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# Corporate Finance BUSN 323

Christopher Newport University

GPA 3.64

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This 64 page Class Notes was uploaded by Belle Kunde DVM on Monday October 5, 2015. The Class Notes belongs to BUSN 323 at Christopher Newport University taught by Arthur Gudikunst in Fall. Since its upload, it has received 31 views. For similar materials see /class/219486/busn-323-christopher-newport-university in Business at Christopher Newport University.

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Date Created: 10/05/15

BUSN 323 Fundamentals of Corporate Finance 7Lh Ed Dr G 200506 SOLUTIONS TO TEXT PROBLEMS Chapter 2 To nd the book value of current assets we use NWC CA 7 CL Rearranging to solve for current assets we get CA NWC CL 900K 22M 31M The market value of current assets and xed assets is given so Book value CA 31M Market value CA 28M Book value NFA 40M Market value NFA 32M Book value assets 31M 40M 71M Market value assets 28M 32M 60M 6 7 39 Taxes 01550K 02525K 03425K 039273K 7 100K 89720 The average tax rate is the total tax paid divided by net income so Average tax rate 89720 273000 3286 The marginal tax rate is the tax rate on the next 1 of earnings so the marginal tax rate To nd the OCF we rst calculate net income Income Statement Sales 145000 Costs 86000 Depreciation 7000 Other expenses 4 900 EBIT 47100 Interest 15 000 Taxable income 32100 Taxes 34 12 840 Net income 19 260 Dividends 8700 Additions to RE 10560 a OCF EBIT Depreciation7 Taxes 47100 7000 7 12840 41260 b CFC Interest 7 Net new LTD 15000 7 6500 21500 Note that the net new longterm debt is negative because the company repaid part of its long term debt 0 CFS Dividends 7 Net new equity 8700 7 6450 2250 9 We know that CFA CFC CFS so CFA 21500 2250 23750 CFA is also equal to OCF 7 Net capital spending 7 Change in NWC We already know OCF Net capital spending is equal to Net capital spending Increase in NFA Depreciation 5000 7000 12000 Now we can use CFA OCF 7 Net capital spending 7 Change in NWC 23750 41260 7 12000 7 Change in NWC Solving for the change in NWC gives 5510 meaning the company increased its NWC by 5 510 The solution to this question works the income statement backwards Starting at the bottom Net income Dividends Addition to ret earnings 900 4500 5400 Now looking at the income statement EBT 7 EBT X Tax rate Net income Recognize that EBT X taX rate is simply the calculation for taxes Solving this for EBT yields EBT NI 17 tax rate 5400 065 8308 Now you can calculate EBIT EBT interest 8308 1600 9908 The last step is to use EBIT Sales 7 Costs 7 Depreciation EBIT 29000 7 13000 7 Depreciation 9908 Solving for depreciation we nd that depreciation 6092 The balance sheet for the company looks like this Balance Sheet Cash 175000 Accounts payable 430000 Accounts receivable 140000 Notes payable 80 000 Inventory 265 000 Current liabilities 610000 Current assets 580000 Longterm debt 1 430 000 Total liabilities 2040000 Tangible net xed assets 2900000 Intangible net xed assets 720 000 Common stock Accumulated ret earnings 1 240 000 Total assets 4 200 000 Total liab amp owners equity 4 200 000 Total liabilities and owners equity is TL amp OE CL LTD Common stock Solving for this equation for equity gives us Common stock 4200000 7 1240000 7 2040000 920000 a Income Statement Sales 12800 Cost of good sold 10400 Depreciation 1 900 EBIT 500 Interest 450 Taxable income 50 Taxes 34 17 Net income 33 b OCF EBIT Depreciation 7 Taxes 500 1900 717 2383 0 Change in NWC NWCend 7 NWCb6g CAend CLend CAbeg CLbeg 3850 7 2100 7 3200 71800 1750 71400 350 Net capital spending NFAend 7 NFAbcg Depreciation 9700 7 9100 1900 2500 CFA OCF 7 Change in NWC 7 Net capital spending 2383 7 350 7 2500 7467 The cash ow from assets can be positive or negative since it represents whether the rm raised funds or distributed funds on a net basis In this problem even though net 4 income and OCF are positive the rm invested heavily in both xed assets and net working capital it had to raise a net 467 in funds from its stockholders and creditors to make these investments 61 Cash ow to creditors Interest 7 Net new LTD 450 7 0 450 Cash ow to stockholders Cash ow from assets 7 Cash ow to creditors 7467 7 450 7917 We can also calculate the cash ow to stockholders as Cash ow to stockholders Dividends 7 Net new equity Solving for net new equity we get Net new equity 500 7 7917 1417 The rm had positive earnings in an accounting sense NI gt 0 and had positive cash ow from operations The rm invested 350 in new net working capital and 2500 in new xed assets The rm had to raise 467 from its stakeholders to support this new investment It accomplished this by raising 1417 in the form of new equity After paying out 500 of this in the form of dividends to shareholders and 450 in the form of interest to creditors 467 was left to meet the rm s cash ow needs for investment Chapter 3 To nd ROE we need to nd total equity TL amp OE TD TE TE TL amp OE 7 TD TE 37M 713M 24M ROE Net income TE Net income TE 261M 24M 1088 3 Receivables turnover Sales Receivables Receivables turnover 2873150 421865 681 times Days sales in receivables 365 days Receivables turnover 365 681 5359 days The average collection period for an outstanding accounts receivable balance was 5359 days gt Inventory turnover COGS Inventory Inventory turnover 2532095 386500 655 times Days sales in inventory 365 days Inventory turnover 365 655 5571 days On average a unit of inventory sat on the shelf 5571 days before it was sold Total debt ratio 044 TD TA Substituting total debt plus total equity for total assets we get 044 TD TD TE Solving this equation yields 044TE 056TE Debtequity ratio TD TE 044 056 079 Equity multiplier 1 D E 179 310K 160K 470K Net income Addition to RE Dividends Earnings per share NI Shares 470K 180K 261 per share Dividends per share Dividends Shares 160K 180K 089 per share Book value per share TE Shares 65M 180K 3611 per share Markettobook ratio Share price BVPS 78 3611 216 times PE ratio Share price EPS 78 261 2987 times ROE PMTATEM ROE 085130175 1934 This question gives all of the necessary ratios for the DuPont Identity except the equity multiplier so using the DuPont Identity ROE PMTATEM ROE 1867 092163EM EM 1867 092163 124 DEEM7112471024 H P H Equot Increase in inventory is a use of cash Increase in accounts payable is a source of cash Decrease in notes payable is a use of cash Increase in accounts receivable is a use of cash Changes in cash sources 7 uses 330 7 600 790 950 72010 Cash decreased by 2010 Payables turnover COGS Accounts payable Payables turnover 13 168 2965 444 times Days sales in payables 365 days Payables turnover Days sales in payables 365 444 8219 days The company left its bills to suppliers outstanding for 8219 days on average A large value for this ratio could imply that either 1 the company is having liquidity problems making it difficult to pay off its shortterm obligations or 2 that the company has successfully negotiated lenient credit terms from its suppliers New investment in fixed assets is found by Net investment in FA NFAend 7 NFAbeg Depreciation Net investment in FA 580 165 745 The company bought 745 in new fixed assets this is a use of cash The equity multiplier is EM1DE EM 1l40 240 One formula to calculate return on equity is ROE 7 ROAEM ROE 7 087240 7 2088 ROE can also be calculated as ROE NI TE So net income is NI 7 ROETE NI 7 2088520000 7 108576 13 through 15 2004 13 2005 13 14 15 Assets Current assets Cash 10168 254 10683 237 10506 0933 lAccounts receivable 27145 677 28613 634 1054109361 Inventory 59 324 1480 64853 1437 10932 09708 Total 96637 2411 104419 2308 10777 09571 Fixed assets Net plant and equipment 304 165 7589 347 168 7692 11414 10136 Total assets 400 802 100 451 317 100 11260 10000 Liabilities and Owners Equity Current liabilities Accounts payable 73185 1826 59309 1314 08104 07197 Notes payable 39125 976 48168 1067 12311 10933 Total 112310 2802 107477 2381 09570 08499 Longterm debt 50000 1247 62000 1374 12400 10102 Owners equity Common stock and paidin surplus 80000 1996 80000 1773 10000 08881 Accumulated retained earnings 158492 3954 201840 4472 12735 11310 Total 238492 5950 281840 6245 11818 10495 Total liabilities and owners equity 400802 100 451317 100 11260 10000 The commonsize balance sheet answers are found by dividing each category by total assets For example the cash percentage for 2004 is 10168 400802 0254 or 254 This means that cash is 254 of total assets The commonbase year answers for Question 14 are found by dividing each category value for 2005 by the same category value for 2004 For example the cash commonbase year number is found by 10683 10168 10506 This means the cash balance in 2005 is 10506 times as large as the cash balance in 2004 The commonsize commonbase year answers for Question 15 are found by dividing the commonsize percentage for 2005 by the commonsize percentage for 2004 For example the cash calculation is found by 237 254 09331 This tells us that cash as a percentage of assets fell by l 7 9331 0669 or 669 percent 16 M SourcesUses Assets Current assets Cash 10168 515 U 10683 Accounts receivable 27l45 l468 U 28613 Inventory 59 324 5 529 U 64 853 Total 96637 75l2 U 104149 Fixed assets Net plant and equipment 304 165 43 003 U 347168 Total assets 400 802 50 515 U 451 317 Liabilities and owners equity Current liabilities Accounts payable 73185 713876 U 59309 Notes payable 39 125 9 043 S 48168 Total 112310 7 4833 U 107477 Longterm debt 50 000 12 000 S 62 000 Owners equity Common stock and paidin surplus 80000 0 80000 Accumulated retained earnings 158 492 43 348 S 201840 Total 238492 43 348 S 281840 Total liabilities and owners equity 400 802 50 515 S 451317 The rm used 50515 in cash to acquire