CHAPTER 12.docx

***CHAPTER 12*** **RISK, COST OF CAPITAL, AND VALUATION** **Answers to Concepts Review and Critical Thinking Questions** **1.** No. The cost of capital depends on the risk of the project, not the source of the money. **2.** Interest expense is tax-deductible. There is no difference between preta...

***CHAPTER 12*** **RISK, COST OF CAPITAL, AND VALUATION** **Answers to Concepts Review and Critical Thinking Questions** **1.** No. The cost of capital depends on the risk of the project, not the source of the money. **2.** Interest expense is tax-deductible. There is no difference between pretax and aftertax equity costs. **3.** You are assuming that the new project's risk is the same as the risk of the firm as a whole and that the firm is financed entirely with equity. **4.** Two primary advantages of the SML approach are that the model explicitly incorporates the relevant risk of the stock and the method is more widely applicable than is the DCF model, since the SML doesn't make any assumptions about the firm's dividends. The primary disadvantages of the SML method are (1) three parameters (the risk-free rate, the expected return on the market, and beta) must be estimated, and (2) the method essentially uses historical information to estimate these parameters. The risk-free rate is usually estimated to be the yield on very short maturity T-bills and is, hence, observable; the market risk premium is usually estimated from historical risk premiums and, hence, is not observable. The stock beta, which is unobservable, is usually estimated either by determining some average historical beta from the firm and the market's return data, or by using beta estimates provided by analysts and investment firms. **5.** The appropriate aftertax cost of debt to the company is the interest rate it would have to pay if it were to issue new debt today. Hence, if the YTM on outstanding bonds of the company is observed, the company has an accurate estimate of its cost of debt. If the debt is privately-placed, the firm could still estimate its cost of debt by (1) looking at the cost of debt for similar firms in similar risk classes, (2) looking at the average debt cost for firms with the same credit rating (assuming the firm's private debt is rated), or (3) consulting analysts and investment bankers. Even if the debt is publicly traded, an additional complication arises when the firm has more than one issue outstanding; these issues rarely have the same yield because no two issues are ever completely homogeneous. **6.** *a.* This only considers the dividend yield component of the required return on equity. *b.* This is the current yield only, not the promised yield to maturity. In addition, it is based on the book value of the liability, and it ignores taxes. *c.* Equity is inherently riskier than debt (except, perhaps, in the unusual case where a firm's assets have a negative beta). For this reason, the cost of equity exceeds the cost of debt. If taxes are considered in this case, it can be seen that at reasonable tax rates, the cost of equity does exceed the cost of debt. **\ ** **7.** *R*~Sup~ =.12 +.75(.08) =.1800, or 18.00% Both should proceed. The appropriate discount rate does not depend on which company is investing; it depends on the risk of the project. Since Superior is in the business, it is closer to a pure play. Therefore, its cost of capital should be used. With an 18% cost of capital, the project has an NPV of \$1 million regardless of who takes it. **8.