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# Cost of Capital Learning

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• 1. 1The Costof CapitalFor Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 2. Learning Goals• Sources of capital• Cost of each type of funding• Calculation of the weighted average cost of capital(WACC)• Construction and use of the marginal cost of capitalschedule (MCC)2For Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 3. Factors Affecting the Cost of Capital• General Economic Conditions– Affect interest rates• Market Conditions– Affect risk premiums• Operating Decisions– Affect business risk• Financial Decisions– Affect financial risk• Amount of Financing– Affect flotation costs and market price ofsecurity3For Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 4. • Compute the cost of each source of capital• Determine percentage of each source ofcapital in the optimal capital structure• Calculate Weighted Average Cost of Capital(WACC)4Weighted Cost of Capital ModelFor Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 5. • Required rate of return for creditors• Same cost found in Chapter 12 as yield to maturityon bonds (kd).• e.g. Suppose that a company issues bonds with abefore tax cost of 10%.• Since interest payments are tax deductible, the truecost of the debt is the after tax cost.• If the company’s tax rate (state and federalcombined) is 40%, the after tax cost of debt• AT kd = 10%(1-.4) = 6%.51. Compute Cost of Debt1. Compute Cost of DebtFor Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 6. • Cost to raise a dollar of preferred stock.611.90%\$5.00\$42.00kp = =The cost of preferred stock:Example: You can issue preferred stock for anetprice of \$42 and the preferred stock pays a\$5 dividend.Dividend (Dp)Market Price (PP) - FRequired rate kp =2. Compute Cost Preferred Stock2. Compute Cost Preferred Stock
• 7. • Two Types of Common Equity Financing– Retained Earnings (internal commonequity)– Issuing new shares of common stock(external common equity)73. Compute Cost of Common3. Compute Cost of CommonEquityEquityFor Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 8. • Cost of Internal Common Equity– Management should retain earnings onlyif they earn as much as stockholder’snext best investment opportunity of thesame risk.– Cost of Internal Equity = opportunitycost of common stockholders’ funds.– Two methods to determine• Dividend Growth Model• Capital Asset Pricing Model83. Compute Cost of Common Equity3. Compute Cost of Common Equity
• 9. • Cost of Internal Common Stock Equity– Dividend Growth Model9D1P0kS = + g3. Compute Cost of Common Equity3. Compute Cost of Common Equity
• 10. • Cost of Internal Common Stock Equity– Dividend Growth Model10Example:The market price of a share of common stock is\$60. The dividend just paid is \$3, and the expectedgrowth rate is 10%.3. Compute Cost of Common Equity3. Compute Cost of Common EquityD1P0kS = + g
• 11. • Cost of Internal Common Stock Equity– Dividend Growth Model113(1+0.10)60kS = + .10 =.155 = 15.5%Example:The market price of a share of common stock is \$60.The dividend just paid is \$3, and the expected growthrate is 10%.3. Compute Cost of Common Equity3. Compute Cost of Common EquityD1P0kS = + g
• 12. • Cost of Internal Common Stock Equity– Capital Asset Pricing Model (Chapter 7)12kS = kRF + β(kM – kRF)3. Compute Cost of Common Equity3. Compute Cost of Common EquityFor Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 13. • Cost of Internal Common Stock Equity– Capital Asset Pricing Model (Chapter 7)13Example:The estimated Beta of a stock is 1.2. The risk-free rateis 5% and the expected market return is 13%.3. Compute Cost of Common Equity3. Compute Cost of Common EquitykS = kRF + β(kM – kRF)
• 14. • Cost of Internal Common Stock Equity– Capital Asset Pricing Model (Chapter 7)14kS = 5% + 1.2(13% – 5%) 14.6%3. Compute Cost of Common Equity3. Compute Cost of Common Equity=Example:Example:The estimated Beta of a stock is 1.2. The risk-free rateis 5% and the expected market return is 13%.kS = kRF + β(kM – kRF)
• 15. • Cost of New Common Stock– Must adjust the Dividend Growth Model equation forfloatation costs of the new common shares.153. Compute Cost of Common Equity3. Compute Cost of Common EquityD1P0 - Fkn = + g
• 16. • Cost of New Common Stock– Must adjust the Dividend Growth Model equationfor floatation costs of the new common shares.163. Compute Cost of Common Equity3. Compute Cost of Common EquityExample:If additional shares are issued floatation costswill be 12%. D0 = \$3.00 and estimated growthis 10%, Price is \$60 as before.D1P0 - Fkn = + g
• 17. • Cost of New Common Stock– Must adjust the Dividend Growth Model equation forfloatation costs of the new common shares.173. Compute Cost of Common Equity3. Compute Cost of Common Equity3(1+0.10)52.80kn = + .10 = .1625 =D1P0 - Fkn = + g16.25%Example:Example:If additional shares are issued floatation costs willbe 12%. D0 = \$3.00 and estimated growth is 10%,Price is \$60 as before.
