And the value of the company if the high-volatility project is undertaken will be: Expected value of equity with high-volatility project = .50(CHK0) + .50(CHK30,000) Expected value of equity with high-volatility project = CHK15,000 c. Risk-neutral investors prefer the strategy with the highest expected value. Thus, the company’s shareholders prefer the high-volatility project since it maximizes the expected value of the company’s equity. d. In order to make shareholders indifferent between the low-volatility project and the high- volatility project, the bondholders will need to raise their required debt payment so that the expected value of equity if the high-volatility project is undertaken is equal to the expected value of equity if the low-volatility project is undertaken. As shown in part a, the expected value of equity if the low-volatility project is undertaken is CHK10,000. If the high-volatility project is undertaken, the value of the firm will be CHK10,000 if the economy is bad and CHK80,000 if the economy is good. If the economy is bad, the entire CHK10,000 will go to the bondholders and shareholders will receive nothing. If the economy is good, shareholders will receive the difference between CHK80,000, the total value of the firm, and the required debt payment. Let X be the debt payment that bondholders will require if the high-volatility project is undertaken. In order for shareholders to be indifferent between the two projects, the expected value of equity if the high-volatility project is undertaken must be equal to Kc10,000, so: Expected value of equity = CHK10,000 = .50(CHK0) + .50(CHK80,000 – X) X = CHK60,000 23. a. The expected payoff to bondholders is the face value of debt or the value of the company, whichever is less. Since the value of the company in a recession is £100 million and the required debt payment in one year is £150 million, bondholders will receive the lesser amount, or £100 million. b. The promised return on debt is: Promised return = (Face value of debt / Market value of debt) – 1 Promised return = (£150,000,000 / £108,930,000) – 1 Promised return = .3770 or 37.70% c. In part a, we determined bondholders will receive £100 million in a recession. In a boom, the bondholders will receive the entire £150 million promised payment since the market value of the company is greater than the payment. So, the expected value of debt is: Expected payment to bondholders = .60(£150,000,000) + .40(£100,000,000) Expected payment to bondholders = £130,000,000 So, the expected return on debt is: Expected return = (Expected value of debt / Market value of debt) – 1 Expected return = (£130,000,000 / £108,930,000) – 1 Expected return = .1934 or 19.34% 24. a. In their no tax model, MM assume that tC, tB, and C(B) are all zero. Under these assumptions, VL = VU, signifying that the capital structure of a firm has no effect on its value. There is no optimal debt-equity ratio. b. In their model with corporate taxes, MM assume that tC > 0 and both tB and C(B) are equal to zero. Under these assumptions, VL = VU + tCB, implying that raising the amount of debt in a firm’s capital structure will increase the overall value of the firm. This model implies that the debt-equity ratio of every firm should be infinite. c. If the costs of financial distress are zero, the value of a levered firm equals: VL = VU + {1 – [(1 – tC) / (1 – tB)}] × B Therefore, the change in the value of this all-equity firm that issues debt and uses the proceeds to repurchase equity is: Change in value = {1 – [(1 – tC) / (1 – tB)}] × B Change in value = {1 – [(1 – .3399) / (1 – .50)]} × €1,000,000 Change in value = -€320,200 d. If the costs of financial distress are zero, the value of a levered firm equals: VL = VU + {1 – [(1 – tC) / (1 – tB)]} × B Therefore, the change in the value of an all-equity firm that issues €1 of perpetual debt instead of €1 of perpetual equity is: Change in value = {1 – [(1 – tC) / (1 – tB)]} × €1 If the firm is not able to benefit from interest deductions, the firm’s taxable income will remain the same regardless of the amount of debt in its capital structure, and no tax shield will be created by issuing debt. Therefore, the firm will receive no tax benefit as a result of issuing debt in place of equity. In other words, the effective corporate tax rate when we consider the change in the value of the firm is zero. Debt will have no effect on the value of the firm since interest payments will not be tax deductible. So, for this firm, the change in value is: Change in value = {1 – [(1 – 0) / (1 – .50)]} × €1 Change in value = –€1 The value of the firm will decrease by €1 if it adds €1 of perpetual debt rather than €1 of equity. 25. a. If the company decides to retire all of its debt, it will become an unlevered firm. The value of an all-equity firm is the present value of the after-tax cash flow to equity holders, which will be: VU = (EBIT)(1 – tC) / R0 VU = (€1,100,000)(1 – .3333) / .20 VU = €3,666,850 b. Since there are no bankruptcy costs, the value of the company as a levered firm is: VL = VU + {1 – [(1 – tC) / (1 – tB)}] × B VL = €3,666,850 + {1 – [(1 – .3333) / (1 – .4)]} × €2,000,000 VL = €3,444,517 c. The bankruptcy costs would not affect the value of the unlevered firm since it could never be forced into bankruptcy. So, the value of the levered firm with bankruptcy would be: VL = VU + {1 – [(1 – tC) / (1 – tB)}] × B – C(B) VL = (€3,666,850 + {1 – [(1 – .3333) / (1 – .4)]} × €2,000,000) – €300,000 VL = €3,144,517 The company should choose the all-equity plan with this bankruptcy cost. 26. Bankruptcy occurs when a firm cannot pay its creditors. Since Islamic financing does not involve the use of debt, this means that non-payment of creditors relates only to trade creditors. As a result, in terms of bankruptcy risk, Islamic financing is similar to all equity firms. However, it doesn’t mean that firms with Islamic financing are better than Western firms. It simply means that they are different. 27. Clearly a pension deficit is a future potential liability. This means that the firm should incorporate the pension deficit as long-term debt, which will have an impact on capital structure. The higher a deficit the more risky the firm is because it is a higher potential liability. It is easy to incorporate pension deficits into the MM framework – it is effectively another source of financing and so should be treated separately. 