** If the different operating divisions were in much different risk classes, then separate cost of capital figures should be used for the different divisions; the use of a single, overall cost of capital would be inappropriate. If the single hurdle rate were used, riskier divisions would tend to receive more funds for investment projects, since their return would exceed the hurdle rate despite the fact that they may actually plot below the SML and, hence, be unprofitable projects on a risk-adjusted basis. The typical problem encountered in estimating the cost of capital for a division is that it rarely has its own securities traded on the market, so it is difficult to observe the market's valuation of the risk of the division. Two typical ways around this are to use a pure play proxy for the division, or to use subjective adjustments of the overall firm hurdle rate based on the perceived risk of the division. **9.** The discount rate for the projects should be lower than the rate implied by the security market line. The security market line is used to calculate the cost of equity. The appropriate discount rate for projects is the firm's weighted average cost of capital. Since the firm's cost of debt is generally less that the firm's cost of equity, the rate implied by the security market line will be too high. **10.** Beta measures the responsiveness of a security\'s returns to movements in the market. Beta is determined by the cyclicality of a firm\'s revenues. This cyclicality is magnified by the firm\'s operating and financial leverage. The following three factors will impact the firm's beta. (1) **Revenues.** The cyclicality of a firm\'s sales is an important factor in determining beta. In general, stock prices will rise when the economy expands and will fall when the economy contracts. As we said above, beta measures the responsiveness of a security\'s returns to movements in the market. Therefore, firms whose revenues are more responsive to movements in the economy will generally have higher betas than firms with less cyclical revenues. (2) **Operating leverage.** Operating leverage is the percentage change in earnings before interest and taxes (EBIT) for a percentage change in sales. A firm with high operating leverage will have greater fluctuations in EBIT for a change in sales than a firm with low operating leverage. In this way, operating leverage magnifies the cyclicality of a firm\'s revenues, leading to a higher beta. (3) **Financial leverage.** Financial leverage arises from the use of debt in the firm\'s capital structure. A levered firm must make fixed interest payments regardless of its revenues. The effect of financial leverage on beta is analogous to the effect of operating leverage on beta. Fixed interest payments cause the percentage change in net income to be greater than the percentage change in EBIT, magnifying the cyclicality of a firm\'s revenues. Thus, returns on highly-levered stocks should be more responsive to movements in the market than the returns on stocks with little or no debt in their capital structure. 1. 不。資本成本取決於項目的風險，而不是資金來源。 2. 利息費用可抵扣稅款。稅前和稅後股權成本沒有區別。 3. 你假設新項目的風險與公司整體風險相同，並且公司完全由股權融資。 4. SML方法的兩個主要優點是模型明確地包含了股票的相關風險，並且該方法比DCF模型更廣泛適用，因為SML不對公司的股利做任何假設。SML方法的主要缺點是（1）必須估計三個參數（無風險利率、市場預期回報和β值），並且（2）該方法基本上使用歷史資訊來估計這些參數。無風險利率通常被估計為非常短期國庫券的收益率，因此是可觀察的；市場風險溢價通常是根據歷史風險溢價來估計的，因此不可觀察。股票β值是不可觀察的，通常可以通過確定公司和市場回報資料的某個平均歷史β值，或者使用分析師和投資公司提供的β值估計來估計。 5. 公司的稅後負債成本應該是如果公司今天要發行新債券所需支付的利率。因此，如果觀察到公司已發行債券的到期收益率（YTM），公司可以準確估計其負債成本。如果債務是私下發行的，公司仍然可以通過以下方式估計其負債成本：（1）查看類似風險類別的類似公司的債務成本，（2）查看具有相同信用評級的公司的平均債務成本（假設公司的私人債務已經評級），或（3）諮詢分析師和投資銀行家。即使債務是公開交易的，當公司有多個未償還債券時，會出現額外的複雜情況；這些債券很少具有相同的收益率，因為沒有兩個債券是完全同質的。 6. *a.* 這只考慮了股權所需回報的股利收益部分。 b. 這只是當前收益率，不是到期收益率。