罗斯公司理财第九版第十八章课后答案对应版.doc

第十八章：杠杆企业的股价与资本预算1、调整的净现值法（APV）如下：（UCFt= 无杠杆企业项目第期流向权益所有者的现金流量R0=无杠杆企业项目的资本成本）2、APV 法用权益资本成本折现现金流得到无杠杆项目的价值，然后加上负债的节税现值，得到有杠杆情况下的项目价值；而WACC 法则将UCF 按RWACC折现，而RWACC低于R0 。3、FTE 法使用的是LCF，而其它两种方法使用的是UCF。4、WACC 法在计算现金流量时使用的是无杠杆企业的现金流量，没有包含利息，但是在计算加权平均成本的时候包含了利息成本。若在计算现金流时要把利息的支付包括进去，可使用FTF 法。5、无杠杆企业的贝塔值可以用杠杆的贝塔来衡量，它是企业业务风险的衡量标准；另外，企业的金融风险也可以由贝塔值来衡量。6.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. The NPV equation for the project is: NPV = Purchase Price + PV(1 tC )(EBTD) + PV(Depreciation Tax Shield) If we let P equal the purchase price of the fleet, then the NPV is: NPV = P + (1 .35)($140,000)PVIFA13%,5 + (.35)(P/5)PVIFA13%,5Setting the NPV equal to zero and solving for the purchase price, we find: 0 = P + (1 .35)($140,000)PVIFA13%,5 + (.35)(P/5)PVIFA13%,5 P = $320,068.04 + (P)(0.35/5)PVIFA13%,5 = $320,068.04 + .2462P .7538P = $320,068.04 则P = $424,609.54b. 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 firms debt, so: APV = NPV(All-Equity) + NPV(Financing Side Effects) So, the NPV of each part of the APV equation is: NPV(All-Equity) = Purchase Price + PV(1 tC )(EBTD) + PV(Depreciation Tax Shield) The company paid $395,000 for the fleet of cars. Because this fleet will be fully depreciated over five years using the straight-line method, annual depreciation expense equals: Depreciation = $395,000/5 = $79,000 So, the NPV of an all-equity project is: NPV = $395,000 + (1 0.35)($140,000)PVIFA13%,5 + (0.35)($79,000)PVIFA13%,5 NPV = $22,319.49NPV(Financing Side Effects) The net present value of financing side effects equals the after-tax present value of cash flows resulting from the firms 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 = $260,000 (1 0.35)(0.08)($260,000)PVIFA8%,5 $260,000/(1.08)5 = $29,066.93 So, the APV of the project is: APV = NPV(All-Equity) + NPV(Financing Side Effects) APV = $22,319.49 + 29,066.93 = $51,386.427. a. In order to value a firms equity using the flow-to-equity approach, discount the cash flows available to equity holders at the cost of the firms levered equity. The cash flows to equity holders will be the firms net income. Remembering that the company has three stores, we find:Sales $3,600,000 COGS 1,530,000 G & A costs 1,020,000 Interest 102,000 EBT $948,000 Taxes 379,200 NI $568,800 Since this cash flow will remain the same forever, the present value of cash flows available to the firms equity holders is a perpetuity. We can discount at the levered cost of equity, so, the value of the companys equity is: PV(Flow-to-equity) = $568,800 / 0.19 = $2,993,684.21b. 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 companys 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 / $2,993,684.21 = 0.40 则B = $1,197,473.68 So, the value of the company is: V = $2,993,684.21 + 1,197,473.68 = $4,191,157.898. a. In order to determine the cost of the firms debt, we need to find the yield to maturity on its current bonds. With semiannual coupon payments, the yield to maturity in the companys bonds is: $975 = $40(PVIFAR%,40) + $1,000(PVIFR%,40) 则R = .0413 or 4.13%Since the coupon payments are semiannual, the YTM on the bonds is: YTM = 4.13% 2 = 8.26%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 + Unlevered(RM RF) = 5% + 1.1(12% 5%) = 12.70% 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) = .1270 + (.40)(.1270 .0826)(1 .34) = .1387 or 13.87%c. In a world with corporate taxes, a firms 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 firms 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) = .4 / 1.4 = .29 And the equity-value ratio is one minus the debt-value ratio, or: S/V = 1 .29= .71 So, the WACC for the company is: RWACC = .29(1 .34)(.0826) + .71(.1387) RWACC = .1147 or 11.47%9. 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 1.25, we can find the equity beta for each. Doing so, we find: North Pole Equity = 1 + (1 tC)(B/S) Unlevered = 1 + (1 .35)($2,900,000/$3,800,000(1.25) = 1.87 South Pole Equity = 1 + (1 tC)(B/S)Unlevered = 1 + (1 .35)($3,800,000/$2,900,000(1.25) = 2.31b. We can use the Capital Asset Pricing Model to find the required return on each firms equity. Doing so, we find: North Pole: RS = RF + Equity(RM RF) = 5.30% + 1.87(12.40% 5.30%) = 18.58% South Pole: RS = RF + Equity(RM RF) = 5.30% + 2.31(12.40% 5.30%) = 21.73%10. First we need to find the aftertax value of the revenues minus expenses. The aftertax value is: Aftertax revenue = $3,800,000(1 .40) = $2,280,000 Next, we need to find the depreciation tax shield. The depreciation tax shield each year is: Depreciation tax shield = Depreciation(tC) = ($11,400,000 / 6)(.40) = $760,000 Now we can find the NPV of the project, which is: NPV = Initial cost + PV of depreciation tax shield + PV of aftertax revenue To find the present value of the depreciation tax shield, we should discount at the risk-free rate, and we need to discount the aftertax revenues at the cost of equity, so: NPV = $11,400,000 + $760,000(PVIFA6%,6) + $2,280,000(PVIFA14%,6) = $1,203,328.4311. 