• 18. 18Weighted Average Cost of CapitalWeighted Average Cost of CapitalGallagher Corporation estimates the followingcosts for each component in its capital structure:Gallagher’s tax rate is 40%Source of Capital CostBonds kd = 10%Preferred Stock kp = 11.9%Common StockRetained Earnings ks = 15%New Shares kn = 16.25%
• 19. 19Weighted Average Cost of CapitalWeighted Average Cost of Capital If using retained earnings to finance thecommon stock portion the capital structure:WACC= ka= (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)For Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 20. 20If using retained earnings to finance thecommon stock portion the capital structure:Weighted Average Cost of CapitalWeighted Average Cost of Capital Assume that Gallagher’s desired capitalstructure is 40% debt, 10% preferred and50% common equity.WACC= ka= (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)
• 21. 21Weighted Average Cost of CapitalWeighted Average Cost of CapitalWACC = .40 x 10% (1-.4) + .10 x 11.9%+ .50 x 15% = 11.09%11.09%WACC= ka= (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)If using retained earnings to finance thecommon stock portion the capital structure: Assume that Gallagher’s desired capitalstructure is 40% debt, 10% preferred and50% common equity.
• 22. 22If using a new equity issue to finance thecommon stock portion the capital structure:Weighted Average Cost of CapitalWeighted Average Cost of CapitalWACC= ka= (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)For Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 23. 23Weighted Average Cost of CapitalWeighted Average Cost of CapitalWACC = .40 x 10% (1-.4) + .10 x 11.9%+ .50 x 16.25% = 11.72%11.72%If using a new equity issue to finance thecommon stock portion the capital structure:WACC= ka= (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)For Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 24. Marginal Cost of CapitalMarginal Cost of Capital• Gallagher’s weighted average cost willchange if one component cost of capitalchanges.• This may occur when a firm raises aparticularly large amount of capital such thatinvestors think that the firm is riskier.• The WACC of the next dollar of capital raisedin called the marginal cost of capital (MCC).24
• 25. Graphing the MCC curveGraphing the MCC curve• Assume now that Gallagher Corporationhas \$100,000 in retained earnings withwhich to finance its capital budget.• We can calculate the point at which theywill need to issue new equity since weknow that Gallagher’s desired capitalstructure calls for 50% common equity.25
• 26. Graphing the MCC curveGraphing the MCC curve• Assume now that Gallagher Corporationhas \$100,000 in retained earnings withwhich to finance its capital budget.• We can calculate the point at which theywill need to issue new equity since weknow that Gallagher’s desired capitalstructure calls for 50% common equity.26Breakpoint = Available Retained EarningsPercentage of Total
• 27. Graphing the MCC curveGraphing the MCC curve27Breakpoint = (\$100,000)/.5 = \$200,000For Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 28. Making Decisions Using MCC28WeightedCostofCapitalTotal Financing10%11%12%13%0 100,000 200,000 300,000 400,000Marginal weighted cost of capital curve:Using internalcommon equityUsing internalcommon equityUsing newcommon equityUsing newcommon equity11.72%11.72%11.09%11.09%
• 29. Making Decisions Using MCCMaking Decisions Using MCC• Graph MIRRs of potential projects29WeightedCostofCapitalTotal Financing9%10%11%12%0 100,000 200,000 300,000 400,000Marginal weighted cost of capital curve:Project 1Project 1MIRR =MIRR =12.4%12.4%Project 2Project 2MIRR =MIRR =12.1%12.1%Project 3Project 3MIRR =MIRR =11.5%
• 30. Making Decisions Using MCCMaking Decisions Using MCC• Graph IRRs of potential projects30WeightedCostofCapitalTotal Financing9%10%11%12%0 100,000 200,000 300,000 400,000Marginal weighted cost of capital curve:Project 1Project 1IRR =IRR =12.4%12.4%Project 2Project 2IRR =IRR =12.1%12.1%Project 3Project 3IRR =IRR =11.5%Graph MCC Curve11.09%11.09%11.72%11.72%
• 31. Making Decisions Using MCCMaking Decisions Using MCC• Graph IRRs of potential projects• Graph MCC Curve31WeightedCostofCapitalTotal Financing9%10%11%12%0 100,000 200,000 300,000 400,000Marginal weighted cost of capital curve:Project 1Project 1IRR = 12.4%IRR = 12.4% Project 2Project 2IRR = 12.1%IRR = 12.1%Project 3Project 3IRR =IRR = 11.5%Accept Projects #1 & #2Accept Projects #1 & #2 Choose projects whose IRR is above the weightedmarginal cost of capital11.72%11.72%11.09%11.09%