此外，它基於負債的帳面價值，並忽略了稅收。 c. 股權本質上比債務更具風險（除非公司的資產具有負beta的特殊情況）。因此，股權成本超過債務成本。如果在這種情況下考慮稅收，可以看出在合理的稅率下，股權成本確實超過債務成本。 7.*R*=.12 +.75(.08) =.1800，或18.00% 兩者都應繼續進行。適當的貼現率不取決於哪個公司進行投資；它取決於項目的風險。由於Superior從事這項業務，因此更接近純粹的業務。因此，應該使用其資本成本。在18%的資本成本下，無論由誰接手，該項目的淨現值都為100萬美元。 8.如果不同的經營部門屬於不同的風險類別，那麼應該為不同的部門使用單獨的資本成本資料；使用單一的整體資本成本是不合適的。如果使用單一的 hurdle rate，風險較高的部門往往會獲得更多的投資項目資金，因為它們的回報率將超過 hurdle rate，儘管實際上它們可能在風險調整基礎上低於 SML，並且是不盈利的項目。在估計部門的資本成本時通常遇到的問題是，部門很少在市場上交易自己的證券，因此很難觀察到市場對部門風險的估值。解決這個問題的兩種典型方法是為部門使用純業務代理，或者根據對部門風險的感知進行對整體公司 hurdle rate 的主觀調整。 9.項目的貼現率應低於證券市場線所暗示的利率。證券市場線用於計算股權的成本。項目的適當貼現率是公司的加權平均資本成本。由於公司的負債成本通常低於股權成本，因此證券市場線所暗示的利率將過高。 10.Beta 衡量了證券收益對市場波動的回應程度。Beta 取決於公司收入的週期性。這種週期性會受到公司經營和財務杠杆的放大影響。以下三個因素將影響公司的Beta值。（1）收入。公司銷售的週期性是確定Beta的重要因素。一般而言，當經濟擴張時，股票價格將上漲，當經濟收縮時，股票價格將下跌。如上所述，Beta衡量了證券收益對市場波動的回應程度。因此，對經濟波動更敏感的公司銷售收入通常比銷售週期性較小的公司具有更高的Beta值。（2）經營杠杆。經營杠杆是銷售額變化引起的利息前稅利潤（EBIT）的百分比變化。具有較高經營杠杆的公司在銷售額變化時，其EBIT的波動幅度比具有較低經營杠杆的公司更大。這樣，經營杠杆放大了公司收入的週期性，導致Beta值較高。（3）財務杠杆。財務杠杆是由公司資本結構中的債務使用引起的。有負債的公司必須支付固定利息，無論其收入如何。財務杠杆對Beta的影響類似於經營杠杆對Beta的影響。固定利息支付導致淨收入的百分比變化大於EBIT的百分比變化，放大了公司收入的週期性。因此，高度負債的股票的收益對市場波動的回應程度應該比其資本結構中沒有或很少負債的股票的收益更高。 **Solutions to Questions and Problems** *NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.* *[Basic]* **1.** With the information given, we can find the cost of equity using the CAPM. The cost of equity is: ***R~S~*** =.037 + 1.08(.10 --.037) ***R~S~*** =.1050, or 10.50% **2.** The pretax cost of debt is the YTM of the company's bonds, so: *P*~0~ = \$950 = \$29.50(PVIFA~*R*%,28~) + \$1,000(PVIF~*R*%,28~) *R* = 3.224% ***R~B~*** = 2 × 3.224% = 6.45% And the aftertax cost of debt is: Aftertax cost of debt =.0645(1 --.21) Aftertax cost of debt =.0509, or 5.09% **3.** *a.* The pretax cost of debt is the YTM of the company's bonds, so: *P*~0~ = \$970 = \$29(PVIFA~*R*%,46~) + \$1,000(PVIF~*R*%,46~) *R* = 3.022% ***R~B~*** = 2 × 3.022% = 6.04% *b.* The aftertax cost of debt is: Aftertax cost of debt =.0604(1 --.21) Aftertax cost of debt =.0477, or 4.77% *c.* The aftertax rate is more relevant because that is the actual cost to the company. **4.** The book value of debt is the total par value of all outstanding debt, so: BV*~B~* = \$65,000,000 + 50,000,000 BV*~B~* = \$115,000,000 To find the market value of debt, we find the price of the bonds and multiply by the number of bonds. Alternatively, we can multiply the price quote of the bond times the par value of the bonds. Doing so, we find: **MV***~B~* =.97(\$65,000,000) +.67(\$50,000,000) **MV***~B~* = \$96,550,000 The YTM of the zero coupon bonds is: P~Z~ = \$730 = \$1,000(PVIF~*R*%,24~) *R* = 1.683% YTM = 2 × 1.683% = 3.37% So, the aftertax cost of the zero coupon bonds is: Aftertax cost of zero coupon bonds =.0337(1 --.21) Aftertax cost of zero coupon bonds =.0266, or 2.66% The aftertax cost of debt for the company is the weighted average of the aftertax cost of debt for all outstanding bond issues. We need to use the market value weights of the bonds. The total aftertax cost of debt for the company is: Aftertax cost of debt =.0477\[.97(\$65)/\$96.55\] +.0266\[.67(\$50)/\$96.55) Aftertax cost of debt =.0404, or 4.04% **5.** Using the equation to calculate the WACC, we find: WACC =.75(.112) +.25(.058)(1 --.21) WACC =.0955, or 9.55% **6.** Here we need to use the debt-equity ratio to calculate the WACC. Doing so, we find: WACC =.12(1/1.80) +.07(.80/1.80)(1 --.21) WACC =.0912, or 9.12% **7.** Here we have the WACC and need to find the debt-equity ratio of the company. Setting up the WACC equation, we find: *WACC* =.0860 =.112(*S**V*)(1 --.21) Rearranging the equation, we find:.0860(*V**S*) Now we must realize that the *V**S* = 1 + *B*S + 1) =.112 +.0506(*B**S* as:.0354(*B**S* =.7336 **8.