28. A guarantor contract has no effect on the MM framework. For a company that has borrowed money under guarantee from another entity, the risk and value of the debt is adjusted by the lower risk of the security. In terms of the guarantor, it is a liability and should be included in the capital structure. The value of the debt in the guarantor’s balance sheet would be a function of the outstanding loan value and the risk of the borrowing company. 29. There are several theories that could explain this trend. Prospect theory argues that low debt levels are a function of the immediate past experience of managers. Since they had financial difficulty during the global debt crisis, their psychological tendency is to keep lower debt levels in the near future. However, it could also be argued that the capital structure is more conservative because the economy is still highly risky. Finally, another view (Market Timing) is that debt is not as valuable in the post economic crisis world and so companies don’t want to issue debt. 30. The patterns of debt ratios across industries in Table 16.3 could be explained by market timing by arguing that they are simply a path dependant function of past demand. In effect, any pattern can be explained in this way. An intuitive explanation is that those industries with high debt ratios also tend to have high levels of tangible assets. These can be used as collateral in debt issues and therefore such firms will have more freedom to issue debt and borrow for their financing needs. Chapter 17 Valuation and Capital Budgeting for the Levered Firm 1. APV is equal to the NPV of the project (i.e. the value of the project for an unlevered firm) plus the NPV of financing side effects. 2. FTE uses levered cash flow and other methods use unlevered cash flow. 3. The WACC approach assumes that a firm has a target debt to equity ratio. Therefore, it is fully consistent with such a concept. 4. This is discussed fully in section 17.4. The adjusted present value (APV) approach first values the project on an all-equity basis. That is, the project’s aftertax cash flows under all-equity financing (called unlevered cash flows, or UCF) are placed in the numerator of the capital budgeting equation. The discount rate, assuming all-equity financing, appears in the denominator. We then add the net present value of the debt. The flow to equity (FTE) approach discounts the aftertax cash flow from a project going to the shareholders of a levered firm (LCF). LCF, which stands for levered cash flow, is the residual to shareholders after interest has been deducted. The discount rate is RS, the cost of capital to the shareholders of a levered firm. WACC approach calculates the project’s aftertax cash flows assuming all-equity financing (UCF). The UCF is placed in the numerator of the capital budgeting equation. The denominator, RWACC, is a weighted average of the cost of equity capital and the cost of debt capital. Use WACC or FTE if the firm’s target debt-to-value ratio applies to the project over its life. Use APV if the project’s level of debt is known over the life of the project. 5. First determine the cost of equity capital using an appropriate methodology such as CAPM. Second, determine the hypothetical cost of equity assuming that the firm has no debt in its capital structure. If we were using APV, this would be the appropriate discount rate to use. If we were using the FTE approach, we would use the cost of levered equity and if we were using WACC, we would calculate the weighted average cost of capital of the firm. 6. You can estimate the unlevered beta from a levered beta. The unlevered beta is the beta of the assets of the firm; as such, it is a measure of the business risk. Note that the unlevered beta will always be lower than the levered beta (assuming the betas are positive). The difference is due to the leverage of the company. Thus, the second risk factor measured by a levered beta is the financial risk of the company. 7. The WACC method does not explicitly include the interest cash flows, but it does implicitly include the interest cost in the WACC. If he insists that the interest payments are explicitly shown, you should use the FTE method. 8. a. The maximum price that the company should be willing to pay for the fleet of cars with all- equity funding is the price that makes the NPV of the transaction equal to zero. For this type of problem, we must use Solver. Start with an starting value because this will be the input for the solver algorithm. We chose £500,000 but this could have been any figure. (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)- 1 £500,000 £100,000 £100,000 £400,000 2 £400,000 £80,000 £180,000 £320,000 3 £320,000 £64,000 £244,000 £256,000 4 £256,000 £51,200 £295,200 £204,800 5 £204,800 £40,960 £336,160 £163,840 Now estimate the operating cash flow: Year EBTD Depreciation 20% EBT Tax Net Income Operating Cash Flow 28% 1 £120,000 £100,000 £20,000 £5,600 £14,400 £114,400 2 £120,000 £80,000 £40,000 £11,200 £28,800 £108,800 3 £120,000 £64,000 £56,000 £15,680 £40,320 £104,320 4 £120,000 £51,200 £68,800 £19,264 £49,536 £100,736 5 £120,000 £40,960 £79,040 £22,131 £56,909 £97,869 And now the cash flow analysis: Year Investment Operating Cash Flow Net Cash Flow PV Cash Flows @ 10% 0 -£500,000 -£500,000 -£500,000 1 £114,400 £114,400 £104,000 2 £108,800 £108,800 £89,917 3 £104,320 £104,320 £78,377 4 £100,736 £100,736 £68,804 5 £163,840 £97,869 £261,709 £162,501 The NPV with a starting value of £500,000 is £3,599. We now use solver where NPV refers to the cell containing the NPV calculation and STARTINGVALUE refers to the cell that contains the starting value. Solver arrives at a Starting Value solution of £505,556. This makes the NPV of the project equal to zero. The print out is given below: Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 £505,556 £101,111 £101,111 £404,444 2 £404,444 £80,889 £182,000 £323,556 3 £323,556 £64,711 £246,711 £258,844 4 £258,844 £51,769 £298,480 £207,076 5 £207,076 £41,415 £339,895 £165,660 Year EBTD Depreciation 20% EBT Tax Net Income Operating Cash Flow 28% 1 £120,000 £101,111 £18,889 £5,289 £13,600 £114,711 2 £120,000 £80,889 £39,111 £10,951 £28,160 £109,049 3 £120,000 £64,711 £55,289 £15,481 £39,808 £104,519 4 £120,000 £51,769 £68,231 £19,105 £49,126 £100,895 5 £120,000 £41,415 £78,585 £22,004 £56,581 £97,996 Year Investment Operating Cash Flow Net Cash Flow PV Cash Flows @ 10% 0 -£505,556 -£505,556 -£505,556 1 £114,711 £114,711 £104,283 2 £109,049 £109,049 £90,123 3 £104,519 £104,519 £78,527 4 £100,895 £100,895 £68,913 5 £165,660 £97,996 £263,657 £163,710 NPV with a starting value of £505,556 is zero. b. The adjusted present value (APV) of a project equals the net present value of the project if it were funded