• 32. 32Answer the following questions and do the followingproblems and include them in you ECP Notes.If the cost of new common equity is higher than the cost of internal equity, why would afirm choose to issue new common stock?Why is it important to use a firm’s MCC and not a firm’s initial WACC to evaluateinvestments?Calculate the AT kd, ks, kn for the following information:Loan rates for this firm = 9%Growth rate of dividends = 4%Tax rate = 30%Common Dividends at t1 = \$ 4.00Price of Common Stock = \$35.00Flotation costs = 6%Your firm’s ks is 10%, the cost of debt is 6% before taxes, and the tax rate is 40%. Giventhe following balance sheet, calculate the firm’s after tax WACC:Total assets = \$25,000Total debt = 15,000Total equity = 10,000
• 33. 33Your firm is in the 30% tax bracket with a before-tax required rate of return on itsequity of 13% and on its debt of 10%. If the firm uses 60% equity and 40% debtfinancing, calculate its after-tax WACC.Would a firm use WACC or MCC to identify which new capital budgeting projectsshould be selected? Why?A firms before tax cost of debt on any new issue is 9%; the cost to issue newpreferred stock is 8%. This appears to conflict with the risk/return relationship. Howcan this pricing exist?What determines whether to use the dividend growth model approach or the CAPMapproach to calculate the cost of equity?For Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 34. Capital BudgetingDecision Methods1
• 35. • The capital budgeting process.• Calculation of payback, NPV, IRR, and MIRR forproposed projects.• Capital rationing.• Measurement of risk in capital budgeting andhow to deal with it.Learning Objectives2
• 36. • Capital Budgeting is the process ofevaluating proposed investment projects fora firm.• Managers must determine which projectsare acceptable and must rank mutuallyexclusive projects by order of desirability tothe firm.The Capital Budgeting Process3
• 37. Four methods:• Payback Period– years to recoup the initial investment• Net Present Value (NPV)– change in value of firm if project is under taken• Internal Rate of Return (IRR)– projected percent rate of return project will earn• Modified Internal Rate of Return (MIRR)The Accept/Reject Decision4
• 38. • Consider Projects A and B that have thefollowing expected cashflows?Capital Budgeting Methods5P R O J E C TP R O J E C TTimeTime A BB0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
• 39. • What is the payback for Project A?Capital Budgeting Methods6P R O J E C TP R O J E C TTimeTime A BB0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
• 40. • What is the payback for Project A?Capital Budgeting Methods0 1 2 3 43,500-6,5003,500-3,0003,500+5003,500(10,000)Cumulative CF7P R O J E C TP R O J E C TTimeTime A BB0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
• 41. • What is the payback for Project A?Capital Budgeting MethodsPayback in2.9 yearsP R O J E C TP R O J E C TTimeTime A BB0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,00080 1 2 3 43,500-6,5003,500-3,0003,500+5003,500(10,000)Cumulative CF0 1 2 3 43,500-6,5003,500-3,0003,500+5003,500(10,000)Cumulative CF
• 42. • What is the payback for Project B?Capital Budgeting Methods90 1 2 3 4500 500 4,600 10,000(10,000)P R O J E C TP R O J E C TTimeTime AA B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
• 43. Payback in3.4 years• What is the payback for Project B?Capital Budgeting Methods100 1 2 3 4500-9,500500-9,0004,600-4,40010,000+5,600(10,000)Cumulative CFP R O J E C TP R O J E C TTimeTime AA B00 (10,000.) (10,000.)11 3,500 50022 3,500 50033 3,500 4,60044 3,500 10,000
• 44. • Accept project if payback is less than thecompany’s predetermined maximum.• If company has determined that it requirespayback in three years or less, then youwould:– accept Project A– reject Project BPayback Decision Rule11
• 45. • Present Value of all costs and benefits(measured in terms of incremental cashflows) of a project.• Concept is similar to Discounted Cashflowmodel for valuing securities but subtractsthe cost of the project.Capital Budgeting MethodsNet Present ValueNet Present Value12
• 46. • Present Value of all costs and benefits (measured interms of incremental cash flows) of a project.• Concept is similar to Discounted Cashflow model forvaluing securities but subtracts of cost of project.Capital Budgeting MethodsNet Present ValueNet Present ValueNPV = PV of Inflows - Initial InvestmentNPV = PV of Inflows - Initial InvestmentNPV = + + – InitialInvestmentCF1(1+ k)1CF2(1+ k)2 ….CFn(1+ k )n13
• 47. What is theNPV forProject B?14P R O J E C TP R O J E C TTimeTime AA B0 (10,000) (10,000)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000k=10%0 1 2 3 4500 500 4,600 10,000(10,000)Capital Budgeting Methods