new assets It raised this amount of cash by increasing liabilities and owners equity by 50515 In particular the needed funds were raised by internal nancing on a net basis out of the additions to retained earnings and by an issue of longterm debt 17 a Current ratio Current assets Current liabilities Current ratio 2004 96637 112310 086 times Current ratio 2005 104149 107477 097 times b Quick ratio Current assets 7 Inventory Current liabilities Quick ratio 2004 96637 7 59324 112310 033 times Quick ratio 2005 104149 7 64853 104477 037 times 0 Cash ratio Cash Current liabilities Cash ratio 2004 10168 112310 009 times Cash ratio 2005 10683 107477 010 times 61 NWC ratio NWC Total assets NWC ratio 2004 96637 7 112310 400802 7391 NWC ratio 2005 104149 7 107477 451317 7074 e Debtequity ratio Total debt Total equity Debtequity ratio 2004 112310 50000 238492 068 times Debtequity ratio 2005 107477 62000 281840 060 times Equity multiplier 1 D E Equity multiplier 2004 1 068 168 Equity multiplier 2005 1 060 160 f Total debt ratio Total assets 7 Total equity Total assets Total debt ratio 2004 400802 7 238492 400802 040 Total debt ratio 2005 451317 7 281840 451317 038 Longterm debt ratio Longterm debt Longterm debt Total equity Longterm debt ratio 2004 50000 50000 238492 017 Longterm debt ratio 2005 62000 62000 281840 018 26 Short term solvency ratios Current ratio Current assets Current liabilities Current ratio 2004 7828 1808 433 times Current ratio 2005 8322 2320 359 times Quick ratio Current assets 7 Inventory Current liabilities Quick ratio 2004 7828 7 4608 1808 178 times Quick ratio 2005 8322 7 4906 2320 147 times Cash ratio Cash Current liabilities Cash ratio 2004 815 1808 045 times Cash ratio 2005 906 2320 039 times Asset utilization ratios Total asset turnover Sales Total assets Total asset turnover 33500 27489 122 times Inventory turnover Cost of goods sold Inventory Inventory turnover 18970 4906 387 times Receivables turnover Sales Accounts receivable Receivables turnover 33500 2510 1335 times Long term solvency ratios Total debt ratio Total assets 7 Total equity Total assets Total debt ratio 2004 22992 7 16367 22992 029 Total debt ratio 2005 27489 7 20209 27489 026 2 2 7 00 Debtequity ratio Debtequity ratio 2004 Debtequity ratio 2005 Total debt Total equity 1808 4817 16367 040 2320 4960 20209 036 Equity multiplier 1 D E Equity multiplier 2004 1 040 140 Equity multiplier 2005 1 036 136 Times interest earned EBIT Interest Times interest earned 12550 486 2582 times Cash coverage ratio Cash coverage ratio EBIT Depreciation Interest 12550 1980 486 2990 times Pro tability ratios Pro t margin Pro t margin Net income Sales 7842 33500 2341 Net income Total assets 7842 27489 2853 Return on assets Return on assets Return on equity Return on equity Net income Total equity 7842 20209 3880 The DuPont identity is ROE PMTATEM ROE 02341122136 03880 or 3880 The number of days a company can operate if cash in ows were suspended is found by the interval measure The interval measure is calculated as Interval measure Current assets Average daily operating costs We can nd the average daily operating costs as follows Average daily operating costs Cost of goods sold 365 days Average daily operating costs 18970 365 5197 per day So the number of days the company can operate if cash in ows are suspended or the interval measure is Interval measure 8322 5197 per day 160 days Chapter 4 4 An increase of sales to 23040 is an increase of Sales increase 23040 7 19200 19200 Sales increase 20 or 20 Assuming costs and assets increase proportionally the pro forma nancial statements will look like this Pro forma income statement Pro forma balance sheet Sales 2304000 Assets 111600 Debt 2040000 Costs 18 66000 Equity 74 33448 EBIT 438000 Total 111 600 Total 94 73448 Taxes34 148920 Net income 2 89080 The payout ratio is constant so the dividends paid this year is the payout ratio from last year times net income or Dividends 7 96360 2409289080 DiVidends 115632 The addition to retained earnings is Addition to retained earnings 289080 7 115632 Addition to retained earnings 173448 And the new equity balance is Equity 7 72600 173448 Equity 7 7433448 So the EFN is EFN Total assets 7 Total liabilities and equity EFN 111600 7 9473448 EFN 1686552 6 To calculate the internal growth rate we rst need to calculate the ROA which is ROA NI TA ROA 2327 38000 ROA 0612 or 612 The plowback ratio b is one minus the payout ratio so b1720 b80 Now we can use the internal growth rate equation to get Internal growth rate ROA X b 1 7 ROA X b Internal growth rate 0061280 1 7 0061280 Internal growth rate 0515 or 515 Assuming costs vary with sales and a 20 percent increase in sales the pro forma income statement will look like this HEIR JORDAN CORPORATION Pro Forma Income Statement Sales 3480000 Costs 1344000 Taxable income 2136000 Taxes 34 7 26240 Net income 14 09760 The payout ratio is constant so the dividends paid this year is the payout ratio from last year times net income or Dividends 7 4935117481409760 DiVidends 592168 And the addition to retained earnings will be Addition to retained earnings 1409760 7 592168 Addition to retained earnings 817592 13 10 Below is the balance sheet with the percentage of sales for each account on the balance sheet Notes payable total current liabilities longterm debt and all equity accounts do not vary directly with sales HEIR JORDAN CORPORATION Balance Sheet Assets Liabilities and Owners Equity Current assets Current liabilities Cash 3525 1216 Accounts payable 3000 1034 Accounts receivable 7500 2586 Notes payable 7 500 na Inventory 6 000 2069 Total 10 500 na Total 17025 5871 Longterm debt 19 500 na Fixed assets Owners equity Net plant and Common stock and equipment 30 000 10345 paidin surplus 15000 na Retained earnings 2 025 na Total 17025 na Total liabilities and owners Total assets 47 025 16216 equity 47 025 na Assuming costs vary with sales and a 20 percent increase in sales the pro forma income statement will look like this HEIR JORDAN CORPORATION Pro Forma Income Statement Sales 3335000 Costs 1288000 Taxable income 2047000 Taxes 34 6 95980 Net income 13 51020 The payout ratio is constant so the dividends paid this year is the payout ratio from last year times net income or Dividends 4935117481351020 Dividends 567494 And the addition to retained earnings will be Addition to retained earnings 1324020 7 567494 Addition to retained ea1nings 783526 The new total addition to retained earnings on the pro forma balance sheet will be New total addition to retained earnings 2025 783526 New total addition to retained earnings 986026 The pro forma balance sheet will look like this HEIR JORDAN CORPORATION Pro Forma Balance Sheet Assets Liabilities and Owners Equity Current assets Current liabilities Cash 405375 Accounts payable 345000 Accounts receivable 862500 Notes payable 7 50000 Inventory 6 90000 Total 1095000 Total 1957875 Longterm debt 19 50000 Fixed assets Net plant and Owners equity equipment 34 50000 Common stock and paidin surplus 1500000 Retained earnings 9 86026 Total 2486026 Total liabilities and owners Total assets 54 07875 equity 55 31026 So the EFN is EFN Total assets 7 Total liabilities and equity EFN 5407875 7 5531026 EFN 7123151 Chapter 11 1 a The total variable cost per unit is the sum ofthe two variable costs so Total variable costs per unit 143 244 Total variable costs per unit 387 b The total costs include all variable costs and xed costs We need to make sure we are including all variable costs for the number of units produced so Total costs Variable costs Fixed costs Total costs 387320000 650000 Total costs 1888400 0 The cash breakeven that is the point where cash ow is zero is Qc 650000 1000 7 387 QC 106036 units And the accounting breakeven is QA 650000 190000 1000 7 387 7 9 QA 137031 units The cash breakeven equation is Qc FCP 7 V And the accounting breakeven equation is QA FC DP 7v Using these equations we nd the following cash and accounting breakeven points 1 Qc 7 15M3000 7 2275 QA 7 15M 7 65M3000 7 2275 Qc 7 20690 QA 7 29655 2 Qc 7 7300039 7 27 QA 7 73000 14000039 7 27 Qc 7 6083 QA 717750 3 Qc 7 12008 7 3 QA 7 1200 8408 7 3 Qc 7 240 QA 7 408 In order to calculate the nancial breakeven we need the OCF of the project We can use the cash and accounting breakeven points to nd this First we will use the cash breakeven to nd the price of the product as follows QC FCP 7 V 13000 120000P 7 23 P 3223 Now that we know the product price we can use the accounting breakeven equation to nd the depreciation Doing so we nd the annual depreciation must be QA FC DP 7 v 19000 7 120000 D3223 7 23 Depreciation 55385 We now know the annual depreciation amount Assuming straightline depreciation is used the initial investment in equipment must be ve times the annual depreciation or Initial investment 555385 276923 The PV of the OCF must be equal to this value at the nancial breakeven since the NPV is zero so 276923 7 OCFPVIFA155 OCF 7 8457491 We can now use this OCF in the nancial breakeven equation to nd the nancial breakeven sales gure is QF 120000 84574913223 7 23 QF 22162 11 We know that the DOL is the percentage change in OCF divided by the percentage change in quantity sold Since we have the original and new quantity sold we can use the DOL equation to nd the percentage change in OCF Doing so we nd DOL AOCF AQ Solving for the percentage change in OCF we get AOCF DOLAQ AOCF 2547000 7 4000040000 AOCF 4375 The new level of operating leverage is lower since FCOCF is smaller H Equot Using the DOL equation we nd DOL1FCOCF 25 1 150000OCF OCF 100000 The percentage change in quantity sold at 35000 units is AQ 35000 7 40000 40000 AQ 71250 or 71250 So using the same equation as in the previous problem we nd AOCF 257125 AQ 73125 or 73125 So the new OCF level will be New OCF 