completely by equity plus the net present value of any financing side effects. In this case, the NPV of financing side effects equals the after-tax present value of the cash flows resulting from the firm’s debt, so: APV = NPV(All-Equity) + NPV(Financing Side Effects) So, the NPV of each part of the APV equation is: NPV(All-Equity) The company paid £375,000 for the fleet of cars. Because this fleet will be fully depreciated over five years using the reducing balance method, the depreciation schedule is: (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 £375,000 £75,000 £75,000 £300,000 2 £300,000 £60,000 £135,000 £240,000 3 £240,000 £48,000 £183,000 £192,000 4 £192,000 £38,400 £221,400 £153,600 5 £153,600 £30,720 £252,120 £122,880 The Operating Cash Flow is: Year EBTD Depreciation 20% EBT Tax Net Income Operating Cash Flow 28% 1 £120,000 £75,000 £45,000 £12,600 £32,400 £107,400 2 £120,000 £60,000 £60,000 £16,800 £43,200 £103,200 3 £120,000 £48,000 £72,000 £20,160 £51,840 £99,840 4 £120,000 £38,400 £81,600 £22,848 £58,752 £97,152 5 £120,000 £30,720 £89,280 £24,998 £64,282 £95,002 The Cash Flow Analysis is: Year Investment Operating Cash Flow Net Cash Flow PV Cash Flows @ 10% 0 -£375,000 -£375,000 -£375,000 1 £107,400 £107,400 £97,636 2 £103,200 £103,200 £85,289 3 £99,840 £99,840 £75,011 4 £97,152 £97,152 £66,356 5 £122,880 £95,002 £217,882 £135,287 So, the NPV of the all-equity project is £84,580. NPV (Financing Side Effects) The net present value of financing side effects equals the after-tax present value of cash flows resulting from the firm’s debt, so: NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Payments) Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt RB. So, the NPV of the financing side effects are: NPV = £250,000 – (1 – 0.28)(0.08)(£250,000)PVIFA8%,5 – [£250,000/(1.08)5] NPV = £250,000 - £57,495 - £170,146 NPV = £22,359 So, the APV of the project is: APV = NPV(All-Equity) + NPV(Financing Side Effects) APV = £84,580 + £22,359 APV = £106,940 9. The adjusted present value (APV) of a project equals the net present value of the project if it were funded completely by equity plus the net present value of any financing side effects. In this case, the NPV of financing side effects equals the after-tax present value of the cash flows resulting from the firm’s debt, so: APV = NPV(All-Equity) + NPV(Financing Side Effects) So, the NPV of each part of the APV equation is: NPV(All-Equity) Depreciation Schedule: Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 € 10,000,000 € 2,000,000 € 2,000,000 € 8,000,000 2 € 8,000,000 € 1,600,000 € 3,600,000 € 6,400,000 3 € 6,400,000 € 1,280,000 € 4,880,000 € 5,120,000 4 € 5,120,000 € 1,024,000 € 5,904,000 € 4,096,000 5 € 4,096,000 € 819,200 € 6,723,200 € 3,276,800 6 € 3,276,800 € 655,360 € 7,378,560 € 2,621,440 7 € 2,621,440 € 524,288 € 7,902,848 € 2,097,152 8 € 2,097,152 € 419,430 € 8,322,278 € 1,677,722 9 € 1,677,722 € 335,544 € 8,657,823 € 1,342,177 10 € 1,342,177 € 1,342,177 € 10,000,000 € 0 Operating Cash Flow: Yea r EBTD Depreciation 20% EBT Tax Net Income Operating Cash Flow 23.00% 1 £2,000,000.00 £2,000,000.00 £- £- £- £2,000,000.00 2 £2,000,000.00 £1,600,000.00 £400,000.00 £92,000.00 £308,000.00 £1,908,000.00 3 £2,000,000.00 £1,280,000.00 £720,000.00 £165,600.00 £554,400.00 £1,834,400.00 4 £2,000,000.00 £1,024,000.00 £976,000.00 £224,480.00 £751,520.00 £1,775,520.00 5 £2,000,000.00 £819,200.00 £1,180,800.00 £271,584.00 £909,216.00 £1,728,416.00 6 £2,000,000.00 £655,360.00 £1,344,640.00 £309,267.20 £1,035,372.80 £1,690,732.80 7 £2,000,000.00 £524,288.00 £1,475,712.00 £339,413.76 £1,136,298.24 £1,660,586.24 8 £2,000,000.00 £419,430.40 £1,580,569.60 £363,531.01 £1,217,038.59 £1,636,468.99 9 £2,000,000.00 £335,544.32 £1,664,455.68 £382,824.81 £1,281,630.87 £1,617,175.19 10 £2,000,000.00 £1,342,177.28 £657,822.72 £151,299.23 £506,523.49 £1,848,700.77 Cash Flow Analysis: Year Investment Operating Cash Flow Net Cash Flow PV Cash Flows @ 13% 0 -£10,000,000 -£10,000,000 -£10,000,000 1 £2,000,000 £2,000,000 £1,769,912 2 £1,908,000 £1,908,000 £1,494,244 3 £1,834,400 £1,834,400 £1,271,331 4 £1,775,520 £1,775,520 £1,088,960 5 £1,728,416 £1,728,416 £938,115 6 £1,690,733 £1,690,733 £812,090 7 £1,660,586 £1,660,586 £705,850 8 £1,636,469 £1,636,469 £615,574 9 £1,617,175 £1,617,175 £538,333 10 £1,848,701 £1,848,701 £544,606 NPV = -£220,986 NPV (Financing Side Effects) The net present value of financing side effects equals the after-tax present value of cash flows resulting from the firm’s debt. So, the NPV of the financing side effects are: NPV = Proceeds (Net of flotation) – After-tax PV(Interest Payments) – PV(Principal Payments) + PV (Flotation Cost Tax Shield) Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt, RB. Since the flotation costs will be amortized over the life of the loan, the annual floatation costs that will be expensed each year are: The after-tax cash flows from the interest payments and flotation amortisation (both are affected by tax) is: Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 £500,000 £100,000 £100,000 £400,000 2 £400,000 £80,000 £180,000 £320,000 3 £320,000 £64,000 £244,000 £256,000 4 £256,000 £51,200 £295,200 £204,800 5 £204,800 £40,960 £336,160 £163,840 6 £163,840 £32,768 £368,928 £131,072 7 £131,072 £26,214 £395,142 £104,858 8 £104,858 £20,972 £416,114 £83,886 9 £83,886 £16,777 £432,891 £67,109 10 £67,109 £67,109 £500,000 £- Yea r Depreciation Interest Payments Total Cash Flow Tax @23% After Tax Cash Flows 1 € 100,000 -€ 1,365,000 -€ 1,265,000 -€ 290,950 -€ 974,050 2 € 80,000 -€ 1,365,000 -€ 1,285,000 -€ 295,550 -€ 989,450 3 € 64,000 -€ 1,365,000 -€ 1,301,000 -€ 299,230 -€ 1,001,770 4 € 51,200 -€ 1,365,000 -€ 1,313,800 -€ 302,174 -€ 1,011,626 5 € 40,960 -€ 1,365,000 -€ 1,324,040 -€ 304,529 -€ 1,019,511 6 € 32,768 -€ 1,365,000 -€ 1,332,232 -€ 306,413 -€ 1,025,819 7 € 26,214 -€ 1,365,000 -€ 1,338,786 -€ 307,921 -€ 1,030,865 8 € 20,972 -€ 1,365,000 -€ 1,344,028 -€ 309,127 -€ 1,034,902 9 € 16,777 -€ 1,365,000 -€ 1,348,223 -€ 310,091 -€ 1,038,132 10 € 67,109 -€ 1,365,000 -€ 1,297,891 -€ 298,515 -€ 999,376 The Cash Flow analysis of the financing effects are: Year Financing Flotation Costs After Tax expenses Balloon Payment Total Cash Flows PV Cash Flows @ 13% 0 £10,500,000 -£500,000 £10,000,000 £10,000,000 1 -€ 974,050 -£974,050 -£861,991 2 -€ 989,450 -£989,450 -£774,884 3 -€ 1,001,770 -£1,001,770 -£694,277 4 -€ 1,011,626 -£1,011,626 -£620,449 5 -€ 1,019,511 -£1,019,511 -£553,350 6 -€ 1,025,819 -£1,025,819 -£492,720 7 -€ 1,030,865 -£1,030,865 -£438,180 8 -€ 1,034,902 -£1,034,902 -£389,289 9 -€ 1,038,132 -£1,038,132 -£345,578 10 -€ 999,376 -£10,500,000 -£11,499,376 -£3,387,582 NPV = £1,441,700 So, the APV of the project is: APV = NPV(All-Equity) + NPV(Financing Side Effects) APV = -£220,986 + £1,441,700 APV = £1,220,714 Since APV is positive, the company should undertake the project. 