• 48. 455\$500(1.10)1What is theNPV forProject B?15P R O J E C TP R O J E C TTimeTime AA B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000k=10%0 1 2 3 4500 500 4,600 10,000(10,000)Capital Budgeting Methods
• 49. 413\$500(1.10) 2What is theNPV forProject B?16P R O J E C TP R O J E C TTimeTime AA B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000455k=10%0 1 2 3 4500 500 4,600 10,000(10,000)Capital Budgeting Methods
• 50. 3,456\$4,600(1.10) 3What is theNPV forProject B?17P R O J E C TP R O J E C TTimeTime AA B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000413\$500(1.10) 2455k=10%0 1 2 3 4500 500 4,600 10,000(10,000)Capital Budgeting Methods
• 51. 6,830\$10,000(1.10) 4What is theNPV forProject B?18P R O J E C TP R O J E C TTimeTime AA B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,0003,456\$4,600(1.10) 3413\$500(1.10) 2455k=10%0 1 2 3 4500 500 4,600 10,000(10,000)Capital Budgeting Methods
• 52. \$11,154What is theNPV forProject B?19P R O J E C TP R O J E C TTimeTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,0006,8303,456413455k=10%0 1 2 3 4500 500 4,600 10,000(10,000)Capital Budgeting Methods
• 53. PV Benefits > PV Costs\$11,154 > \$ 10,000What is theNPV forProject B?20P R O J E C TP R O J E C TTimeTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000\$11,1546,8303,456413455k=10%0 1 2 3 4500 500 4,600 10,000(10,000)
• 54. NPV > \$0\$1,154 > \$0- \$10,000 =- \$10,000 = \$1,154\$1,154 == NPVNPVWhat is theNPV forProject B?21P R O J E C TP R O J E C TTimeTime AA B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000PV Benefits > PV Costs\$11,154 > \$ 10,000\$11,154\$11,1546,8303,456413455k=10%0 1 2 3 4500 500 4,600 10,000(10,000)
• 55. 22• Additional Keys used to enterCash Flows and compute theNet Present Value (NPV)Financial Calculator:
• 56. NPV IRRP/YRCFN I/Y PV PMT FVKey used to enter expected cash flows in order oftheir receipt.NoteNote:: the initial investment (CF0) must beentered as a negative number since it is anoutflow.23• Additional Keys used toenter Cash Flows andcompute the NetPresent Value (NPV)Financial Calculator:
• 57. NPV IRRP/YRCFN I/Y PV PMT FV• Additional Keys used toenter Cash Flows andcompute the Net PresentValue (NPV)Financial Calculator:Key used to calculate the net present value ofthe cashflows that have been entered in thecalculator.24
• 58. NPV IRRP/YRCFN I/Y PV PMT FV• Additional Keys usedto enter Cash Flowsand compute the NetPresent Value (NPV)Financial Calculator:Key used to calculate the internal rate of returnfor the cashflows that have been entered in thecalculator. 25
• 59. Calculate the NPV for Project B with calculator.26NPV IRRP/YRCFN I/Y PV PMT FVP R O J E C TP R O J E C TTime ATime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
• 60. NPV IRRP/YRCFN I/Y PV PMT FVCalculate the NPV for Project B with calculator.Keystrokes for TI BAII PLUS:CFCF00 = -10,000= -10,00027CF 10000 +/- ENTER
• 61. NPV IRRP/YRCFN I/Y PV PMT FVCalculate the NPV for Project B with calculator.C01 =C01 = 500500500 ENTER28CF 10000 +/- ENTERKeystrokes for TI BAII PLUS:
• 62. NPV IRRP/YRCFN I/Y PV PMT FVCalculate the NPV for Project B with calculator.F01 =F01 = 22F stands for “frequency”. Enter 2 since thereare two adjacent payments of 500 in periods 1 and 2.292 ENTER500 ENTERCF 10000 +/- ENTERKeystrokes for TI BAII PLUS:
• 63. NPV IRRP/YRCFN I/Y PV PMT FVCalculate the NPV for Project B with calculator.C02 =C02 = 460046004600 ENTER302 ENTER500 ENTERCF 10000 +/- ENTERKeystrokes for TI BAII PLUS:
• 64. NPV IRRP/YRCFN I/Y PV PMT FVCalculate the NPV for Project B with calculator.F02 =F02 = 111 ENTER314600 ENTER2 ENTER500 ENTERCF 10000 +/- ENTERKeystrokes for TI BAII PLUS:
• 65. NPV IRRP/YRCFN I/Y PV PMT FVCalculate the NPV for Project B with calculator.C03 =C03 = 100001000010000 ENTER321 ENTER4600 ENTER2 ENTER500 ENTERCF 10000 +/- ENTERKeystrokes for TI BAII PLUS:
• 66. NPV IRRP/YRCFN I/Y PV PMT FVCalculate the NPV for Project B with calculator.F03 =F03 = 111 ENTER3310000 ENTER1 ENTER4600 ENTER2 ENTER500 ENTERCF 10000 +/- ENTERKeystrokes for TI BAII PLUS:
• 67. NPV IRRP/YRCFN I/Y PV PMT FVCalculate the NPV for Project B with calculator.I =I = 1010k = 10%34Keystrokes for TI BAII PLUS:10 ENTERNPV
• 68. NPV IRRP/YRCFN I/Y PV PMT FVCalculate the NPV for Project B with calculator.NPV = 1,153.95CPTThe net present value of Project B = \$1,154as we calculated previously.3510 ENTERNPVKeystrokes for TI BAII PLUS:
• 69. • Accept the project if the NPV is greaterthan or equal to 0.Example:NPVA = \$1,095NPVB = \$1,154NPV Decision Rule> 0> 0> 0> 0AcceptAcceptAcceptAccept•If projects are independent, accept both projects.•If projects are mutually exclusive, accept the projectwith the higher NPV.36