7173125100000 New OCF 7 68750 And the new DOL will be New DOL 1 15000068750 New DOL 3182 13 The DOL ofthe project is DOL 1 4500071000 DOL 16338 If the quantity sold changes to 8500 units the percentage change in quantity sold is AQ 8500 7 80008000 AQ 0625 or 625 So the OCF at 8500 units sold is AOCF DOLAQ AOCF 163380625 AOCF 1021 or 1021 This makes the new OCF New OCF 7100011021 New OCF 7825000 And the DOL at 8500 units is DOL 1 450007825000 DOL 15751 We can use the equation for DOL to calculate xed costs The xed cost must be DOL 275 1 FCOCF FC 275 7116000 FC 28000 If the output rises to 11000 units the percentage change in quantity sold is AQ 11000 71000010000 AQ 10 or 1000 The percentage change in OCF is AOCF 27510 AOCF 2750 or 2750 So the operating cash ow at this level of sales will be OCF 160001275 OCF 20400 If the output falls to 9000 units the percentage change in quantity sold is AQ 9000 7 1000010000 AQ 710 or 71000 The percentage change in OCF is AOCF 7 2757 10 AOCF 7 72750 or 72750 So the operating cash ow at this level of sales will be OCF 160001 7 275 OCF 11600 We can now use this OCF in the nancial breakeven equation to nd the nancial breakeven sales gure is QF 120000 84574913223 7 23 QF 22162 Chapter 17 1 a A table outlining the income statement for the three possible states of the economy is shown below The EPS is the net income divided by the 2500 shares outstanding The last row shows the percentage change in EPS the company will experience in a recession or an expansion economy Recession Normal Expansion EBIT 5600 14000 18200 Interest 0 0 0 N1 5 600 14 000 18 200 EPS 224 560 7284 AEPS 760 7 30 b If the company undergoes the proposed recapitalization it will repurchase Share price Equity Shares outstanding Share price 1500002500 Share price 60 Shares repurchased Debt issued Share price Shares repurchased 60000 60 Shares repurchased 1000 The interest payment each year under all three scenarios will be Interest payment 6000005 3000 19 The last row shows the percentage change in EPS the company will experience in a recession or an expansion economy under the proposed recapitalization Recession Normal Expansion EBIT 5600 14000 18200 Interest 3 000 3 000 3 000 NI 2 600 11 000 15 200 EPS 173 733 1013 AEPS 77636 7 3818 A table outlining the income statement with taxes for the three possible states of the economy is shown below The share price is still 60 and there are still 2500 shares outstanding The last row shows the percentage change in EPS the company will experience in a recession or an expansion economy Recession Normal Expansion EBIT 5600 14000 18200 Interest 0 0 0 Taxes 1 960 4 900 6 370 NI 3 640 9 100 11 830 EPS 146 364 473 AEPS 760 7 30 A table outlining the income statement with taxes for the three possible states of the economy and assuming the company undertakes the proposed capitalization is shown below The interest payment and shares repurchased are the same as in part b of Problem 1 Recession Normal Expansion EBIT 5600 14000 18200 Interest 3000 3000 3000 Taxes 910 3 850 5 320 NI 1 690 7 150 9 880 EPS 113 477 659 AEPS 77636 7 3818 Notice that the percentage change in EPS is the same both with and without taxes Since the company has a markettobook ratio of 10 the total equity of the rm is equal to the market value of equity Using the equation for ROE ROE NI150000 The ROE for each state of the economy under the current capital structure and no taxes is Recession Normal Expansion ROE 0373 0 33 1213 AROE 760 7 30 The second row shows the percentage change in ROE from the normal economy 20 b If the company undertakes the proposed recapitalization the new equity value will be Equity 150000 7 60000 Equity 90000 So the ROE for each state of the economy is ROE NT90000 Recession Normal Expansion ROE 0222 1156 1622 AROE 77636 7 3818 0 If there are corporate taxes and the company maintains its current capital structure the ROE is ROE 0243 0607 0789 AROE 0 7 30 If the company undertakes the proposed recapitalization and there are corporate taxes the ROE for each state of the economy is ROE 0144 0751 1054 AROE 77636 7 3818 Notice that the percentage change in ROE is the same as the percentage change in EPS The percentage change in ROE is also the same with or Without taxes 4 a Under Plan I the unlevered company net income is the same as EBIT with no corporate taX The EPS under this capitalization will be EPS 200000150000 shares EPS 133 Under Plan 11 the levered company EBIT will be reduced by the interest payment The interest payment is the amount of debt times the interest rate so N1 200000 7 101500000 N1 50000 And the EPS will be EPS 5000060000 shares EPS 083 Plan I has the higher EPS when EBIT is 200000 b Under Plan I the net income is 700000 and the EPS is EPS 700000150000 shares EPS 467 Under Plan 11 the net income is 6 21 NT 700000 7 101500000 NI 550000 And the EPS is EPS 55000060000 shares EPS 917 Plan 11 has the higher EPS when EBIT is 700000 0 To nd the breakeven EBIT for two different capital structures we simply set the equations for EPS equal to each other and solve for EBIT The breakeven EBIT is EBIT150000 EBIT 7 10150000060000 EBIT 250000 We can nd the price per share by dividing the amount of debt used to repurchase shares by the number of shares repurchased Doing so we nd the share price is Share price 1500000150000 7 60000 Share price 1667 per share The value of the company under the allequity plan is V 1667150000 shares 2500000 And the value of the company under the levered plan is V 166760000 shares 1500000 debt 2500000 a The income statement for each capitalization plan is I H All equity EBIT 10000 10000 10000 Interest 1 650 2 750 N1 8 350 7 250 10 000 EPS 759 806 714 Plan 11 has the highest EPS the allequity plan has the lowest EPS b The breakeven level of EBIT occurs when the capitalization plans result in the same EPS The EPS is calculated as EPS EBIT 7 RDDShares outstanding This equation calculates the interest payment RDD and subtracts it from the EBIT which results in the net income Dividing by the shares outstanding gives us the EPS For the allequity capital structure the interest term is zero To nd the breakeven EBIT for two different capital structures we simply set the equations equal to each other and solve for EBIT The breakeven EBIT between the allequity capital structure and Plan I is 22 EBIT1400 EBIT 7 10165001100 EBIT 7700 And the breakeven EBIT between the allequity capital structure and Plan 11 is EBIT1400 EBIT 7 1027500900 EBIT 7700 The breakeven levels of EBIT are the same because of MampM Proposition 1 Setting the equations for EPS from PlanI and Plan 11 equal to each other and solving for EBIT we get EBIT 7 10165001100 EBIT 7 1027500900 EBIT 7700 This breakeven level of EBIT is the same as in part 17 again because of MampM Proposition 1 The income statement for each capitalization plan with corporate income taxes is I H All equity EBIT 10000 10000 10000 Interest 1650 2750 0 Taxes 3 340 2 900 4 000 N1 5 010 4 3 0 6 000 EPS 455 483 429 Plan 11 still has the highest EPS the allequity plan still has the lowest EPS We can calculate the EPS as EPS EBIT 7 RDD1 7 tcShares outstanding This is similar to the equation we used before except now we need to account for taxes Again the interest eXpense term is zero in the allequity capital structure So the breakeven EBIT between the allequity plan and Plan I is EBIT17401400 EBIT 7 10165001 7 401100 EBIT 7700 The breakeven EBIT between the allequity plan and Plan 11 is EBIT1 7 401400 EBIT 7 10275001 7 40900 EBIT 7700 And the breakeven between Plan I and Plan 11 is EBIT 7 10165001 7 401100 EBIT 7 10275001 7 40900 EBIT 7700 23 The breakeven levels of EBIT do not change because the addition of taxes reduces the income of all three plans by the same percentage therefore they do not change relative to one another To nd the value per share of the stock under each capitalization plan we can calculate the price as the value of shares repurchased divided by the number of shares repurchased So under Plan I the value per share is P ll000200 shares P 55 per share And under Plan 11 the value per share is P 27500500 shares P 55 per share This shows that when there are no corporate taxes the stockholder does not care about the capital structure decision of the rm This is MampM Proposition I without taxes Chapter 5 1 The simple interest per year is 5000 X 07 350 So after 10 years you will have 350 X 10 3500 in interest The total balance will be 5000 3500 8500 With compound interest we use the future value formula FV PV1 rt FV 500010710 983576 The difference is 983576 7 8500 133576 To nd the FV of a lump sum we use FV PV1 r FV 225011019 1376080 FV 931010813 2531970 Fv763551224 16915187 FV 1837961078 31579575 4 ans 7 are 24 To nd the PV of a lump sum we use PvFV1r 13v154511056 1152977 Pv515571119 2015491 PV 886073 11623 2916995 PV 550164 11918 2402409 To answer this question we can use either the FV or the PV formula Both will give the same wer since they are the inverse of each other We will use the FV formula that is FV PV1 r Solving for r we get rFVPV1 71 FV 307 2651 r2 r 307 265 2 41 763 FV 896 3601 0 r 896 360 4 1 1066 FV 162181 390001 r r 16218139000 15 41 997 FV 483500 465231 r r 483500 46523 30 41 812 To answer this question we can use either the FV or the PV formula Both will give the same answer since they are the inverse of each other We will use the FV formula that is FV PV1 r Solving for t we get lnFV PV 1n1 r FV 1284 625108 t 1n1284 625 In 108 936 yrs FV 4341 810107 t 1n4341 810 In 107 2481 yrs FV 402662 18400121 t 1n402662 18400 In 121 1619 yrs FV 173439 21500129 t 1n173439 21500 In 129 820 yrs To answer this question we can use either the FV or the PV formula Both will give the same answer since they are the inverse of each other We will use the FV formula