** *a.* The book value of equity is the book value per share times the number of shares, and the book value of debt is the face value of the company's debt, so: Equity = 5,800,000(\$4) Equity = \$23,200,000 Debt = \$50,000,000 + 40,000,000 Debt = \$90,000,000 So, the total book value of the company is: Book value = \$23,200,000 + 90,000,000 Book value = \$113,200,000 And the book value weights of equity and debt are: Equity/Value = \$23,200,000/\$113,200,000 Equity/Value =.2049 Debt/Value = 1 -- Equity/Value Debt/Value =.7951 *b.* The market value of equity is the share price times the number of shares, so: *S* = 5,800,000(\$52) *S* = \$301,600,000 Using the relationship that the total market value of debt is the price quote times the par value of the bond, we find the market value of debt is: *B* = 1.083(\$50,000,000) + 1.089(\$40,000,000) *B* = \$97,710,000 This makes the total market value of the company: *V* = \$301,600,000 + 97,710,000 *V* = \$399,310,000 And the market value weights of equity and debt are: *S**V* =.7553 *B**V* *B**V* = \$156,000,000/\$488,100,000 *B**V* = \$332,100,000/\$488,100,000 *S**V*) +.03(*B**S*) =.07 +.03(*B**S* term is the equity multiplier, which is (1 + *B**S* + 1) =.07 +.03(*B**S* =.8729 **19.** *a.* Using the dividend discount model, the cost of equity is: *R~S~* = \[(\$.95)(1.039)/\$71\] +.039 *R~S~* =.0529, or 5.29% *b.* Using the CAPM, the cost of equity is: *R~S~* =.043 + 1.15(.11 --.043) *R~S~* =.1201, or 12.01% *c.* When using the dividend growth model or the CAPM, you must remember that both are estimates for the cost of equity. Additionally, and perhaps more importantly, each method of estimating the cost of equity depends upon different assumptions. **20.** We are given the total cash flow for the current year. To value the company, we need to calculate the cash flows until the growth rate levels off at a constant perpetual rate. So, the cash flows each year will be: Year 1: \$7,300,000(1 +.09) = \$7,957,000 Year 2: \$7,957,000(1 +.09) = \$8,673,130 Year 3: \$8,673,130(1 +.09) = \$9,453,712 Year 4: \$9,453,712(1 +.09) = \$10,304,546 Year 5: \$10,304,546(1 +.09) = \$11,231,955 Year 6: \$11,231,955(1 +.04) = \$11,681,233 We can calculate the terminal value in Year 5 since the cash flows begin a perpetual growth rate. Since we are valuing Arras, we need to use the cost of capital for that company since this rate is based on the risk of Arras. The cost of capital for Schultz is irrelevant in this case. So, the terminal value is: TV~5~ = CF~6~/(WACC -- *g*) TV~5~ = \$11,681,233/(.10 --.04) TV~5~ = \$194,687,218 Now we can discount the cash flows for the first 5 years as well as the terminal value back to today. Again, using the cost of capital for Arras, we find the value of the company today is: *V*~0~ = \$7,957,000/1.10 + \$8,673,130/1.10^2^ + \$9,453,712/1.10^3^ + \$10,304,546/1.10^4^ \+ (\$11,231,955 + 194,687,218)/1.10^5^ *V*~0~ = \$156,401,974 The market value of the equity is the market value of the company minus the market value of the debt, or: *S* = \$156,401,974 -- 30,000,000 *S* = \$126,401,974 To find the maximum offer price, we divide the market value of equity by the shares outstanding, or: Share price = \$126,401,974/1,900,000 Share price = \$66.53 **\ ** **21.** *a.