• 70. • IRR (Internal Rate of Return)– IRR is the discount rate that forces the NPV to equalzero.– It is the rate of return on the project given its initialinvestment and future cash flows.• The IRR is the rate earned only if all CFs are reinvested at theIRR rate.Capital Budgeting Methods37
• 71. Calculate the IRR for Project B with calculator.39NPV IRRP/YRCFN I/Y PV PMT FVP R O J E C TP R O J E C TTime ATime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000
• 72. Enter CFs as for NPVNPV IRRP/YRCFN I/Y PV PMT FVCalculate the IRR for Project B with calculator.IRR =IRR = 13.5%13.5%40P R O J E C TP R O J E C TTimeTime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000IRRIRR CPTCPT
• 73. • Accept the project if the IRR is greater than orequal to the required rate of return (k).• Reject the project if the IRR is less than therequired rate of return (k).Example:k = 10%IRRA = 14.96%IRRB = 13.50%IRR Decision Rule> 10%> 10%> 10%> 10%AcceptAcceptAcceptAccept41
• 74. • MIRR (Modified Internal Rate of Return)– This is the discount rate which causes the project’s PV ofthe outflows to equal the project’s TV (terminal value) ofthe inflows.– Assumes cash inflows are reinvested at k, the safe re-investment rate.– MIRR avoids the problem of multiple IRRs.– We accept if MIRR > the required rate of return.Capital Budgeting MethodsPVPVoutflowoutflow ==TVinflows(1 + MIRR)n42
• 75. What is theMIRR forProject B?P R O J E C TP R O J E C TTime ATime A B0 (10,000.) (10,000.)1 3,500 5002 3,500 5003 3,500 4,6004 3,500 10,000Safe =2%0 1 2 3 4500500 500500 4,6004,600 10,00010,000(10,000)(10,000)(10,000)(10,000)10,000(1.02)010,0004,600(1.02)1500(1.02)2500(1.02)34,69252053115,74310,000 =15,743(1 + MIRR)4(10,000)/(1.02)0MIRR = .12 = 12%MIRR = .12 = 12%43
• 76. NPV IRRP/YRCFN I/Y PV PMT FVCalculate the MIRR for Project B with calculator.10000 ENTER1 ENTER1 ENTER4600 ENTER2 ENTER500 ENTERCF 0 +/- ENTERKeystrokes for TI BAII PLUS:Step 1. Calculate NPV using cash inflows44
• 77. NPV IRRP/YRCFN I/Y PV PMT FVCalculate the MIRR for Project B with calculator.NPV = 14,544NPV = 14,544CPTThe net present value of Project B cash inflows = \$14,544(use as PV)452 ENTERNPVKeystrokes for TI BAII PLUS:Step 1. Calculate NPV using cash inflowsStep 1. Calculate NPV using cash inflows
• 78. NPV IRRP/YRCFN I/Y PV PMT FVCalculate the MIRR for Project B with calculator.FV =FV = 15,74315,74346Step 2. Calculate FV of cash inflows using previous NPVThis is the Terminal ValueCalculator Enter:N = 4I/YR = 2PV = -14544PMT= 0CPT FV = ?
• 79. NPV IRRP/YRCFN I/Y PV PMT FVCalculate the MIRR for Project B with calculator.MIRRMIRR 12.0112.0147Step 3. Calculate MIRR using PV of outflows and calculatedTerminal Value.Calculator Enter:N = 4PV = -10000PMT = 0FV = 15,743CPT I/YR = ??
• 80. • Capital rationing is the practice of placinga dollar limit on the total size of thecapital budget.• This practice may not be consistent withmaximizing shareholder value but may benecessary for other reasons.• Choose between projects by selecting thecombination of projects that yields thehighest total NPV without exceeding thecapital budget limit.What is capital rationing?54
• 81. • Calculate the coefficient of variation ofreturns of the firm’s asset portfolio with theproject and without it.• This can be done by following a five stepprocess. Observe the following example.Measurement of Project Risk55For Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 82. • Step 1:Step 1: Find the CV of the Existing Portfolio– Assume Company X has an existing rate of returnof 6% and standard deviation of 2%.Measurement of Project Risk56Standard DeviationMean, or expected valueCV== .02.06= .3333, or 33.33%
• 83. • Step 2:Step 2: Find the Expected return of the NewPortfolio (Existing plus Proposed)– Assume the New Project (Y) has an IRR of 5.71%and a Standard Deviation of 2.89%– Assume further that Project Y will account for 10%of X’s overall investment.Measurement of Project Risk57(wx x E(Rx)) + (wy x E(Ry))= (.10 x .0571) + (.90 x .06)= .00571 + .05400= .05971, or 5.971%E(Rp) =
• 84. • Step 3:Step 3: Find the Standard Deviation of the NewPortfolio (Existing plus Proposed).– Assume the proposed is uncorrelated with theexisting project. rxy = 0Measurement of Project Risk58[wx2σx2+ wy2σy2+ 2wxwyrxyσxσy]1/2= [(.102)(.02892) + (.902)(.022) + (2)(.10)(.90)(0.0)(.0289)(02)]1/2= [(.01)(.000835) + (.81)(.0004) + 0]1/2= .0182, or 1.82%= [.00000835 + .000324]1/2= [.00033235]1/2σp =