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 = ($3 / $19)(.035)(1 .35) + ($10 / $19)(.068)(1 .35) + ($6 / $19)(.145) RWACC = 0.0726 or 7.26%b. Using the market value weights, the companys WACC is: RWACC = (wSTD)(RSTD)(1 tC) + (wLTD)(RLTD)(1 tC) + (wEquity)(REquity) RWACC = ($3 / $40)(.035)(1 .35) + ($11 / $40)(.068)(1 .35) + ($26 / $40)(.145) RWACC = 0.1081 or 10.81%c. Using the target debt-equity ratio, the target debt-value ratio for the company is: B/S = 0.60 则B = 0.6S Substituting this in the debt-value ratio, we get: B/V = .6S / (.6S + S) = .6 / 1.6 = .375 And the equity-value ratio is one minus the debt-value ratio, or: S/V = 1 .375 = .625We 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 = 0.20 则STD = 0.2LTD Substituting this in the short-term debt to total debt ratio, we get: STD/B = .2LTD / (.2LTD + LTD) = .2 / 1.2 = .167 And the long-term debt to total debt ratio is one minus the short-term debt to total debt ratio, or: LTD/B = 1 .167 = .833Now 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) = .167(.375) = .063And the long-term debt to value ratio is: LTD/V = (LTD/B)(B/V) = .833(.375) = .313 So, using the target capital structure weights, the companys WACC is: RWACC = (wSTD)(RSTD)(1 tC) + (wLTD)(RLTD)(1 tC) + (wEquity)(REquity) RWACC = (.06)(.035)(1 .35) + (.31)(.068)(1 .35) + (.625)(.145) = 0.1059 or 10.59% d. The differences in the WACCs are due to the different weighting schemes. The companys 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 evaluation12.略13. 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 0.40) 则R0 = 0.1438 or 14.38% Now we can find the NPV of an all-equity project, which is: NPV = PV(Unlevered Cash Flows) NPV = $21,000,000 + $6,900,000/1.1438 + $11,000,000/(1.1438)2 + $9,500,000/(1.1438)3 NPV = $212,638.89Next, 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 firms 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 = $7,000,000 (1 .40)(.09)($7,000,000) / (1.09) $2,333,333.33/(1.09) (1 .40)(.09)($4,666,666.67)/(1.09)2 $2,333,333.33/(1.09)2 (1 .40)(.09)($2,333,333.33)/(1.09)3 $2,333,333.33/(1.09)3 = $437,458.31 So, the APV of project is: APV = NPV(All-equity) + NPV(Financing side effects) APV = $212,638.89 + 437,458.31 = $224,819.4214. a. To calculate the NPV of the project, we first need to find the companys WACC. In a world with corporate taxes, a firms weighted average cost of capital equals: RWACC = B / (B + S)(1 tC)RB + S / (B + S)RS The market value of the companys equity is: Market value of equity = 6,000,000($20) = $120,000,000 So, the debt-value ratio and equity-value ratio are: Debt-value = $35,000,000 / ($35,000,000 + 120,000,000) = .2258 Equity-value = $120,000,000 / ($35,000,000 + 120,000,000) = .7742Since the CEO believes its current capital structure is optimal, these values can be used as the target weights in the firms weighted average cost of capital calculation. The yield to maturity of the companys debt is its pretax cost of debt. To find the companys cost of equity, we need to calculate the stock beta. The stock beta can be calculated as: = 标准差S,M / 方差M = .036 / .202 = 0.90 Now we can use the Capital Asset Pricing Model to determine the cost of equity. The Capital Asset Pricing Model is: RS = RF + (RM RF) = 6% + 0.90(7.50%) = 12.75%Now, we can calculate the companys WACC, which is: RWACC = B / (B + S)(1 tC)RB + S / (B + S)RS = .2258(1 .35)(.08) + .7742(.1275) RWACC = .1105 or 11.05% Finally, we can use the WACC to discount the unlevered cash flows, which gives us an NPV of: NPV = $45,000,000 + $13,500,000(PVIFA11.05%,5) = $4,837,978.59b. 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 target15. 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 $83,000 Tax 33,200 Net income $49,800 So, the value of the company is: VU = $49,800 / .15 = $332,000b. 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 = $195,000 (1 .40)(.09)($195,000) / 0.09 = $78,000 So, using the APV method, the value of the company is: APV = VU + NPV(Financing side effects) = $332,000 + 78,000 = $410,000 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 = $410,000 195,000 = $215,000c. 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 = .15 + ($195,000 / $215,000)(.15 .09)(1 .40) = .1827 or 18.27%d. In order to value a firms equity using the flow-to-equity approach, we can discount the cash flows available to equity holders at the cost of the firms levered equity. First, we need to calculate the levered cash flows available to shareholders, which are:EBIT $83,000 Interest 17,550 EBT $65,450 Tax 26,180 Net income $39,270 So, the value of equity with the flow-to-equity method is: S = Cash flows available to equity holders / RS = $39,270 / .1827 = $215,00016. 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 + (MRP) = 5% + 1.2(7%) = 13.40% 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) =.1340 = R0 + (.3