that is FV PV1 r Solving for r we get rFVPV1 71 r 250000 43000 18 4 1 1027 To nd the length of time for money to double triple etc the present value and future value irrelevant as long as the future value is twice the present value for doubling three times as large 25 for tripling etc To answer this question we can use either the FV or the PV formula Both will give the same answer since they are the inverse of each other We will use the FV formula that is FV PV1 r Solving for t we get I lnFV PV ln1 r The length of time to double your money is FV 2 1107 t In 2 In 107 1024 years The length of time to quadruple your money is FV 4 1107 t In 4 In 107 2049 years Notice that the length of time to quadruple your money is twice as long as the time needed to double your money the difference in these answers is due to rounding This is an important concept of time value of money To answer this question we can use either the FV or the PV formula Both will give the same answer since they are the inverse of each other We will use the FV formula that is FV PV1 r Solving for r we get rFVPV1 71 r 28835 21608 5 71 594 To answer this question we can use either the FV or the PV formula Both will give the same answer since they are the inverse of each other We will use the FV formula that is FV PV1 r Solving for t we get I lnFV PV lnl r t In 150000 40000 ln 1055 2469 years To find the PV of a lump sum we use PvFV1r PV 800000000 109520 13025895912 To find the PV of a lump sum we use PvFV1r 26 PV 1M 11080 48819 p t N To nd the FV of a lump sum we use FV PV1 r FV 50105102 724901 13 To answer this question we can use either the FV or the PV formula Both will give the same answer since they are the inverse of each other We will use the FV formula that is FV PV1 r Solving for r we get rFVPV1 71 r 1080000 150 108 71 857 To nd the FV of the rst prize we use FV PV1 r FV 10800001085737 2264213085 p t A To nd the PV of a lump sum we use PvFV1r PV 350000 1260965 010 Chapter 6 1 To solve this problem we must nd the PV of each cash ow and add them To nd the PV of a lump sum we use PvFV1r PV10 1200 110 6001102 8551103 14801104 324001 PV18 1200 118 600 1182 855 1183 1480 1184 273161 PV24 1200 124 6001242 855 1243 14801244 243240 2 To nd the PVA we use the equation PVA C1711 r r 27 At a 5 percent interest rate X5 PVA 40001 7 11059 05 2843129 Y5 PVA 60001 7 11055 05 2597686 And at a 22 percent interest rate X22 PVA 40001 7 11229 22 1514514 Y22 PVA 6000171122522 1718184 Notice that the PV of Cash ow X has a greater PV at a 5 percent interest rate but a lower PV at a 22 percent interest rate The reason is that X has greater total cash ows At a lower interest rate the total cash ow is more important since the cost of waiting the interest rate is not as great At a higher interest rate Y is more valuable since it has larger cash ows At the higher interest rate these bigger cash ows early are more important since the cost of waiting the interest rate is so much greater 28 To solve this problem we must nd the FV of each cash ow and add them To nd the FV of a lump sum we use FV 7 PV1 r FV8 7 8001083 9001082 1000108 4 1100 7 423753 FV11 7 8001113 9001112 1000111 4 1100 7 441299 FV24 7 8001243 9001242 1000124 1100 7 524914 Notice we are nding the value at Year 4 the cash ow at Year 4 is simply added to the FV of the other cash ows In other words we do not need to compound this cash ow To nd the PVA we use the equation PVA C1711 r r PVA15 yrs PVA 36001711101510 2738189 PVA40 yrs PVA 36001711104010 3520458 PVA75 yrs PVA 36001711107510 3597170 To nd the PV of a perpetuity we use the equation PV C r PV 3600 10 3600000 Notice that as the length of the annuity payments increases the present value of the annuity approaches the present value of the perpetuity The present value of the 75 year annuity and the present value of the perpetuity imply that the value today of all perpetuity payments beyond 75 years is only 2830 Here we have the PVA the length of the annuity and the interest rate We want to calculate the annuity payment Using the PVA equation PVA C1711 r r PVA 7 28000 7 C1 4 11076514 0765 We can now solve this equation for the annuity payment Doing so we get C 28000 84145 332758 To nd the PVA we use the equation PVA C1711 r r PVA 7 800001 4 110828 082 7 45626225 29 Here we need to nd the FVA The equation to nd the FVA is FVA C1 r 71r FVA for 20 years 2000110520 7 1 105 12126162 FVA for 40 years 2000110540 7 1 105 101450316 Notice that doubling the number of periods does not double the FVA Here we have the FVA the length of the annuity and the interest rate We want to calculate the annuity payment Using the FVA equation FVAC1 r 71r 80000 C105810 7 1 058 We can now solve this equation for the annuity payment Doing so we get C 80000 1305765 612668 Here we have the PVA the length of the annuity and the interest rate We want to calculate the annuity payment Using the PVA equation PVA C1711 r r 40000 C171109709 We can now solve this equation for the annuity payment Doing so we get C 40000 503295 794762 This cash ow is a perpetuity To nd the PV of a perpetuity we use the equation PV C r PV 15000 08 18750000 Here we need to nd the interest rate that equates the perpetuity cash ows with the PV of the cash ows Using the PV of a perpetuity equation PV C r 195000 15000 r We can now solve for the interest rate as follows r 15000 195000 769 12 30 For discrete compounding to nd the EAR we use the equation EAR 1 APR m39 71 EAR1114471 1146 EAR 1 07 1212 71 723 EAR 1 09 365365 71 942 To nd the EAR with continuous compounding we use the equation EAReq71 EARe391771 1853 Here we are given the EAR and need to nd the APR Using the equation for discrete compounding EAR 1 APR m39 71 We can now solve for the APR Doing so we get APR m1 EAR1 quot 7 1 APR 21081 2 71 EAR 081 1 APR2271 794 EAR 076 1 APR 1212 71 APR 121076 12 71 735 EAR 168 1 APR 5252 71 APR 521168 52 71 1555 Solving the continuous compounding EAR equation EAR eq 41 We get APR 1n1 EAR APR 1n1 262 APR 2327 For discrete compounding to nd the EAR we use the equation EAR 1 APRmm71 So for each bank the EAR is First National EAR 1 122 1212 71 1291 First United EAR 1 124 22 41 1278 31 Notice that the higher APR does not necessarily mean the higher EAR The number of compounding periods within a year will also affect the EAR 15 p t 0 p t W The reported rate is the APR so we need to convert the EAR to an APR as follows EAR 1 APR m39quot 71 APR ml EAR1 quot 7 1 APR 365117 365 71 1570 This is deceptive because the borrower is actually paying annualized interest of 17 per year not the 1570 reported on the loan contract For this problem we simply need to nd the FV of a lump sum using the equation FV PV1 r It is important to note that compounding occurs semiannually To account for this we will diVide the interest rate by two the number of compounding periods in a year and multiply the number ofperiods by two Doing so we get FV 8001 104240 607742 For this problem we simply need to nd the FV of a lump sum using the equation FV PV1 r It is important to note that compounding occurs daily To account for this we will diVide the interest rate by 365 the number of days in a year ignoring leap year and multiply the number ofperiods by 365 Doing so we get FV in 5 years 60001 0713655365 855679 FV in 10 years 60001 07136510365 1220310 FV in 20 years 60001 07136520365 2481930 For this problem we simply need to nd the PV of a lump sum using the equation PVFV1r It is important to note that compounding occurs daily To account for this we will diVide the interest rate by 365 the number of days in a year ignoring leap year and multiply the number ofperiods by 365 Doing so we get PV 24000 1 113656365 1240567 32 19 The APR is simply the interest rate per period times the number of periods in a year In this case the interest rate is 30 percent per month and there are 12 months in a year so we get APR 1230 360 To nd the EAR we use the EAR formula EAR 1 APR mm 71 EAR 1 30 7 1 222981 Chapter 7 Bonds Basic The yield to maturity is the required rate of return on a bond expressed as a nominal annual interest rate For noncallable bonds the yield to maturity and required rate of return are interchangeable terms Unlike YTM and required return the coupon rate is not a return used as the interest rate in bond cash ow valuation but is a xed percentage of par over the life of the bond used to set the coupon payment amount For the example given the coupon rate on the bond is still 10 percent and the YTM is 8 percent Price and yield move in opposite directions if interest rates rise the price of the bond will fall This is because the xed coupon payments determined by the xed coupon rate are not as valuable when interest rates riseihence the price of the bond decreases NOTE Most problems do not explicitly list a par value for bonds Even though a bond can have any par value in general corporate bonds in the United States will have a par value of 1 000 We will use this par value in all problems unless a ali erent par value is explicitly stated 3 The price of any bond is the PV of the interest payment plus the PV of the par value Notice this problem assumes an annual coupon The price of the bond will be P 801 7 11 0610 06 10001 1 0610 114720 We would like to introduce shorthand notation here Rather than write or type as the case may be the entire equation for the PV of a lump sum or the PVA equation it is common to abbreviate the equations as PVIFR 1 1 r which stands for Bresent Xalue lnterest Eactor PVIFAR1 711 r r which stands for Bresent Xalue Interest Eactor of an Annuity 33 These abbreviations are short hand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved We will use this shorthand notation in remainder of the solutions key Here we need to nd the YTM of a bond The equation for the bond