• 85. • Step 4:Step 4: Find the CV of the New Portfolio(Existing plus Proposed)Measurement of Project Risk59Standard DeviationMean, or expected valueCV== .0182.05971= .3048, or 30.48%
• 86. • Step 5:Step 5: Compare the CV of the portfoliowith and without the Proposed Project.– The difference between the two coefficientsof variation is the measure of risk of thecapital budgeting project.Measurement of Project Risk60CV without Y Change in CVCV with Y33.33% -2.8530.48%
• 87. • Firms often compensate for risk byadjusting the discount rate used tocalculate NPV.– Higher risk, use a higher discount rate.– Lower risk, use a lower discount rate• The risk adjusted discount rate (RADR) canalso be used as a risk adjusted hurdle ratefor IRR comparisons.Comparing risky projects using riskadjusted discount rates (RADRs)61
• 88. • Non-simple projects have one ormore negative future cash flowsafter the initial investment.Non-simple Projects62
• 89. • How would a negative cash flow in year 4affect Project Z’s NPV?Non-simple projectsProject Z should be rejected in this case.638,336-4,0983,7574,1324,545k=10%0 1 2 3 45,000 5,000 5,000 -6,000(10,000)- \$10,000 = -\$1,664 NPV
• 90. • Mutually exclusive projects with unequalproject lives can be compared by using twomethods:– Replacement Chain– Equivalent Annual AnnuityMutually Exclusive Projects WithUnequal Lives68
• 91. • Assumes each project can be replicated until acommon period of time has passed, allowingthe projects to be compared.• Example– Project Cheap Talk has a 3-year life, with an NPVof \$4,424.– Project Rolles Voice has a 12-year life, with anNPV of \$4,510.Replacement Chain Approach69
• 92. • Project Cheap Talk could be repeated fourtimes during the life of Project Rolles Voice.• The NPVs of Project Cheap Talk, in years t3, t6,and t9,are discounted back to year t0.Replacement Chain Approach70
• 93. • The NPVs of Project Cheap Talk, in years t3,t6, and t9,are discounted back to year t0,whichresults in an NPV of \$12,121.Replacement Chain Approach3,32412,1212,4971,8760 3 6 94,424 4,424 4,4244,424k=10%71
• 94. • Amount of the annuity payment thatwould equal the same NPV as the actualfuture cash flows of a project.• EAA = NPVPVIFAk,nEquivalent Annual Annuity72
• 95. Equivalent Annual Annuity73Project Rolles VoiceProject Rolles Voice\$4,510((1-(1.1)-12) / .1)= \$661.90• Project Cheap TalkProject Cheap Talk\$4,244((1-(1.1)-3) / .1)= \$1778.96
• 96. ECP HomeworkECP Homework1. The following net cash flows are projected for two separate projects. Your required rateof return is 12%.Year Project A Project B0 (\$150,000) (\$400,000)1 \$30,000 \$100,0002 \$30,000 \$100,0003 \$30,000 \$100,0004 \$30,000 \$100,0005 \$30,000 \$100,0006 \$30,000 \$100,000 a. Calculate the payback period for each project.b. Calculate the NPV of each project.c. Calculate the MIRR of each project.d. Which project(s) would you accept and why?
• 97. 2. What is meant by risk adjusted discount rates?3. Explain why the NPV method of capital budgeting is preferable over the payback method.4. A firm has a net present value of zero. Should the project be rejected? Explain.5. You have estimated the MIRR for a new project with the following probabilities: Possible MIRR Value Probability4% 5%7% 15%10% 15%11% 50%14% 15% a. Calculate the expected MIRR of the project. b. Calculate the standard deviation of the project. c. Calculate the coefficient of variation. d. Calculate the expected MIRR of the new portfolio with the new project. The currentportfolio has an expected MIRR of 9% and a standard deviation of 3% and willrepresent 60% of the total portfolio.ECP HomeworkECP Homework
• 99. Learning Objectives• Understand the importance of business valuation.• Understand the importance of stock and bondvaluation.• Learn to compute the value and yield to maturity ofbonds.• Learn to compute the value and expected yield onpreferred stock and common stock.• Learn to compute the value of a complete business.99
• 100. General Valuation Model• To develop a general model for valuing abusiness, we consider three factors that affectfuture earnings:– Size of cash flows– Timing of cash flows– Risk• We then apply the factors to the Discounted CashFlow (DCF) Model (Equation 12-1)100
• 101. Bond Valuation Model• Bond Valuation is an application of time valuemodel introduced in chapter 8.• The value of the bond is the present value ofthe cash flows the investor expects toreceive.• What are the cashflows from a bondinvestment?101
• 102. Bond Valuation Model• 3 Types of Cash Flows– Amount paid to buy the bond (PV)– Coupon interest payments made to thebondholders (PMT)– Repayment of Par value at end of Bond’s life(FV).102For Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 103. Bond Valuation Model• 3 Types of Cash Flows– Amount paid to buy the bond (PV)– Coupon interest payments made to thebondholders (PMT)– Repayment of Par value at end of Bond’s life(FV).103Discount rate (I/YR)• Bond’s time to maturity (N)