10. The adjusted present value (APV) of a project equals the net present value of the project if it were funded completely by equity plus the net present value of any financing side effects. In this case, the NPV of financing side effects equals the after-tax present value of the cash flows resulting from the firm’s debt, so: APV = NPV(All-Equity) + NPV(Financing Side Effects) So, the NPV of each part of the APV equation is: NPV(All-Equity) Depreciation Schedule: (a) (b) (c) (d) Year Starting Value Depreciation 25% Accumulated Depreciation Residual Value 25% (a)-(b) 1 €2,400,000 €600,000 €600,000 €1,800,000 2 €1,800,000 €450,000 €1,050,000 €1,350,000 3 €1,350,000 €337,500 €1,387,500 €1,012,500 4 €1,012,500 €253,125 €1,640,625 €759,375 Operating Cash Flow: Year EBTD Depreciation 25% EBT Tax Net Income Operating Cash Flow 12.5% 1 €850,000 €600,000 €250,000 €31,250 €218,750 €818,750 2 €850,000 €450,000 €400,000 €50,000 €350,000 €800,000 3 €850,000 €337,500 €512,500 €64,063 €448,438 €785,938 4 €850,000 €253,125 €596,875 €74,609 €522,266 €775,391 Cash Flow Analysis: Year Investment Operating Cash Flow Net Cash Flow PV Cash Flows @ 13% 0 -€2,400,000 -€2,400,000 -€2,400,000 1 €818,750 €818,750 €724,558 2 €800,000 €800,000 €626,517 3 €785,938 €785,938 €544,694 4 €759,375 €775,391 €1,534,766 €941,301 NPV = €437,069 NPV(Financing Side Effects) The net present value of financing side effects equals the aftertax present value of cash flows resulting from the firm’s debt. So, the NPV of the financing side effects are: NPV = Proceeds(Net of flotation) – Aftertax PV(Interest Payments) – PV(Principal Payments) + PV(Flotation Cost Tax Shield) Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt, RB. Since the flotation costs will be amortized over the life of the loan, the annual floatation costs that will be expensed each year are: Year Starting Value Depreciation 25% Accumulated Depreciation Residual Value Tax shield on depreciation 25% (a)-(b) 12.50% 1 €24,000 €6,000 €6,000 €18,000 €750 2 €18,000 €4,500 €10,500 €13,500 €563 3 €13,500 €3,375 €13,875 €10,125 €422 4 €10,125 €10,125 €24,000 €0 €1,266 The after-tax cash flows from the interest payments and flotation amortisation (both are affected by tax) is: Year Depreciation Interest Payments Total Cash Flow Tax @12.5% After Tax Cash Flows 1 €6,000 -€228,000 -€222,000 -€27,750 -€194,250 2 €4,500 -€228,000 -€223,500 -€27,938 -€195,563 3 €3,375 -€228,000 -€224,625 -€28,078 -€196,547 4 €10,125 -€228,000 -€217,875 -€27,234 -€190,641 The Cash Flow analysis of the financing effects are: Year Financing Flotation Costs After Tax expenses Balloon Payment Total Cash Flows PV Cash Flows @ 9.5% 0 €2,400,000 -€24,000 €2,376,000 €2,376,000 1 -€194,250 -€194,250 -€177,397 2 -€195,563 -€195,563 -€163,101 3 -€196,547 -€196,547 -€149,701 4 -€190,641 -€2,400,000 -€2,590,641 -€1,801,983 NPV = €83,818 So, the APV of the project is: APV = NPV(All-Equity) + NPV(Financing Side Effects) APV = €437,069 + €83,818 APV = €520,887 Since APV is positive, the company should undertake the project. 11. a. In order to value a firm’s equity using the flow-to-equity approach, discount the cash flows available to equity holders at the cost of the firm’s levered equity. The cash flows to equity holders will be the firm’s net income. Remembering that the company has three stores, we find for each store: Sales €1,000,000 COGS 450,000 Other Costs 325,000 Interest 29,500 EBT €195,500 [email protected]% 72,726 Net Income €122,774 Since this cash flow will remain the same forever, the present value of cash flows available to the firm’s equity holders is a perpetuity. We can discount at the levered cost of equity, so, the value of the company’s equity is: PV(Flow-to-equity) = 3(€122,744 / 0.19) PV(Flow-to-equity) = 3(€646,179) = €1,938,537 b. The value of a firm is equal to the sum of the market values of its debt and equity, or: VL = B + S We calculated the value of the company’s equity in part a, so now we need to calculate the value of debt. The company has a debt-to-equity ratio of 0.40, which can be written algebraically as: B / S = 0.40 We can substitute the value of equity and solve for the value of debt, doing so, we find: B / €1,938,537 = 0.40 B = €775,415 So, the value of the company is: V = €1,938,537 + €775,415 V = €2,713,952 12. Since the debt is issued at par, the cost of debt is equal to the coupon. In the case of Cryo, it is 8 per cent. The cost of equity prior to the debt issue is equal to E(r0) = rf + [E(rm) – rf] = 3.4% + .8(9.6%) = 11.08% Now we can find the cost of levered equity. According to Modigliani-Miller Proposition II with corporate taxes RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .1108 + (.25)(.1108 – .08)(1 – .23) RS = .1167 or 11.67% Since B/S = 0.25, this implies that B/(B+S) = 0.2. In a world with corporate taxes, a firm’s weighted average cost of capital is equal to: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS RWACC = 0.2(1-.23)(.08) + .8(.1167) = 10.57% 13. a. In order to determine the cost of the firm’s debt, we need to find the yield to maturity on its current bonds. With semi-annual coupon payments, the yield to maturity in the company’s bonds is: £97.50 = £4.50(PVIFAR%,40) + £100(PVIFR%,40) R = .0464 or 4.64% Since the coupon payments are semi-annual, the YTM on the bonds is: YTM = 4.64% × 2 YTM = 9.28% b. We can use the Capital Asset Pricing Model to find the return on unlevered equity. According to the Capital Asset Pricing Model: R0 = RF + βUnlevered(RM – RF) R0 = 7% + 1.1(13% – 7%) R0 = 13.60% Now we can find the cost of levered equity. According to Modigliani-Miller Proposition II with corporate taxes RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .1360 + (.40)(.1360 – .0928)(1 – .28) RS = .1484 or 14.84% c. In a world with corporate taxes, a firm’s weighted average cost of capital is equal to: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS The problem does not provide either the debt-value ratio or equity-value ratio. However, the firm’s debt-equity ratio of is: B/S = 0.40 Solving for B: B = 0.4S Substituting this in the debt-value ratio, we get: B/V = .4S / (.4S + S) B/V = .4 / 1.4 B/V = .285714 And the equity-value ratio is one minus the debt-value ratio, or: S/V = 1 – .29 S/V = .714286 So, the WACC for the company is: RWACC = .285714(1 – .28)(.0928) + .714286(.1484) RWACC = .1251 or 12.51 % 14. a. The equity beta of a firm financed entirely by equity is equal to its unlevered beta. Since each firm has an unlevered beta of 0.9, we can find the equity beta for each. Doing so, we find: Maersk A/S βEquity = [1 + (1 – tC)(B/S)]βUnlevered βEquity = [1 + (1 – .25)(Dkr11,400,000/Dkr25,600,000](.9) βEquity = 1.30 Lundberg A/S βEquity = [1 + (1 – tC)(B/S)]βUnlevered βEquity = [1 + (1 – .25)(Dkr25,600,000/Dkr11,400,000](.9) βEquity = 2.52 b. We can use the Capital Asset Pricing Model to find the required return on each firm’s equity. Doing so, we find: Maersk A/S: RS = RF + βEquity(RM – RF) RS = 2.3% + 1.3(9% – 2.3%) RS = 11.01% Lundberg A/S: RS = RF + βEquity(RM – RF) RS = 2.30% + 2.52(9% – 2.3%) RS = 19.16% 15. a. If flotation costs are not taken into account, the net present value of a loan equals: NPVLoan = Gross Proceeds – After-tax present value of interest and principal payments NPVLoan = €9,000,000 – .13(€9,000,000)(1 – .35)PVIFA13%,6 – €9,000,000/1.136 NPVLoan = €1,636,997 b. The floatation costs of the loan will be: Floatation costs = €9,000,000(.01) Floatation costs = €90,000 Given that floatation costs are depreciated using 25% reducing balances, the depreciation schedule must be determined and the present value of the tax shield must be estimated. Year Starting Value Depreciation 25% Accumulated Depreciation Residual Value Tax Shield @ 35% 1 £90,000 £22,500 £22,500 £67,500 £7,875 2 £67,500 £16,875 £39,375 £50,625 £5,906 3 £50,625 £12,656 £52,031 £37,969 £4,430 4 £37,969 £9,492 £61,523 £28,477 £3,322 5 £28,477 £7,119 £68,643 £21,357 £2,492 6 £21,357 £5,339 £73,982 £- £1,869 If flotation costs are taken into account, the net present value of a loan equals: Year Loan Flotation Cost Tax Shield Flotation Costs After Tax Interest Payments Repayment of Principal Net Cash Flows PV Cash Flows@13% 0 € 9,000,000 € 90,000 € 8,910,000 € 8,910,000 1 € 7,875 € 760,500 -€ 752,625 -€ 666,040 2 € 5,906 € 760,500 -€ 754,594 -€ 590,958 3 € 4,430 € 760,500 -€ 756,070 -€ 523,995 4 € 3,322 € 760,500 -€ 757,178 -€ 464,391 5 € 2,492 € 760,500 -€ 758,008 -€ 411,417 6 € 1,869 € 760,500 € 9,000,000 -€ 9,758,631 -€ 4,687,251 NPVLoan = €1,565,949 16. Step 1: Calculate the depreciation schedule and tax shield of the flotation costs. Flotation costs: 0.8% of €10 million = €80,000 Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value Tax Shield @ 33% 20% (a)-(b) 1 €80,000 €16,000 €16,000 €64,000 €5,280 2 €64,000 €12,800 €28,800 €51,200 €4,224 3 €51,200 €10,240 €39,040 €40,960 €3,379 4 €40,960 €8,192 €47,232 €32,768 €2,703 5 €32,768 €6,554 €53,786 €26,214 €2,163 6 €26,214 €5,243 €59,028 €20,972 €1,730 7 €20,972 €4,194 €63,223 €16,777 €1,384 8 €16,777 €3,355 €66,578 €13,422 €1,107 9 €13,422 €2,684 €69,263 €10,737 €886 10 €10,737 €10,737 €80,000 €- €3,543 Step 2: If flotation costs are taken into account, the net present value of a loan equals: Year Loan Flotation Cost Tax Shield Flotation Costs After Tax Interest Payments Repayment of Principal Net Cash Flows PV Cash Flows@13% 0 € 10,000,000 € 80,000 € 9,920,000 € 9,920,000 1 € 5,280 € 1,139,000 -€ 108,620 -€ 92,838 2 € 4,224 € 1,139,000 -€ 109,676 -€ 80,120 3 € 3,379 € 1,139,000 -€ 110,521 -€ 69,006 4 € 2,703 € 1,139,000 -€ 111,197 -€ 59,340 5 € 2,163 € 1,139,000 -€ 111,737 -€ 50,965 6 € 1,730 € 1,139,000 -€ 112,170 -€ 43,728 7 € 1,384 € 1,139,000 -€ 112,516 -€ 37,490 8 € 1,107 € 1,139,000 -€ 112,793 -€ 32,121 9 € 886 € 1,139,000 -€ 113,014 -€ 27,508 10 € 3,543 € 1,139,000 € 10,000,000 -€ 10,110,35 7 -€ 2,103,332 NPV of the loan is Germany is thus €7,323,552 If the bond is issued in Switzerland, flotation costs are greater but the higher visibility will lead to stronger cash flows. This must be taken into account in any NPV analysis. Calculate the amortization schedule of the flotation costs. Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value Tax Shield @ 33% 20% (a)-(b) 1 €120,000 €24,000 €24,000 €96,000 €7,920 2 €96,000 €19,200 €43,200 €76,800 €6,336 3 €76,800 €15,360 €58,560 €61,440 €5,069 4 €61,440 €12,288 €70,848 €49,152 €4,055 5 €49,152 €9,830 €80,678 €39,322 €3,244 6 €39,322 €7,864 €88,543 €31,457 €2,595 7 €31,457 €6,291 €94,834 €25,166 €2,076 8 €25,166 €5,033 €99,867 €20,133 €1,661 9 €20,133 €4,027 €103,894 €16,106 €1,329 10 €16,106 €16,106 €120,000 €- €5,315 Then the NPV: Year Loan Flotation Cost Tax Shield Flotation Costs After Tax Interest Payments Additional Cash Flows Repayment of Principal Net Cash Flows PV Cash Flows@13% 0 € 10,000,000 € 120,000 € 9,880,000 € 9,880,000 1 € 7,920 € 1,139,000 € 200,000 € 94,020 € 80,359 2 € 6,336 € 1,139,000 € 200,000 € 92,436 € 67,526 3 € 5,069 € 1,139,000 € 200,000 € 91,169 € 56,923 4 € 4,055 € 1,139,000 € 200,000 € 90,155 € 48,111 5 € 3,244 € 1,139,000 € 200,000 € 89,344 € 40,751 6 € 2,595 € 1,139,000 € 200,000 € 88,695 € 34,577 7 € 2,076 € 1,139,000 € 200,000 € 88,176 € 29,380 8 € 1,661 € 1,139,000 € 200,000 € 87,761 € 24,993 9 € 1,329 € 1,139,000 € 200,000 € 87,429 € 21,280 10 € 5,315 € 1,139,000 € 200,000 € 10,000,000 -€ 9,908,585 -€ 2,061,356 The NPV of issuing the bond in Switzerland is €8,222,544. The company should issue the bond in Switzerland because the NPV is greater. 17. First we need to find the depreciation schedule of the asset. Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 £8,000,000 £1,600,000 £1,600,000 £6,400,000 2 £6,400,000 £1,280,000 £2,880,000 £5,120,000 3 £5,120,000 £1,024,000 £3,904,000 £4,096,000 4 £4,096,000 £819,200 £4,723,200 £3,276,800 5 £3,276,800 £3,276,800 £8,000,000 £- The present values of each cash flows are given below: Year 0 1 2 3 4 5 Initial outlay (£) -£8,000,000 Depreciation tax shield (£) £ 368,000 £ 294,400 £ 235,520 £ 188,416 £ 753,664 After-tax revenue less expenses(£) £ 2,300,000 £ 2,300,000 £ 2,300,000 £ 2,300,000 £ 2,300,000 CF -£ 8,000,000 £ 2,668,000 £ 2,594,400 £2,535,520 £ 2,488,416 £ 3,053,664 NPV= -£420,584 Since the NPV of the project is negtive, the company should not accept the project. 18. Whether the company issues bonds or issues equity to finance the project is irrelevant. The company’s optimal capital structure determines the WACC. In a world with corporate taxes, a firm’s weighted average cost of capital equals: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS RWACC = .80(1 – .34)(.072) + .20(.1090) RWACC = .0598 or 5.98% Now we can use the weighted average cost of capital to discount NEC’s unlevered cash flows. Doing so, we find the NPV of the project is: NPV = –€50,000,000 + €3,500,000 / 0.0598 NPV = €8,528,428 Since NPV is positive, NEC should accept the project. 