price is P 88450 90PVIFAR9 1000PVIFR79 Notice the equation cannot be solved directly for R Using a spreadsheet a nancial calculator or trial and error we nd R YTM 1109 If you are using trial and error to nd the YTM of the bond you might be wondering how to pick an interest rate to start the process First we know the YTM has to be higher than the coupon rate since the bond is a discount bond That still leaves a lot of interest rates to check One way to get a starting point is to use the following equation which will give you an approximation of the YTM Approximate YTM Annual interest payment Price difference from par Years to maturity Price Par value 2 Solving for this problem we get Approximate YTM 90 11550 9 88450 1000 2 1091 This is not the exact YTM but it is close and it will give you a place to start Here we need to nd the coupon rate of the bond All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows P 870 CPVIFA5815 1000PVIF6816 Solving for the coupon payment we get C 5442 The coupon payment is the coupon rate times par value Using this relationship we get Coupon rate 5442 1000 544 To nd the price of this bond we need to realize that the maturity of the bond is 10 years The bond was issued one year ago with 11 years to maturity so there are 10 years left on the bond Also the coupons are semiannual so we need to use the semiannual interest rate and the number of semiannual periods The price of the bond is P 4100PVIFA37720 1000PVIF37720 105583 34 Here we are nding the YTM of a semiannual coupon bond The bond price equation is P 970 43PVIFAR720 1000PVIFR720 Since we cannot solve the equation directly for R using a spreadsheet a nancial calculator or trial and error we nd R 4531 Since the coupon payments are semiannual this is the semiannual interest rate The YTM is the APR ofthe bond so YTM 2 X 4531 906 Here we need to nd the coupon rate of the bond All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows P 1145 CPVIFA375729 1000PVIF375729 Solving for the coupon payment we get C 4579 Since this is the semiannual payment the annual coupon payment is 2 X 4579 9158 And the coupon rate is the coupon rate diVided by par value so Coupon rate 9158 1000 916 35 The approximate relationship between nominal interest rates R real interest rates r and in ation h is R r h Approximate r 06 7045 015 or 150 The Fisher equation which shows the exact relationship between nominal interest rates real interest rates and in ation is 1 R1r1 11 1061r1045 Exactr 7 1 061 045 4 1 7 0144 or 144 The Fisher equation which shows the exact relationship between nominal interest rates real interest rates and in ation is 1 R1 r1 h R 7 1 041 0254 1 7 0660 or 660 The Fisher equation which shows the exact relationship between nominal interest rates real interest rates and in ation is 1 R 1 r1 h h 1 151 09 7 1 0550 or 550 The Fisher equation which shows the exact relationship between nominal interest rates real interest rates and in ation is 1 R1r1 11 V 1 1341045 4 1 7 0852 or 852 This is a bond since the maturity is greater than 10 years The coupon rate located in the rst column ofthe quote is 6125 The bid price is Bid price 11027 110 2732 11084375 gtlt 1000 11084375 The preVious day s ask price is found by Previous day s asked price Today s asked price 7 Change 110 2732 7 71032 111 0532 The preVious day s price in dollars was Previous day s dollar price 11115625 gtlt 1000 11115625 36 Chapter 8 Stocks 1 1 The constant dividend growth model is PDm1gRig So the price of the stock today is P0 D0 1 g R 7g 140 106 12 7 06 2473 The dividend at year 4 is the dividend today times the FVIF for the growth rate in dividends and four years so P3 D3 1 gR7g D0 1 g4R7g 140 106412 4 06 2946 We can do the same thing to nd the dividend in Year 16 which gives us the price in Year 15 so P15 D15 1 g R 7g D0 1 g16 R 7g 140 10616 12 4 06 5927 There is another feature of the constant dividend growth model The stock price grows at the dividend growth rate So if we know the stock price today we can nd the future value for any time in the future we want to calculate the stock price In this problem we want to know the stock price in three years and we have already calculated the stock price today The stock price in three years will be P3 P01g3 24731063 2946 And the stock price in 15 years will be P15 P01g15 247310615 5927 2 We need to find the required return of the stock Using the constant growth model we can solve the equation for R Doing so we find R D1 P0 g 310 4800 05 1146 3 The dividend yield is the dividend next year divided by the current price so the dividend yield is Dividend yield D1 Po 310 4800 646 The capital gains yield or percentage increase in the stock price is the same as the dividend growth rate so 37 Capital gains yield 5 Using the constant growth model we nd the price of the stock today is P0 D1 R 7g 360 13 7 045 4235 The required return of a stock is made up of two parts The diVidend yield and the capital gains yield So the required return of this stock is R DiVidend yield Capital gains yield 039 09 990 We know the stock has a required return of 12 percent and the diVidend and capital gains yield are equal so DiVidend yield l2 12 06 Capital gains yield Now we know both the diVidend yield and capital gains yield The diVidend is simply the stock price times the diVidend yield so D1 0670 420 This is the diVidend next year The question asks for the diVidend this year Using the relationship between the diVidend this year and the diVidend next year D1 D01 g We can solve for the diVidend that was just paid D1 420106 Do 420 106 396 The price of any nancial instrument is the PV of the future cash ows The future diVidends of this stock are an annuity for eight years so the price of the stock is the PVA which will be P0 1200PVIFA108 6402 The price a share of preferred stock is the diVidend diVided by the required return This is the same equation as the constant growth model with a diVidend growth rate of zero percent Remember most preferred stock pays a fixed diVidend so the growth rate is zero Using this equation we find the price per share of the preferred stock is R DPo 825113 730 Intermediate This stock has a constant growth rate of diVidends but the required return changes twice To find the value of the stock today we will begin by finding the price of the stock at Year 6 C p t N 38 when both the dividend growth rate and the required return are stable forever The price of the stock in Year 6 will be the dividend in Year 7 divided by the required return minus the growth rate in dividends So P6 D6 1 gR7g D0 1 g7R7g 300 105711 7 05 7036 Now we can nd the price of the stock in Year 3 We need to nd the price here since the required return changes at that time The price of the stock in Year 3 is the PV of the dividends in Years 4 5 and 6 plus the PV of the stock price in Year 6 The price of the stock in Year 3 is P3 30010504 114 300105051142 30010561143 7036 1143 P3 5635 Finally we can nd the price of the stock today The price today will be the PV of the dividends in Years 1 2 and 3 plus the PV of the stock in Year 3 The price of the stock today is P0 3001050 116 30010502 1162 30010503 1163 5635 116 4350 Here we have a stock that pays no dividends for 10 years Once the stock begins paying dividends it will have a constant growth rate of dividends We can use the constant growth model at that point It is important to remember that general constant dividend growth formula is Psz1g1Reg This means that since we will use the dividend in Year 10 we will be nding the stock price in Year 9 The dividend growth model is similar to the PVA and the PV of a perpetuity The equation gives you the PV one period before the rst payment So the price of the stock in Year 9 will be P9 D10 R 7g 800 13 7 06 11429 The price of the stock today is simply the PV of the stock price in the future We simply discount the future stock price at the required return The price of the stock today will be P0 114291139 3804 The price of a stock is the PV of the future dividends This stock is paying four dividends so the price of the stock is the PV of these dividends using the required return The price of the stock is P0 12111151112181113 211114 4998 With supemormal dividends we nd the price of the stock when the dividends level off at a constant growth rate and then nd the PV of the future stock price plus the PV of all 39 dividends during the supernormal growth period The stock begins constant growth in Year 4 so we can nd the price of the stock in Year 3 one year before the constant dividend growth begins as P4 D4 1 g R 7g 200105 13 7 05 2625 The price of the stock today is the PV of the rst three dividends plus the PV of the Year 3 stock price So the price ofthe stock today will be P0 800 113 600 1132 3001133 2625 1133 3118 13 With supernormal dividends we nd the price of the stock when the dividends level off at a constant growth rate and then nd the PV of the futuresstock price plus the PV of all dividends during the supernormal growth period The stock begins constant growth in Year 4 so we can nd the price of the stock in Year 3 one year before the constant dividend growth begins as P3 D3 1 g R 7g D0 1 g13 1 g2 R 7g 2801253107 13 7 07 9753 The price of the stock today is the PV of the rst three dividends plus the PV of the Year 3 stock price The price of the stock today will be P0 7 280125 113 28012521132 28012531133 97531133 P0 7790 Chapter 9 Capital Budgeting Basic 1 To calculate the payback period we need to nd the time that the project has recovered its initial investment After two years the project has created 1200 2500 3700 in cash ows The project still needs to create another 4800 7 3700 1100 in cash ows During the third year the cash ows from the project will be 3400 So the payback period will be 2 years plus