* To begin the valuation of Joe's, we will begin by calculating the WACC for Happy Times. Since both companies are in the same industry, it is likely that the WACC for both companies will be the same. The weights of debt and equity are: *X~B~* = \$95,000,000/(\$95,000,000 + 340,000,000) *X~B~* =.2184, or 21.84% *X~S~* = \$340,000,000/(\$95,000,000 + 340,000,000) *X~S~* =.7816, or 78.16% The WACC for Happy Times is: WACC =.2184(.06)(1 --.21) +.7816(.11) WACC =.0963, or 9.63% Next, we need to calculate the cash flows for each year. The EBIT will grow at 10 percent per year for 5 years. Net working capital, capital spending, and depreciation are 9 percent, 15 percent, and 8 percent of EBIT, respectively. So, the cash flows for each year over the next 5 years will be:   *Year 1* *Year 2* *Year 3* *Year 4* *Year 5* -- ----------------------- -------------- -------------- -------------- -------------- -------------- EBIT \$10,300,000 \$11,330,000 \$12,463,000 \$13,709,300 \$15,080,230 Taxes 2,163,000 2,379,300 2,617,230 2,878,953 3,166,848 Net income \$8,137,000 \$8,950,700 \$9,845,770 \$10,830,347 \$11,913,382 Depreciation 824,000 906,400 997,040 1,096,744 1,206,418   OCF \$8,961,000 \$9,857,100 \$10,842,810 \$11,927,091 \$13,119,800 -- Capital spending 1,545,000 1,699,500 1,869,450 2,056,395 2,262,035 -- Change in NWC 927,000 1,019,700 1,121,670 1,233,837 1,357,221 Cash flow from assets \$6,489,000 \$7,137,900 \$7,851,690 \$8,636,859 \$9,500,545 After Year 5 the cash flows will grow at 3 percent in perpetuity. We can find the terminal value of the company in Year 5 using the cash flow in Year 6, as: TV~5~ = CF~6~/(WACC -- *g*) TV~5~ = \$9,500,545(1 +.03)/(.0963 --.03) TV~5~ = \$147,531,250 Now we can discount the cash flows and terminal value to today. Doing so, we find: *V*~0~ = \$6,489,000/1.0963 + \$7,137,900/1.0963^2^ + \$7,851,690/1.0963^3^ \+ \$8,636,859/1.0963^4^ + (\$9,500,545 + 147,531,250)/1.0963^5^ *V*~0~ = \$122,942,488 The market value of the equity is the market value of the company minus the market value of the debt, or: *S* = \$122,942,488 -- 26,500,000 *S* = \$96,442,488 To find the maximum offer price, we divide the market value of equity by the shares outstanding, or: Share price = \$96,442,488/1,850,000 Share price = \$52.13 *b.* To calculate the terminal value using the EV/EBITDA multiple we need to calculate the Year 5 EBITDA, which is EBIT plus depreciation, or: EBITDA = \$15,080,230 + 1,206,418 EBITDA = \$16,286,648 TV~5~ = \$16,286,648(8) TV~5~ = \$130,293,187 Note, this is the terminal value in Year 5 since we used the Year 5 EBITDA. We need to calculate the present value of the cash flows for the first 4 years, plus the present value of the Year 5 terminal value. We do not need to include the Year 5 cash flow since it is included in the Year 5 terminal value. So, the value of the company today is: *V*~0~ = \$6,489,000/1.0963 + \$7,137,900/1.0963^2^ + \$7,851,690/1.0963^3^ \+ \$8,636,859/1.0963^4^ + \$130,293,187/1.0963^5^ *V*~0~ = \$106,060,064 The market value of the equity is the market value of the company minus the market value of the debt, or: *S* = \$106,060,064 -- 26,500,000 *S* = \$79,560,064 To find the maximum offer price, we divide the market value of equity by the shares outstanding, or: Share price = \$79,560,064/1,850,000 Share price = \$43.01 *[Challenge]* **22.** We can use the debt-equity ratio to calculate the weights of equity and debt. The debt of the company has a weight for long-term debt and a weight for accounts payable. We can use the target given for accounts payable to calculate the weight of accounts payable and the weight of long-term debt. The weight of each will be: Accounts payable weight =.20/1.20 Accounts payable weight =.17 Long-term debt weight = 1/1.20 Long-term debt weight =.83 Since the accounts payable has the same cost as the overall WACC, we can write the equation for