• 104. 104Cur NetBonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 05 6.6 228 965/8 -1/8Kroger 9s99 8.8 74 1017/8 -¼IBM 63/8 09 6.6 228 965/8 -1/8IBM Bond Wall Street Journal Information:For Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 105. 105Suppose IBM makes annual coupon payments. Theperson who buys the bond at the beginning of 2005 for\$966.25 will receive 5 annual coupon payments of\$63.75 each and a \$1,000 principal payment in 5 years(at the end of 2009). Assume t0 is the beginning of2005.Suppose IBM makes annual coupon payments. Theperson who buys the bond at the beginning of 2005 for\$966.25 will receive 5 annual coupon payments of\$63.75 each and a \$1,000 principal payment in 5 years(at the end of 2009). Assume t0 is the beginning of2005.IBM Bond Wall Street JournalInformation:Cur NetBonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 05 6.6 228 965/8 -1/8Kroger 9s99 8.8 74 1017/8 -¼IBM 63/8 09 6.6 228 965/8 -1/8
• 106. 106IBM Bond Timeline:0 1 2 3 4 52005 2006 2007 2008 200963.75 63.75 63.75 63.75 63.751000.00Suppose IBM makes annual coupon payments. The personwho buys the bond at the beginning of 2005 for \$966.25 willreceive 5 annual coupon payments of \$63.75 each and a\$1,000 principal payment in 5 years (at the end of 2009).Suppose IBM makes annual coupon payments. The personwho buys the bond at the beginning of 2005 for \$966.25 willreceive 5 annual coupon payments of \$63.75 each and a\$1,000 principal payment in 5 years (at the end of 2009).Cur NetBonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 05 6.6 228 965/8 -1/8Kroger 9s99 8.8 74 1017/8 -¼IBM 63/8 09 6.6 228 965/8 -1/8
• 107. 107Compute the Value for the IBM Bond given that you require anCompute the Value for the IBM Bond given that you require an8% return on your investment.8% return on your investment.Compute the Value for the IBM Bond given that you require anCompute the Value for the IBM Bond given that you require an8% return on your investment.8% return on your investment.0 1 2 3 4 52005 2006 2007 2008 200963.75 63.75 63.75 63.75 63.751000.00IBM Bond Timeline:IBM Bond Timeline:
• 108. 108\$63.75 Annuity for 5 years\$63.75 Annuity for 5 years\$63.75 Annuity for 5 years\$63.75 Annuity for 5 yearsVB = (INT x PVIFAk,n) + (M x PVIFk,n )\$1000 Lump Sum in 5 years\$1000 Lump Sum in 5 years\$1000 Lump Sum in 5 years\$1000 Lump Sum in 5 years0 1 2 3 4 52005 2006 2007 2008 200963.75 63.75 63.75 63.75 63.751000.00IBM Bond Timeline:IBM Bond Timeline:
• 109. 109VB = (INT x PVIFAk,n) + (M x PVIFk,n )= 63.75(3.9927) + 1000(.6806)= 254.53 + 680.60 = 935.13\$63.75 Annuity for 5 years\$63.75 Annuity for 5 years\$63.75 Annuity for 5 years\$63.75 Annuity for 5 years \$1000 Lump Sum in 5 years\$1000 Lump Sum in 5 years\$1000 Lump Sum in 5 years\$1000 Lump Sum in 5 years0 1 2 3 4 52005 2006 2007 2008 200963.75 63.75 63.75 63.75 63.751000.00IBM Bond Timeline:IBM Bond Timeline:
• 110. 110.01 roundingdifferenceN I/YR PV PMT FV––935.12935.125 8 ? 63.75 1,000IBM Bond Timeline:IBM Bond Timeline:\$63.75 Annuity for 5 years\$63.75 Annuity for 5 years\$63.75 Annuity for 5 years\$63.75 Annuity for 5 years0 1 2 3 4 52005 2006 2007 2008 200963.75 63.75 63.75 63.75 63.751000.00\$1000 Lump Sum in 5 years\$1000 Lump Sum in 5 years\$1000 Lump Sum in 5 years\$1000 Lump Sum in 5 years
• 111. 111Most Bonds Pay Interest Semi-Annually:e.g. semiannual coupon bond with 5 yearsto maturity, 9% annual coupon rate.Instead of 5 annual payments of \$90, the bondholderreceives 10 semiannual payments of \$45.0 1 2 3 4 52005 2006 2007 2008 200945 45100045 45 45 45 45 45 45 45
• 112. 112Compute the value of the bond given that yourequire a 10% return on your investment.Compute the value of the bond given that yourequire a 10% return on your investment.Since interest is received every 6 months, we need to usesemiannual compoundingVB = 45( PVIFA10 periods,5%) + 1000(PVIF10 periods, 5%)10%210%2Semi-AnnualCompoundingMost Bonds Pay Interest Semi-Annually:Most Bonds Pay Interest Semi-Annually:0 1 2 3 4 52005 2006 2007 2008 200945 45100045 45 45 45 45 45 45 45
• 113. 113Most Bonds Pay Interest Semi-Annually:= 45(7.7217) + 1000(.6139)= 347.48 + 613.90 = 961.38Compute the value of the bond given that youCompute the value of the bond given that yourequire a 10% return on your investment.require a 10% return on your investment.Compute the value of the bond given that youCompute the value of the bond given that yourequire a 10% return on your investment.require a 10% return on your investment.Since interest is received every 6 months, we need to usesemiannual compoundingVB = 45( PVIFA10 periods,5%) + 1000(PVIF10 periods, 5%)0 1 2 3 4 52005 2006 2007 2008 200945 45100045 45 45 45 45 45 45 45