what we still need to make divided by what we will make during the third year The payback period is Payback 2 1100 3400 232 years 40 To calculate the payback period we need to nd the time that the project has recovered its initial investment The cash ows in this problem are an annuity so the calculation is simpler If the initial cost is 3000 the payback period is Payback 3 480 840 357 years There is a shortcut to calculate the future cash ows are an annuity Just divide the initial cost by the annual cash ow For the 3000 cost the payback period is Payback 3000 840 357 years For an initial cost of 5000 the payback period is Payback 5 800 840 595 years The payback period for an initial cost of 7000 is a little trickier Notice that the total cash in ows after eight years will be Total cash in ows 8840 6720 If the initial cost is 7000 the project never pays back Notice that if you use the shortcut for annuity cash ows you get Payback 7000 840 833 years This answer does not make sense since the cash ows stop after eight years so again we must conclude the payback period is never Project A has cash ows of Cash ows 30000 18000 48000 during this first two years The cash ows are still short by 2000 of recapturing the initial investment so the payback for Project A is Payback 2 2000 10000 220 years Project B has cash ows of Cash ows 9000 25000 35000 69000 during this first two years The cash ows are still short by 1000 of recapturing the initial investment so the payback for Project B is B Payback 3 1000 425000 3002 years Using the payback criterion and a cutoff of 3 years accept project A and reject project B 41 When we use discounted payback we need to nd the value of all cash ows today The value today of the project cash ows for the rst four years is Value today of Year 1 cash ow 70001 14 614035 Value today of Year 2 cash ow 75001142 577101 Value today of Year 3 cash ow 80001143 539977 Value today of Year 4 cash ow 85001144 503268 To nd the discounted payback we use these values to nd the payback period The discounted rst year cash ow is 614035 so the discounted payback for an 8000 initial cost is Discounted payback 1 8000 7 614035577101 132 years For an initial cost of 13000 the discounted payback is Discounted payback 2 13000 7 614035 7 577101539977 220 years Notice the calculation of discounted payback We know the payback period is between two and three years so we subtract the discounted values of the Year 1 and Year 2 cash ows from the initial cost This is the numerator which is the discounted amount we still need to make to recover our initial investment We divide this amount by the discounted amount we will earn in Year 3 to get the fractional portion of the discounted payback If the initial cost is 18000 the discounted payback is Discounted payback 3 18000 7 614035 7 5771017 539977 503268 314 years R 0 4 1600 2100 476 years discounted payback regular payback 476 years R 7 5 2100105 21001052 21001053 21001054 21001055 7 909190 21001056 7 156705 discounted payback 5 10000 7 909190 156705 558 years R152100115 21001152 21001153 21001154 21001155 21001156 794741 The project never pays back Our de nition of AAR is the average net income divided by the average book value The average net income for this project is Average net income 1416000 1868000 1562000 985000 4 1457750 And the average book value is Average book value 15M 0 2 75M So the AAR for this project is AAR Average net income Average book value 1457750 7500000 1944 42 The IRR is the interest rate that makes the NPV of the project equal to zero So the equation that de nes the IRR for this project is 0 7 7 30000 200001IRR 140001IRR2 1 100011RR3 Using a spreadsheet nancial calculator or trial and error to nd the root of the equation we nd that IRR 2648 Since the IRR is greater than the required return we would accept the project The NPV of a project is the PV of the out ows minus by the PV of the in ows The equation for the NPV of this project at an 11 percent required return is NPV 7 30000 20000111 140001112 110001113 742384 At an 11 percent required return the NPV is positive so we would accept the project The equation for the NPV of the project at a 30 percent required return is NPV 7 30000 20000130 140001302 110001303 7 132453 At a 30 percent required return the NPV is negative so we would reject the project The NPV of a project is the PV of the out ows minus by the PV of the in ows Since the cash in ows are an annuity the equation for the NPV of this project at an 8 percent required return 1s NPV 7 70000 14000PVIFA3 9 1745643 At an 8 percent required return the NPV is positive so we would accept the project The equation for the NPV of the project at a 16 percent required return is NPV 7 70000 14000PVIFA15 9 7550839 At a 16 percent required return the NPV is negative so we would reject the project We would be indifferent to the project if the required return was equal to the IRR of the project since at that required return the NPV is zero The IRR of the project is 0 7 40000 14000PVIFA1RR 9 IRR 1370 The IRR is the interest rate that makes the NPV of the project equal to zero So the equation that de nes the IRR for this project is 12 43 0 7 7 8000 32001IRR 400011RR2 61001IRR3 Using a spreadsheet nancial calculator or trial and error to nd the root of the equation we nd that IRR 2683 The NPV of a project is the PV of the out ows minus by the PV of the in ows At a zero discount rate and only at a zero discount rate the cash ows can be added together across time So the NPV of the project at a zero percent required return is NPV 7 8000 3200 4000 6100 5300 The NPV at a 10 percent required return is 7 8000 3200ll 4000ll2 279790 NPV 7 6100113 7 The NPV at a 20 percent required return is NPV 7 8000 3200l2 4000l22 6100l23 97454 And the NPV at a 30 percent required return is NPV 7 8000 3200l3 4000l32 6100l33 7 39508 Notice that as the required return increases the NPV of the project decreases This will always be true for projects with conventional cash ows Conventional cash ows are negative at the beginning of the project and positive throughout the rest of the project a The IRR is the interest rate that makes the NPV of the project equal to zero The equation for the IRR of Project A is 0 7 734000 165001IRR 1400011RR2 1000011RR3 60001IRR4 Using a spreadsheet nancial calculator or trial and error to nd the root of the equation we nd that IRR 1660 The equation for the IRR of Project B is 0 734000 50001IRR 100001IRR2 180001IRR3 190001IRR4 Using a spreadsheet nancial calculator or trial and error to nd the root of the equation we nd that IRR 1572 44 Examining the IRRs of the projects we see that the IRRA is greater than the IRRB so IRR decision rule implies accepting project A This may not be a correct decision however because the IRR criterion has a ranking problem for mutually exclusive projects To see if the IRR decision rule is correct or not we need to evaluate the project NPVs b The NPV of Project A is NPVA 734000 16500111 140001112 100001113 60001114 NPVA 349188 And the NPV of Project B is NPVB 734000 5000111 100001112 180001113 190001114 NPVB 429806 The NPVB is greater than the NPVA so we should accept Project B c To nd the crossover rate we subtract the cash ows from one project from the cash ows of the other project Here we will subtract the cash ows for Project B from the cash ows of Project A Once we nd these differential cash ows we nd the IRR The equation for the crossover rate is Crossover rate 0 115001R 40001R2 7 80001R3 7 130001R4 Using a spreadsheet nancial calculator or trial and error to nd the root of the equation we nd that R 1375 At discount rates above 1375 choose project A for discount rates below 1375 choose project B indifferent between A and B at a discount rate of 1375 13 The IRR is the interest rate that makes the NPV of the project equal to zero The equation to calculate the IRR of Project X is 0 75000 27001IRR 170011RR2 230011RR3 Using a spreadsheet nancial calculator or trial and error to nd the root of the equation we nd that IRR 1682 For Project Y the equation to nd the IRR is 0 75000 23001IRR 18001IRR2 27001IRR3 Using a spreadsheet nancial calculator or trial and error to nd the root of the equation we nd that IRR 1660 45 To nd the crossover rate we subtract the cash ows from one project from the cash ows of the other project and nd the IRR of the differential cash ows We will subtract the cash ows from Project Y from the cash ows from Project X It is irrelevant which cash ows we subtract from the other Subtracting the cash ows the equation to calculate the IRR for these differential cash ows is Crossover rate 0 4001R 7 1001R2 7 4001R3 Using a spreadsheet nancial calculator or trial and error to nd the root of the equation we nd that R 1328 The table below shows the NPV of each project for different required returns Notice that Project Y always has a higher NPV for discount rates below 1328 percent and always has a lower NPV for discount rates above 1328 percent 3 erX ME 0 170000 180000 5 110021 115549 10 58753 60706 15 14556 13635 20 23843 27083 25 57440 62560 a The equation for the NPV of the project is NPV 7 28M 53M117 8M112 1357024793 The NPV is greater than 0 so we would accept the project b The equation for the IRR of the project is 0 728M 53M1IRR 7 8M1IRR2 From Descartes rule of signs we know there are two IRRs since the cash ows change signs twice From trial and error the two IRRs are IRR 7275 78346 When there are multiple IRRs the IRR decision rule is ambiguous Both IRRs are correct that is both interest rates make the NPV of the project equal to zero If we are evaluating whether or not to accept this project we would not want to use the IRR to make our decision 15 The pro tability index is de ned as the PV of the cash in ows divided by the PV of the