the WACC as: WACC = (1/1.45)(.13) + (.45/1.45)\[(.20/1.2)WACC + (1/1.2)(.07)(1 --.21)\] Solving for WACC, we find: WACC =.0897 +.3103\[(.20/1.2)WACC +.0461\] WACC =.0897 + (.0517)WACC +.0143 (.9483)WACC =.1040 WACC =.1096, or 10.96% We will use the same equation to calculate the weighted average flotation cost, except we will use the flotation cost for each form of financing. Doing so, we get: Flotation costs = (1/1.45)(.08) + (.45/1.45)\[(.20/1.2)(0) + (1/1.2)(.04)\] Flotation costs =.0655, or 6.55% The total amount we need to raise to fund the new equipment will be: Amount raised cost = \$40,000,000/(1 --.0655) Amount raised = \$42,804,428.04 Since the cash flows go to perpetuity, we can calculate the present value using the equation for the PV of a perpetuity. The NPV is: NPV = --\$42,804,428.04 + \$5,400,000/.1096 NPV = \$6,453,387.70 **23.** We can use the debt-equity ratio to calculate the weights of equity and debt. The weight of debt in the capital structure is: *X~B~* =.65/1.65 *X~B~* =.3939, or 39.39% And the weight of equity is: *X~S~* = 1 --.3939 *X~S~* =.6061, or 60.61% Now we can calculate the weighted average flotation costs for the various percentages of internally-raised equity. To find the portion of equity flotation costs, we can multiply the equity costs by the percentage of equity raised externally, which is one minus the percentage raised internally. So, if the company raises all equity externally, the flotation costs are: *f~T~* = (.6061)(.07)(1 -- 0) + (.3939)(.025) *f~T~* =.0523, or 5.23% The initial cash outflow for the project needs to be adjusted for the flotation costs. To account for the flotation costs: Amount raised(1 --.0523) = \$145,000,000 Amount raised = \$145,000,000/(1 --.0523) Amount raised = \$152,997,602 If the company uses 60 percent internally generated equity, the flotation cost is: *f~T~* = (.6061)(.07)(1 --.60) + (.3939)(.025) *f~T~* =.0268, or 2.68% And the initial cash flow will be: Amount raised(1 --.0268) = \$145,000,000 Amount raised = \$145,000,000/(1 --.0268) Amount raised = \$148,995,796 If the company uses 100 percent internally generated equity, the flotation cost is: *f~T~* = (.6061)(.07)(1 -- 1) + (.3939)(.025) *f~T~* =.0098, or.98% And the initial cash flow will be: Amount raised(1 --.0098) = \$145,000,000 Amount raised = \$145,000,000/(1 --.0098) Amount raised = \$146,442,234 **24.** The \$7.5 million cost of the land 3 years ago is a sunk cost and irrelevant; the \$7.1 million appraised value of the land is an opportunity cost and is relevant. The \$7.4 million land value in 5 years is a relevant cash flow as well. The fact that the company is keeping the land rather than selling it is unimportant. The land is an opportunity cost in 5 years and is a relevant cash flow for this project. The market value capitalization weights are: *B* = 280,000(\$1,000)(1.03) *B* = \$288,400,000 *S* = 9,800,000(\$73) *S* = \$715,400,000 *P* = 450,000(\$87) *P* = \$39,150,000 The total market value of the company is: V = \$288,400,000 + 715,400,000 + 39,150,000 V = \$1,042,950,000 The weight of each form of financing in the company's capital structure is: *X~B~* = \$288,400,000/\$1,042,950,000 *X~B~* =.2765 *X~S~* = \$715,400,000/\$1,042,950,000 *X~S~* =.6859 *X~P~* = \$39,150,000/\$1,042,950,000 *X~P~* =.0375 Next we need to find the cost of funds. We have the information available to calculate the cost of equity using the CAPM, so: *R~S~* =.032 + 1.20(.075) *R~S~* =.1220, or 12.20% The cost of debt is the YTM of the company's outstanding bonds, so: *P*~0~ = \$1,030 = \$32(PVIFA~*R*%,50~) + \$1,000(PVIF~*R*%,50~) *R* = 3.082% YTM = 3.082% × 2 = 6.16% And the aftertax cost of debt is: *R~B~* = (1 --.24)(.0616) *R~B~* =.0468, or 4.68% The cost of preferred stock is: *R~P~* = \$5.10/\$87 *R~P~* =.0586, or 5.86% *a.