19. First of all, we should calculate the respective weights of each financing class in the firm in terms of book value and market value scales. These are: wbook wmarketvalue cost LTD 0.117647059 0.0625 3.50% STD 0.529411765 0.25 6.80% Equity 0.352941176 0.6875 14.50% 1 1 a. The company has a capital structure with three parts: long-term debt, short-term debt, and equity. Since interest payments on both long-term and short-term debt are tax-deductible, multiply the pretax costs by (1 – tC) to determine the aftertax costs to be used in the weighted average cost of capital calculation. The WACC using the book value weights is: RWACC = (wSTD)(RSTD)(1 – tC) + (wLTD)(RLTD)(1 – tC) + (wEquity)(REquity) RWACC = (0.1176)(.035)(1 – .28) + (0.5294)(.068)(1 – .28) + (0.3529)(.145) RWACC = 0.0801 or 8.01% NPV(CF) -£ 8,000,000 £ 2,186,885 £ 1,743,080 £ 1,396,328 £ 1,123,269 £ 1,129,853 b. Using the market value weights, the company’s WACC is: RWACC = (wSTD)(RSTD)(1 – tC) + (wLTD)(RLTD)(1 – tC) + (wEquity)(REquity) RWACC = (.0625)(.035)(1 – .28) + (.25)(.068)(1 – .28) + (.6875)(.145) RWACC = 0.1135 or 11.35% c. Using the target debt-equity ratio, the target debt-value ratio for the company is: B/S = 0.60 B = 0.6S Substituting this in the debt-value ratio, we get: B/V = .6S / (.6S + S) B/V = .6 / 1.6 B/V = .375 And the equity-value ratio is one minus the debt-value ratio, or: S/V = 1 – .375 S/V = .625 We can use the ratio of short-term debt to long-term debt in a similar manner to find the short-term debt to total debt and long-term debt to total debt. Using the short-term debt to long-term debt ratio, we get: STD/LTD = .2 STD = .2LTD Substituting this in the short-term debt to total debt ratio, we get: STD/B = .2LTD / (.2LTD + LTD) STD/B = .2/ 1.2 STD/B = .1667 And the long-term debt to total debt ratio is one minus the short-term debt to total debt ratio, or: LTD/B = 1 – .1667 LTD/B = .8333 Now we can find the short-term debt to value ratio and long-term debt to value ratio by multiplying the respective ratio by the debt-value ratio. So: STD/V = (STD/B)(B/V) STD/V = .1667(.375) STD/V = .0625 And the long-term debt to value ratio is: LTD/V = (LTD/B)(B/V) LTD/V = .8333(.375) LTD/V = .3125 So, using the target capital structure weights, the company’s WACC is: RWACC = (wSTD)(RSTD)(1 – tC) + (wLTD)(RLTD)(1 – tC) + (wEquity)(REquity) RWACC = (.0625)(.035)(1 – .28) + (.3125)(.068)(1 – .28) + (.625)(.145) RWACC = 0.1075 or 10.75% d. The differences in the WACCs are due to the different weighting schemes. The company’s WACC will most closely resemble the WACC calculated using target weights since future projects will be financed at the target ratio. Therefore, the WACC computed with target weights should be used for project evaluation. 20. The adjusted present value of a project equals the net present value of the project under all- equity financing plus the net present value of any financing side effects. In the joint venture’s case, the NPV of financing side effects equals the aftertax present value of cash flows resulting from the firms’ debt. So, the APV is: APV = NPV(All-Equity) + NPV(Financing Side Effects) The NPV for an all-equity firm is: NPV(All-Equity) Depreciation schedule (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 £12,000,000 £2,400,000 £2,400,000 £9,600,000 2 £9,600,000 £1,920,000 £4,320,000 £7,680,000 3 £7,680,000 £1,536,000 £5,856,000 £6,144,000 4 £6,144,000 £1,228,800 £7,084,800 £4,915,200 5 £4,915,200 £983,040 £8,067,840 £3,932,160 Given that the life of the equipment is different from the life of the project it is better to calculate the present value of the depreciation effect separately from the project cash flows. Depreciation Tax shield PV Tax Shield 1 £2,400,000 £552,000 £463,865.55 2 £1,920,000 £441,600 £311,842.38 3 £1,536,000 £353,280 £209,641.94 4 £1,228,800 £282,624 £140,935.76 5 £983,040 £226,099 £94,746.73 NPV Depreciation Tax Shield = £1,221,032 Now calculate the NPV of the project over 20 years: NPV = –£12,000,000 + (1 – 0.23)(£800,000)PVIFA20,19% NPV = -£8,857,869 So, the NPV of the overall investment is £1,221,032+ (-£8,857,869) = £7,636,837. NPV (Financing Side Effects) The NPV of financing side effects equals the after-tax present value of cash flows resulting from the firm’s debt. The coupon rate on the debt is relevant to determine the interest payments, but the resulting cash flows should still be discounted at the pretax cost of debt. So, the NPV of the financing effects is: NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Repayments) NPV = £10,000,000 – (1 – 0.23)(0.07)(£10,000,000)PVIFA15,8.5% – £10,000,000/1.08515 NPV = £2,582,618 So, the APV of the project is: APV = NPV(All-Equity) + NPV(Financing Side Effects) APV = -£7,636,837 + £2,582,618 APV = -£5,054,219 21. If the company had to issue debt under the terms it would normally receive, the interest rate on the debt would increase to the company’s normal cost of debt. The NPV of an all- equity project would remain unchanged, but the NPV of the financing side effects would change. The NPV of the financing side effects would be: NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Repayments) NPV = £10,000,000 – (1 – 0.23)(0.085)(£10,000,000)PVIFA15,8.5% – £10,000,000/1.08515 NPV = £1,623,478 So, the APV of the project is: APV = NPV(All-Equity) + NPV(Financing Side Effects) APV = -£7,636,837 + £1,623,478 APV = -£6,013,358 The gain to the company from issuing subsidized debt is the difference between the two APVs, so: Gain from subsidized debt = -£5,054,219-(-£6,013,358) Gain from subsidized debt = £959,139 Since the NPV is still negative the subsidized debt did not make any difference to the decision. 22. The adjusted present value of a project equals the net present value of the project under all-equity financing plus the net present value of any financing side effects. First, we need to calculate the unlevered cost of equity. According to Modigliani-Miller Proposition II with corporate taxes: RS = R0 + (B/S)(R0 – RB)(1 – tC) .16 = R0 + (0.50)(R0 – 0.09)(1 – 0.298) R0 = 0.1418 or 14.18% Now we can find the NPV of an all-equity project, which is: NPV = PV(Unlevered Cash Flows) NPV = –€24,000,000 + €8,000,000/1.1418 + €13,000,000/(1.1418)2 + €10,000,000/(1.1418)3 NPV = –€304,667.35 Next, we need to find the net present value of financing side effects. This is equal the aftertax present value of cash flows resulting from the firm’s debt. So: NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Payments) Each year an equal principal payment will be made, which will reduce the interest accrued during the year. Given a known level of debt, debt cash flows should be discounted at the pre- tax cost of debt, so the NPV of the financing effects are: NPV = €12,000,000 – (1 – .298)(.09)(€12,000,000) / (1.09) – €4,000,000/(1.09) – (1 – .298)(.09)(€8,000,000)/(1.09)2 – €4,000,000/(1.09)2 – (1 – .298)(.09)(€4,000,000)/(1.09)3 – €4,000,000/(1.09)3 NPV = €558,696.76 So, the APV of project is: APV = NPV(All-equity) + NPV(Financing side effects) APV = –€304,667.35 + €558,696.76 APV = €254,029.41 Since APV is positive, the company should proceed with the expansion. 