cash out ows The equation for the pro tability index at a required return of 10 percent is 46 PI320011 3900112 2600113 7000 1155 The equation for the pro tability index at a required return of 15 percent is PI 3200115 39001152 26001153 7000 1063 The equation for the pro tability index at a required return of 22 percent is PI 3200122 39001222 26001223 7000 0954 We would accept the project if the required return were 10 percent or 15 percent since the PI is greater than one We would reject the project if the required return were 22 percent since the PI is less than one a The pro tability index is the PV of the future cash ows diVided by the initial investment The cash ows for both projects are an annuity so PII 15000PVIFA103 30000 1243 P111 2800PVIFA1073 5000 1393 The pro tability index decision rule implies that we accept project 11 since P111 is greater than the P11 b The NPV of each project is NPV1 7 30000 15000PVIFA103 730278 NPVH 7 5000 2800PVIFA103 196319 The NPV decision rule implies accepting Project 1 since the NPVI is greater than the NPVH c Using the pro tability index to compare mutually exclusive projects can be ambiguous when the magnitude of the cash ows for the two projects are of different scale In this problem project I is roughly 3 times as large as project 11 and produces a larger NPV yet the pro tability index criterion implies that project 11 is more acceptable 47 CHAPTER 10 Capital Budgeting Cash ow Analysis 2 Sales due solely to the new product line are 2100012000 252000000 Increased sales of the motor home line occur because of the new product line introduction thus 500045000 225000000 in new sales is relevant Erosion of luxury motor coach sales is also due to the new midsize campers thus 130085000 110500000 loss in sales is relevant The net sales gure to use in evaluating the new line is thus 252000000 225000000 7 110500000 366500000 3 We need to construct a basic income statement The income statement is 4 To nd the OCF we need to complete the income statement as follows Sales 650000 Variable costs 390000 Fixed costs 158000 Depreciation 75 000 27000 Taxes35 9 450 Netincome 17 550 Sales 912400 Costs 593600 Depreciation 135 000 183800 Taxes34 62 492 Netincome 121308 The OCF for the company is OCF EBIT Depreciation 7 Taxes OCF 183800 135000 7 62492 OCF 256308 The depreciation tax shield is the depreciation times the tax rate so Depreciation tax shield thepreciation Depreciation tax shield 34135000 Depreciation tax shield 45900 48 The depreciation tax shield shows us the increase in OCF by being able to expense depreciation 5 To calculate the OCF we rst need to calculate net income The income statement is Using the most common nancial calculation for OCF we get OCF EBIT Depreciation 7 Taxes 39000 3000 7 13650 Sales 85000 Variable costs 43000 Depreciation 3 000 39000 Taxes35 13 650 Net income 25 350 OCF 28350 The topdown approach to calculating OCF yields OCF Sales 7 Costs 7 Taxes 85000 7 43000 713650 OCF 28350 49 7 50 The taXshield approach is OCF Sales 7 Costs1 7 tc thepreciation OCF 85000 7 430001 7 35 353000 OCF 28350 And the bottomup approach is OCF Net income Depreciation 25350 3000 OCF 28350 All four methods of calculating OCF should always give the same answer The MACRS depreciation schedule is shown in Table 107 The ending book value for any year is the beginning book value minus the depreciation for the year Remember to nd the amount of depreciation for any year you multiply the purchase price of the asset times the MACRS percentage for the year The depreciation schedule for this asset is Be ginning Book Year Value MACRS Depreciation Ending Book value 1 84700000 01429 12103630 72596370 2 72596370 02449 20743030 51853340 3 51853340 01749 14814030 37039310 4 37039310 01249 10579030 26460280 5 26460280 00893 7563710 18896570 6 18896570 00893 7563710 11332860 7 11332860 00893 7563710 3769150 8 3769150 00445 3769150 0 The asset has an 8 year useful life and we want to nd the BV of the asset after 5 years With straightline depreciation the depreciation each year will be Annual depreciation 440000 8 Annual depreciation 55000 So after ve years the accumulated depreciation will be Accumulated depreciation 555000 Accumulated depreciation 275000 The book value at the end of year ve is thus BV5 440000 7 275000 BV5 165000 51 The asset is sold at a loss to book value so the depreciation taX shield of the loss is recaptured AftertaX salvage value 55000 165000 7 55000035 AftertaX salvage value 93500 To nd the taxes on salvage value remember to use the equation Taxes on salvage value BV 7 MVtC This equation will always give the correct sign for a taX in ow refund or out ow payment To nd the EV at the end of four years we need to nd the accumulated depreciation for the rst four years We could calculate a table as in Problem 6 but an easier way is to add the MACRS depreciation amounts for each of the rst four years and multiply this percentage times the cost of the asset We can then subtract this from the asset cost Doing so we get BV4 93M 7 93M02000 03200 01920 01152 BV4 1607040 The asset is sold at a gain to book value so this gain is taxable AftertaX salvage value 2100000 1607040 7 210000035 AftertaX salvage value 1927464 Using the taX shield approach to calculating OCF Remember the approach is irrelevant the nal answer will be the same no matter which of the four methods you use we get OCF Sales 7 Costs1 7 tc thepreciation OCF 24M 7 960K17 035 03527M3 OCF 1251000 Since we have the OCF we can nd the NPV as the initial cash outlay plus the PV of the OCFs which are an annuity so the NPV is NPV 727M 1251000PVIFA1573 NPV 15631462 The cash out ow at the beginning of the project will increase because of the spending on NWC At the end of the project the company will recover the NWC so it will be a cash in ow The sale of the equipment will result in a cash in ow but we also must account for the taxes which will be paid on this sale So the cash ows for each year of the project will be M Cash Flow 0 7 727M 7 300K 3000000 1 1251000 2 1251000 3 1687500 1251000 300000 210000 0 7 21000035 N 4 52 And the NPV of the project is NPV 73000000 1251000500PVIFA1572 1687500 1153 NPV 14332046 First we will calculate the annual depreciation for the equipment necessary for the project The depreciation amount each year will be Year 1 depreciation 27M03333 899910 Year 2 depreciation 27M04444 1199880 Year 3 depreciation 27M0 1482 400140 So the book value of the equipment at the end of three years which will be the initial investment minus the accumulated depreciation is Book value in 3 years 27M 7 899910 1199880 400140 Book value in 3 years 200070 The asset is sold at a gain to book value so this gain is taxable AftertaX salvage value 210000 200070 7 210000035 AftertaX salvage value 206525 To calculate the OCF we will use the taX shield approach so the cash ow each year is OCF Sales 7 Costs1 7 tc thepreciation Year Cash Flow 0 7 727M 7 300K 3000000 1 12509685 144000065 035899910 0 2 13559580 144000065 0351199880 0 3 15825735 144000065 035400140 206525 0 00000 Remember to include the NWC cost in Year 0 and the recovery of the NWC at the end of the project The NPV of the project with these assumptions is NPV 7 7 30M 1250968501 15 13559581152 1582573501153 NPV 7 15366552 First we will calculate the annual depreciation of the new equipment It will be Annual depreciation 390000 5 Annual depreciation 78000 53 Now we calculate the aftertaX salvage value The aftertaX salvage value is the market price minus or plus the taxes on the sale of the equipment so AftertaX salvage value MV BV 7 MVtC 5 54 Very often the book value of the equipment is zero as it is in this case If the book value is zero the equation for the aftertaX salvage value becomes AftertaX salvage value MV 0 7 MVtc AftertaX salvage value MVl 7 tc We will use this equation to nd the aftertaX salvage value since we know the book value is zero So the aftertaX salvage value is AftertaX salvage value 60000l 7 034 AftertaX salvage value 39600 Using the taX shield approach we nd the OCF for the project is OCF 120000l 7 034 03478000 OCF 105720 Now we can nd the project NPV Notice we include the NWC in the initial cash outlay The recovery of the NWC occurs in Year 5 along with the aftertaX salvage value NPV 7 7390000 7 28000 105720Pv1FA105 39600 28000 115 NPV 7 2473626 First we will calculate the annual depreciation of the new equipment It will be Annual depreciation charge 925000 5 Annual depreciation charge 185000 The aftertaX salvage value of the equipment is AftertaX salvage value 90000l 7 035 AftertaX salvage value 58500 Using the taX shield approach the OCF is OCF 360000l 7 035 035l85000 OCF 298750 Now we can nd the project IRR There is an unusual feature that is a part of this project Accepting this project means that we will reduce NWC This reduction in NWC is a cash in ow at Year 0 This reduction in NWC implies that when the project ends we will have to increase NWC So at the end of the project we will have a cash out ow to restore the NWC to its level before the project We also must include the aftertaX salvage value at the end of the project The IRR ofthe project is NPV 7 0 7 7925000 125000 298750PVIFAIRR5 58500 7 125000 1IRR5 IRR 2385 18 55 To nd the bid price we need to calculate all other cash ows for the project and then solve for the bid price The aftertaX salvage value of the equipment is AftertaX salvage value 50000l 7 035 32500 Now we can solve for the necessary OCF that will give the project a zero NPV The equation for the NPV ofthe project is NPV 0 7 780000 7 75000 OCFPVIFA155 75000 32500 1165 Solving for the OCF we nd the OCF that makes the project NPV equal to zero is OCF 80381785 PVIFA155 24549351 The easiest way to calculate the bid price is the taX shield approach so OCF 24549351 