* The weighted average flotation cost is the sum of the weight of each source of funds in the capital structure of the company times the flotation costs, so: *f~T~* =.6859(.065) +.2765(.03) +.0375(.045) *f~T~* =.0546, or 5.46% The initial cash outflow for the project needs to be adjusted for the flotation costs. To account for the flotation costs: Amount raised(1 --.0546) = \$45,000,000 Amount raised = \$45,000,000/(1 --.0546) Amount raised = \$47,597,436 So the cash flow at Time 0 will be: CF~0~ = --\$7,100,000 -- 47,597,436 -- 1,400,000 CF~0~ = --\$56,097,436 There is an important caveat to this solution. This solution assumes that the increase in net working capital does not require the company to raise outside funds; therefore the flotation costs are not included. However, this is an assumption and the company could need to raise outside funds for the NWC. If this is true, the initial cash outlay includes these flotation costs, so: Total cost of NWC including flotation costs: \$1,400,000/(1 --.0546) = \$1,480,809 This would make the total initial cash flow: CF~0~ = --\$7,100,000 -- 47,597,436 -- 1,480,809 CF~0~ = --\$56,178,245 *b.* To find the required return on this project, we first need to calculate the WACC for the company. The company's WACC is: *WACC* =.6859(.1220) +.2765(.0468) +.0375(.0586)\] *WACC* =.0988, or 9.88% The company wants to use the subjective approach to this project because it is located overseas. The adjustment factor is 2 percent, so the required return on this project is: Project required return = 9.88% + 2% Project required return = 11.88% *c.* The annual depreciation for the equipment will be: \$45,000,000/8 = \$5,625,000 So, the book value of the equipment at the end of five years will be: BV~5~ = \$45,000,000 -- 5(\$5,625,000) BV~5~ = \$16,875,000 So, the aftertax salvage value will be: Aftertax salvage value = \$8,500,000 +.24(\$16,875,000 -- 8,500,000) Aftertax salvage value = \$10,510,000 *d.* Using the tax shield approach, the OCF for this project is: OCF = \[(*P* -- *v*)*Q* -- FC\](1 -- *T*~C~) + *T*~C~*D* OCF = \[(\$12,900 -- 11,250)(18,000) -- 8,100,000\](1 --.24) +.24(\$45,000,000/8) OCF = \$17,766,000 *e.* The accounting break-even sales figure for this project is: Q~A~ = (FC + *D*)/(*P* -- *v*) Q~A~ = (\$8,100,000 + 5,625,000)/(\$12,900 -- 11,250) Q~A~ = 8,318.18 units *f.* We have calculated all cash flows of the project. We just need to make sure that in Year 5 we add back the aftertax salvage value and the recovery of the initial NWC. The cash flows for the project are: *[Year]* *[Flow Cash]* 0 --\$56,097,436 1 17,766,000 2 17,766,000 3 17,766,000 4 17,766,000 5 37,076,000 Using the required return of 11.88 percent, the NPV of the project is: NPV = --\$56,097,436 + \$17,766,000(PVIFA~11.88%,4~) + \$37,076,000/1.1188^5^ NPV = \$19,143,948.95 And the IRR is: NPV = 0 = --\$56,097,436 + \$17,766,000(PVIFA~IRR%,4~) + \$37,076,000/(1 + IRR)^5^ IRR = 23.43% If the initial NWC is assumed to be financed from outside sources, the cash flows are: *[Year]* *[Flow Cash]* 0 --\$56,178,245 1 17,766,000 2 17,766,000 3 17,766,000 4 17,766,000 5 37,076,000 With this assumption, and the required return of 11.88 percent, the NPV of the project is: NPV = --\$56,178,245 + \$17,766,000(PVIFA~11.88%,4~) + \$37,076,000/1.1188^5^ NPV = \$19,063,139.82 And the IRR is: NPV = 0 = --\$56,178,245 + \$17,766,000(PVIFA~IRR%,4~) + \$37,076,000/(1 + IRR)^5^ IRR = 23.37%