23. a. To calculate the NPV of the project, we first need to find the company’s WACC. In a world with corporate taxes, a firm’s weighted average cost of capital equals: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS The market value of the company’s equity is: Market value of equity = 5,000,000(£20) Market value of equity = £100,000,000 So, the debt-value ratio and equity-value ratio are: Debt-value = £30,000,000 / (£30,000,000 + (£100,000,000) Debt-value = .2308 Equity-value = £100,000,000 / (£30,000,000 + (£100,000,000) Equity-value = .7692 Since the CEO believes its current capital structure is optimal, these values can be used as the target weights in the firm’s weighted average cost of capital calculation. The yield to maturity of the company’s debt is its pretax cost of debt. To find the company’s cost of equity, we need to calculate the equity beta. The equity beta can be calculated as: = S,M / M2 = .048 / .202 = 1.20 Now we can use the Capital Asset Pricing Model to determine the cost of equity. The Capital Asset Pricing Model is: RS = RF + β(RM – RF) RS = 6% + 1.20(7.50%) RS = 15.00% Now, we can calculate the company’s WACC, which is: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS RWACC = .2308(1 – .28)(.08) + .7692(.15) RWACC = .1287 or 12.87% Finally, we can use the WACC to discount the unlevered cash flows, which gives us an NPV of: NPV = –£40,000,000 + £13,000,000(PVIFA12.87%,5) NPV = £5,872,200 (based on unrounded value) Since the NPV is positive, the company should purchase the equipment. b. The weighted average cost of capital used in part a will not change if the firm chooses to fund the project entirely with debt. The weighted average cost of capital is based on optimal capital structure weights. Since the current capital structure is optimal, all-debt funding for the project simply implies that the firm will have to use more equity in the future to bring the capital structure back towards the target. 24. a. The company is currently an all-equity firm, so the value as an all-equity firm equals the present value of after-tax cash flows, discounted at the cost of the firm’s unlevered cost of equity. So, the current value of the company is: VU = [(Pre-tax earnings)(1 – tC)] / R0 VU = [(£35,000,000)(1 – .28)] / .20 VU = £126,000,000 The price per share is the total value of the company divided by the shares outstanding, or: Price per share = £126,000,000 / 1,500,000 Price per share = £84 b. The adjusted present value of a firm equals its value under all-equity financing plus the net present value of any financing side effects. In this case, the NPV of financing side effects equals the after-tax present value of cash flows resulting from the firm’s debt. Given a known level of debt, debt cash flows can be discounted at the pre-tax cost of debt, so the NPV of the financing effects are: NPV = Proceeds – After-tax PV(Interest Payments) NPV = £40,000,000 – (1 – .28)(.09)(£40,000,000) / .09 NPV = £11,200,000 So, the value of the company after the recapitalization using the APV approach is: V = £126,000,000 + £11,200,000 V = £137,200,000 Since the company has not yet issued the debt, this is also the value of equity after the announcement. So, the new price per share will be: New share price = £137,200,000 / 1,500,000 New share price = £91.47 c. The company will use the entire proceeds to repurchase equity. Using the share price we calculated in part b, the number of shares repurchased will be: Shares repurchased = £40,000,000 / £91.47 Shares repurchased = 437,318 And the new number of shares outstanding will be: New shares outstanding = 1,500,000 – 437,318 New shares outstanding = 1,062,682 The value of the company increased, but part of that increase will be funded by the new debt. The value of equity after recapitalization is the total value of the company minus the value of debt, or: New value of equity = £137,200,000 – £40,000,000 New value of equity = £97,200,000 So, the price per share of the company after recapitalization will be: New share price = £97,200,000 / 1,062,682 New share price = £91.47 The price per share is unchanged. d. In order to value a firm’s equity using the flow-to-equity approach, we must discount the cash flows available to equity holders at the cost of the firm’s levered equity. According to Modigliani-Miller Proposition II with corporate taxes, the required return of levered equity is: RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .20 + (£40,000,000 / £97,200,000)(.20 – .09)(1 – .28) RS = .2326 or 23.26% After the recapitalization, the net income of the company will be: EBIT £35,000,000 Interest 3,600,000 EBT £31,400,000 Taxes 8,792,000 Net income £22,608,000 The firm pays all of its earnings as dividends, so the entire net income is available to shareholders. Using the flow-to-equity approach, the value of the equity is: S = Cash flows available to equity holders / RS S = £22,608,000 / .2326 S = £97,200,000 25. a. If the company were financed entirely by equity, the value of the firm would be equal to the present value of its unlevered after-tax earnings, discounted at its unlevered cost of capital. First, we need to find the company’s unlevered cash flows, which are: Sales £23,500,000 Variable costs 14,100,000 EBT £9,400,000 Tax 2,632,000 Net income £6,768,000 So, the value of the unlevered company is: VU = £6,768,000 / .17 VU = £39,811,764.71 b. According to Modigliani-Miller Proposition II with corporate taxes, the value of levered equity is: RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .17 + (.45)(.17 – .09)(1 – .28) RS = .19592 or 19.592% c. In a world with corporate taxes, a firm’s weighted average cost of capital equals: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS So we need the debt-value and equity-value ratios for the company. The debt-equity ratio for the company is: B/S = 0.45 B = 0.45S Substituting this in the debt-value ratio, we get: B/V = .45S / (.45S + S) B/V = .45 / 1.45 B/V = 0.310344828 And the equity-value ratio is one minus the debt-value ratio, or: S/V = 1 – 0.310344828 S/V = 0.689655172 So, using the capital structure