P 7 vQ 7 FC17tc th 24549351 P 7 850150000 7 240000 1 7 035 0357800005 P 1206 Intermediate First we will calculate the depreciation each year which will be D1 48000002000 96000 D2 48000003200 153600 D3 4800000l920 92160 D4 4800000ll52 55296 2 C 56 The book value of the equipment at the end of the project is BV4 480000 7 96000 153600 92160 55296 82944 The asset is sold at a loss to book value so this creates a taX refund Aftertax salvage value 70000 82944 7 70000035 7453040 So the OCF for each year will be OCF1 16000017 035 03596000 13760000 OCFz 16000017 035 035153600 15776000 OCF3 16000017 035 03592160 13625600 OCF4 16000017 035 03555296 12335360 Now we have all the necessary information to calculate the project NPV We need to be careful with the NWC in this project Notice the project requires 20000 of NWC at the beginning and 3000 more in NWC each successive year We will subtract the 20000 from the initial cash ow and subtract 3000 each year from the OCF to account for this spending In Year 4 we will add back the total spent on NWC which is 29000 The 3000 spent on NWC capital during Year 4 is irrelevant Why Well during this year the project required an additional 3000 but we would get the money back immediately So the net cash ow for additional NWC would be zero With all this the equation for the NPV of the project is NPV 7 480000 7 20000 137600 7 30001 14 157760 7 30001142 136256 7 30001143 12335360 29000 74530401144 73856948 NPV 7 If we are trying to decide between two projects that will not be replaced when they wear out the proper capital budgeting method to use is NPV Both projects only have costs associated with them not sales so we will use these to calculate the NPV of each project Using the taX shield approach to calculate the OCF the NPV of System A is OCFA 7l200001 7 034 0344300004 OCFA 742650 NPVA 7 7430000 7 42650PVIFA2074 NPVA 7 754040953 And the NPV of System B is OCFB 7 7800001 7 034 0345400006 OCFB 7 722200 NPVB 7 7540000 7 22200PVIFA2076 NPVB 7 761382632 If the system will not be replaced when it wears out then System A should be chosen because it has the more positive NPV 57 21 If the equipment will be replaced at the end of its useful life the correct capital budgeting technique is EAC Using the NPVs we calculated in the previous problem the EAC for each system is EACA 4 54040953 PVIFA204 EACA 20875432 EACB 4 61382632 PVIFAms EACB 18458110 If the conveyor belt system will be continually replaced we should choose System B since it has the more positive NPV CHAPTER 15 Cost of Capital 1 With the information given we can nd the cost of equity using the dividend growth model Using this model the cost of equity is RE 24510645 06 1177 or 1177 2 Here we have information to calculate the cost of equity using the CAPM The cost of equity is RE 045 130 12 7 045 1425 or 1425 3 We have the information available to calculate the cost of equity using the CAPM and the dividend growth model Using the CAPM we find RE 04 11508 1320 or 1320 58 And using the dividend growth model the cost of equity is RE 18010534 05 1056 or 1056 Both estimates of the cost of equity seem reasonable If we remember the historical return on large capitalization stocks the estimate from the CAPM model is about one percent higher than average and the estimate from the dividend growth model is about one percent lower than the historical average so we cannot de nitively say one of the estimates is incorrect Given this we will use the average of the two so RE 1320 10562 1188 or 1188 To use the dividend growth model we rst need to nd the growth rate in dividends So the increase in dividends each year was g1 9177878 1667 or 1667 g2 93 7 9191 0220 or 220 g3 100 7 9393 0753 or 753 g4 122 7100100 2200 or 2200 So the average arithmetic growth rate in dividends was g 1667 0220 0753 22004 1210 or 1210 Using this growth rate in the dividend growth model we nd the cost of equity is RE 122112104500 1210 1514 or 1514 Calculating the geometric growth rate in dividends we nd 122 7 0781 g4 g1183 or 1183 The cost of equity using the geometric dividend growth rate is RE 122111834500 1183 1486 The cost of preferred stock is the dividend payment divided by the price so Rp 692 0652 or 652 The pretax cost of debt is the YTM of the company s bonds so P0 1050 40PVIFAR724 1000PVIFR724 R 3683 YTM 2 X 3683 737 And the aftertaX cost of debt is RD 07371 7 35 0479 or 479 59 7 8 60 a The pretax cost of debt is the YTM of the company s bonds so P0 7 1080 7 50PVIFAR746 1000Pv1FR46 R 458 YTM 2 X 458 916 b The aftertaX cost of debt is RD 09161 7 35 0595 or 595 c The aftertax rate is more relevant because that is the actual cost to the company The book value of debt is the total par value of all outstanding debt so BVD 20M 80M 100M To nd the market value of debt we nd 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 nd MVD 10820M 5880M 68M The YTM of the zero coupon bonds is P2 7 580 7 1000PVIFR77 R 7 809 So the aftertaX cost of the zero coupon bonds is Rz 08091 7 35 0526 or 526 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 RD 059521668 052646468 0548 or 548 a Using the equation to calculate the WACC we nd WACC 501605075 45091 735 1101 or 1101 b Since interest is taX deductible and dividends are not we must look at the aftertax cost of debt w 39c is 091735 0585 or 585 Hence on an aftertax basis debt is cheaper than the preferred stock 10 61 Here we need to use the debtequity ratio to calculate the WACC Doing so we nd WACC 181160 10601601 7 35 1369 or 1369 Here we have the WACC and need to nd the debtequity ratio of the company Setting up the WACC equation we nd WACC 1150 16EV085DV1735 Rearranging the equation we nd 115VE 16 08565DE Now we must realize that the V E is just the equity multiplier which is equal to VE 1 DE 115DE 1 16 05525DE Now we can solve for DE as 05975DE 0450 DE 7531 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 BVE 95M5 475M BVD 75M 60M 135M So the total value of the company is V 475M 135M 1825M And the book value weights of equity and debt are EV 4751825 2603 DV 1 iEV 7397 62 b The market value of equity is the share price times the number of shares so MVE 95M53 5035M Using the relationship that the total market value of debt is the price quote times the par value of the bond we nd the market value of debt is MVD 9375M 96560M 12765M This makes the total market value of the company V 5035 12765M 63115 And the market value weights of equity and debt are EV 503563115 7978 DV 1 iEV 2022 c The market value weights are more relevant 15 We will begin by nding the market value of each type of nancing We nd MvD 40001000103 412M MVE 9000057 513M MVP 13000104 1352M And the total market value of the rm is V 412M 513M 1352M 10602M Now we can nd the cost of equity using the CAPM The cost of equity is RE 06 11008 1480 or 1480 The cost of debt is the YTM ofthe bonds so P0 1030 35PVIFAR40 1000PVIFR740 R 336 YTM 336 X 2 672 And the aftertaX cost of debt is RD l 7 350672 0437 or 437 The cost of preferred stock is Rp 6104 0577 or 577 63 Now we have all of the components to calculate the WACC The WACC is WACC 043741210602 l48051310602 0577135210602 960 Notice that we didn t include the 1 7 tc term in the WACC equation We simply used the aftertaX cost of debt in the equation so the term is not needed here a We will begin by nding the market value of each type of nancing We nd MVD 1200001000093 1116M MVE 9M34 306M MVP 50000083 415M And the total market value of the rm is V 1116M 306M 415M 4591M So the market value weights of the company s nancing is DV 1116M4591M 2431 PV 415M4591M 0904 EN 306M4591M 6665 For projects equally as risky as the rm itself the WACC should be used as the discount rate First we can nd the cost of equity using the CAPM The cost of equity is RE 05 12010 1700 or 1700 The cost of debt is the YTM of the bonds so P0 930 425PVIFARW30 1000PVIFR730 R 469 YTM 469 X 2 938 And the aftertaX cost of debt is RD 1 7 350938 0610 or 610 The cost of preferred stock is RP 783 0843 or 843 Now we can calculate the WACC as WACC 17006665 08430904 0610 2431 1358 2 O C 64 a Projects X Y and Z b Using the CAPM to consider the projects we need to calculate the expected return of the project given its level of risk This eXpected return should then be compared to the eXpected return of the project If the return calculated using the CAPM is higher than the project eXpected return we should accept the project if not we reject the project After considering risk via the CAPM EW 7 05 6012 7 05 EX 7 05 9012 7 05 EY 05 12012 7 05 EZ 05 17012 7 05 0920 lt 11 so accept W 1130 lt 13 so accept X 1340 lt 14 so accept Y 1690 gt 16 so reject Z 0 Project W would be incorrectly rejected Project Z would be incorrectly accepted a He should look at the weighted average otation cost not just the debt cost b The weighted average oatation cost is the weighted average of the oatation costs for debt and equity so fT 04919 10119 072 or 720 c The total cost of the equipment including oatation costs is Amount raised1 7 072 15M Amount raised 15M1 7 072 16156463 Even if the speci c funds are actually being raised completely from debt the otation costs and hence true investment cost should be valued as if the rm s target capital structure is used We rst need to nd the weighted average oatation cost Doing so we nd fT 6011 1007 3004 085 or 85 And the total cost of the equipment including oatation costs is Amount raised1 7 08500 25M Amount raised 25M1 7 0850 27322404 Intermediate Using the debtequity ratio to calculate the WACC we nd WACC 7 65165055 116515 7 1126 or 1126 Since the project is riskier than the company we need to adjust the project discount rate for the additional risk Using the subjective risk factor given we nd Project discount rate 1126 200 1326

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