weights, the company’s WACC is: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS RWACC =0.310344828 (1 – .28)(.09) + 0.689655172 (.19592) RWACC = 0.155227586 We can use the weighted average cost of capital to discount the firm’s unlevered aftertax earnings to value the company. Doing so, we find: VL =£6,768,000/0.155227586 VL = £43,600,497.60 Now we can use the debt-value ratio and equity-value ratio to find the value of debt and equity, which are: B = VL(Debt-value) B =£43,600,497.60(.31) B = £13,531,188.91 S = VL(Equity-value) S =£43,600,497.60(.69) S = £30,069,308.69 d. In order to value a firm’s equity using the flow-to-equity approach, we can discount the cash flows available to equity holders at the cost of the firm’s levered equity. First, we need to calculate the levered cash flows available to shareholders, which are: Sales £23,500,000 Variable costs £14,100,000 EBIT £9,400,000 Interest £1,217,807 EBT £8,182,193 Tax £2,291,014.04 Net income £5,891,178.96 So, the value of equity with the flow-to-equity method is: S = Cash flows available to equity holders / RS S = £5,891,178.96/ .19592 S = £30,069,308.69 26. a. Since the company is currently an all-equity firm, its value equals the present value of its unlevered after-tax earnings, discounted at its unlevered cost of capital. The cash flows to shareholders for the unlevered firm are: EBIT £75,000 Tax 21,000 Net income £54,000 So, the value of the company is: VU = £54,000 / .18 VU = £300,000 b. The adjusted present value of a firm equals its value under all-equity financing plus the net present value of any financing side effects. In this case, the NPV of financing side effects equals the after-tax present value of cash flows resulting from debt. Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt, so: NPV = Proceeds – Aftertax PV(Interest payments) NPV = £160,000 – (1 – .28)(.10)(£160,000) / 0.10 NPV = £44,800 So, using the APV method, the value of the company is: APV = VU + NPV(Financing side effects) APV = £300,000 + £44,800 APV = £344,800 The value of the debt is given, so the value of equity is the value of the company minus the value of the debt, or: S = V – B S = £344,800 – £160,000 S = £184,800 c. According to Modigliani-Miller Proposition II with corporate taxes, the required return of levered equity is: RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .18 + (£160,000 / £184,800)(.18 – .10)(1 – .28) RS = .22987 or 22.987% d. In order to value a firm’s equity using the flow-to-equity approach, we can discount the cash flows available to equity holders at the cost of the firm’s levered equity. First, we need to calculate the levered cash flows available to shareholders, which are: EBIT £75,000 Interest 16,000 EBT £59,000 Tax 16,520 Net income £42,480 So, the value of equity with the flow-to-equity method is: S = Cash flows available to equity holders / RS S = £42,480 / .22987 S = £184,800 27. Since the company is not publicly traded, we need to use the industry numbers to calculate the industry levered return on equity. We can then find the industry unlevered return on equity, and re-lever the industry return on equity to account for the different use of leverage. So, using the CAPM to calculate the industry levered return on equity, we find: RS = RF + β(MRP) RS = 7% + 1.2(8%) RS = 16.60% Next, to find the average cost of unlevered equity in the holiday gift industry we can use Modigliani-Miller Proposition II with corporate taxes, so: RS = R0 + (B/S)(R0 – RB)(1 – tC) .1660 = R0 + (.35)(R0 – .07)(1 – .28) R0 = .1467 or 14.67% Now, we can use the Modigliani-Miller Proposition II with corporate taxes to re-lever the return on equity to account for this company’s debt-equity ratio. Doing so, we find: RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .1467 + (.40)(.1467 – .07)(1 – .28) RS = .16876 or 16.876% Since the project is financed at the firm’s target debt-equity ratio, it must be discounted at the company’s weighted average cost of capital. In a world with corporate taxes, a firm’s weighted average cost of capital equals: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS So we need the debt-value and equity-value ratios for the company. The debt-equity ratio for the company is: B/S = 0.40 B = 0.40S Substituting this in the debt-value ratio, we get: B/V = .40S / (.40S + S) B/V = .40 / 1.40 B/V = 0.28571 And the equity-value ratio is one minus the debt-value ratio, or: S/V = 1 – 0.28571 S/V = 0.71429 So, using the capital structure weights, the company’s WACC is: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS RWACC =0.28571 (1 – .28)(.07) +0.71429 (.1688) RWACC = .13497 or 13.497% Now we need the project’s cash flows. The cash flows increase for the first five years before levelling off into perpetuity. So, the cash flows from the project for the next six years are: Year 1 cash flow £75,000.00 Year 2 cash flow £78,750.00 Year 3 cash flow £82,687.50 Year 4 cash flow £86,821.88 Year 5 cash flow £91,162.97 Year 6 cash flow £95,721.12 So, the NPV of the project is: NPV = –£450,000 + £75,000/1.13497 + £78,750/1.134972 + £82,687.50/1.134973 + £86,821.88/1.134974 + £91,162.97/1.134975 + (£95,721.12/.13497)/1.134975 NPV = £211,211.76 Since NPV is positive, Blue Angel should invest in the project. 28. This question is for more advanced students and prepares them for reading academic papers. Students should be able to provide an overview of the main findings from the introduction and the abstract. However, of more difficulty to discuss are the implications of the research. A greater proportion of marks should be awarded to those students who take the question seriously and explore new ideas. 29. This question is for more advanced students and prepares them for reading academic papers. Students should be able to provide an overview of the main findings from the introduction and the abstract. However, of more difficulty to discuss are the implications of the research. A greater proportion of marks should be awarded to those students who take the question seriously and explore new ideas. 30. a) For a start-up firm with no debt, there is no benefit from using either WACC or APV since both incorporate debt in the calculations. b) APV would probably be better in this situation because you can separately calculate each cash flow stream separately. WACC would be less efficient because it works better in equilibrium. C) WACC or APV could be used. Solution Manual for Corporate Finance David Hillier, Stephen Ross, Randolph Westerfield, Jeffrey Jaffe, Bradford Jordan 9780077139148
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