• 114. 114Calculator Solution:N I/YR PV PMT FV––961.38961.3810 5 ? 45 1,0000 1 2 3 4 52005 2006 2007 2008 200945 45100045 45 45 45 45 45 45 45
• 115. Yield to Maturity• If an investor purchases a 6.375% annual couponbond today for \$966.25 and holds it until maturity(5 years), what is the expected annual rate ofreturn ?115-966.25??0 1 2 3 4 52005 2006 2007 2008 200963.75 63.75 63.75 63.75 63.751000.00+ ??966.25966.25
• 116. Yield to Maturity116VB = 63.75(PVIFA5, x%) + 1000(PVIF5,x%)Solve by trial and error.• If an investor purchases a 6.375% annual couponbond today for \$966.25 and holds it until maturity(5 years), what is the expected annual rate ofreturn ?-966.25??0 1 2 3 4 52005 2006 2007 2008 200963.75 63.75 63.75 63.75 63.751000.00+ ??966.25966.25
• 117. Yield to Maturity7.203%117Calculator Solution:N I/YR PV PMT FV5 ? -966.25 63.75 1,000-966.250 1 2 3 4 52005 2006 2007 2008 200963.75 63.75 63.75 63.75 63.751000.00
• 118. Yield to Maturity118 If YTM > Coupon Rate bond Sells at a DISCOUNT If YTM < Coupon Rate bond Sells at a PREMIUM-966.250 1 2 3 4 52005 2006 2007 2008 200963.75 63.75 63.75 63.75 63.751000.00
• 119. Interest Rate Risk• Bond Prices fluctuate over Time– As interest rates in the economy change,required rates on bonds will also changeresulting in changing market prices.119InterestRatesVVBB
• 120. Interest Rate Risk120• Bond Prices fluctuate over Time– As interest rates in the economy change,required rates on bonds will also changeresulting in changing market prices.InterestRatesVVBBInterestRates VVBB
• 121. Valuing Preferred Stock121P0 = Value of Preferred Stock= PV of ALL dividends discounted at investor’sRequired Rate of Return52 Weeks Yld Vol NetHi Lo Stock Sym Div % PE 100s Hi Lo Close Chgs 42½ 29 QuakerOats OAT 1.14 3.3 24 5067 35 34¼ 34¼ -¾s 36¼ 25 RJR Nabisco RN .08p ... 12 6263 29¾ 285/8 287/8 -¾237/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235/8 23¾ ...7¼ 5½ RJR Nab pfC .60 9.4 ... 2248 6½ 6¼ 63/8 -1/80 1 2 3 ∞P0=23.75 D1=2.31 D2=2.31 D3=2.31 D∞ =2.31237/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235/8 23¾ ...
• 122. Valuing Preferred Stock122P0 = + + +···2.31(1+ kp)2.31(1+ kp)22.31(1+ kp)3∞52 Weeks Yld Vol NetHi Lo Stock Sym Div % PE 100s Hi Lo Close Chgs 42½ 29 QuakerOats OAT 1.14 3.3 24 5067 35 34¼ 34¼ -¾s 36¼ 25 RJR Nabisco RN .08p ... 12 6263 29¾ 285/8 287/8 -¾237/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235/8 23¾ ...7¼ 5½ RJR Nab pfC .60 9.4 ... 2248 6½ 6¼ 63/8 -1/80 1 2 3 ∞P0=23.75 D1=2.31 D2=2.31 D3=2.31 D∞ =2.31237/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235/8 23¾ ...
• 123. Valuing Preferred Stock123P0 =Dpkp=2.31.10 = \$23.10P0 = + + +···2.31(1+ kp)2.31(1+ kp )22.31(1+ kp )3∞52 Weeks Yld Vol NetHi Lo Stock Sym Div % PE 100s Hi Lo Close Chgs 42½ 29 QuakerOats OAT 1.14 3.3 24 5067 35 34¼ 34¼ -¾s 36¼ 25 RJR Nabisco RN .08p ... 12 6263 29¾ 285/8 287/8 -¾237/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235/8 23¾ ...7¼ 5½ RJR Nab pfC .60 9.4 ... 2248 6½ 6¼ 63/8 -1/80 1 2 3 ∞P0=23.75 D1=2.31 D2=2.31 D3=2.31 D∞ =2.31237/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235/8 23¾ ...
• 124. Valuing Individual Shares of CommonStock124P0 = PV of ALL expected dividends discounted at investor’sRequired Rate of ReturnNot like Preferred Stock since D0 = D1 = D2 = D3 = DN , therefore the cashflows are no longer an annuity.Not like Preferred Stock since D0 = D1 = D2 = D3 = DN , therefore the cashflows are no longer an annuity.P0 = + + +···∞D1(1+ ks )D2(1+ ks )2D3(1+ ks )3D1 D2 D3P0 D∞0 1 2 3 ∞
• 125. Valuing Individual Shares of CommonStock125P0 = PV of ALL expected dividends discounted at investor’sRequired Rate of ReturnInvestors do not know the values ofD1, D2, .... , DN. The future dividends must beestimated.Investors do not know the values ofD1, D2, .... , DN. The future dividends must beestimated.D1 D2 D3P0 D∞0 1 2 3 ∞P0 = + + +···∞D1(1+ ks )D2(1+ ks )2D3(1+ ks )3
• 126. Constant Growth Dividend Model126Assume that dividends grow at a constant rate (g).D1=D0 (1+g)D0D2=D0 (1+g)2D3=D0 (1+g)3D∞=D0 (1+g)∞0 1 2 3 ∞
• 127. Constant Growth Dividend Model127Requiresks > gRequiresks > gReduces to:P0 = + + + ··· +D0 (1+ g)(1+ ks )D0 (1+ g)2(1+ ks )2D0 (1+ g)3(1+ ks )3 ∞P0 = =D0(1+g)ks – gD1ks – gAssume that dividends grow at a constant rate (g).D1=D0 (1+g)D0D2=D0 (1+g)2D3=D0 (1+g)3D∞=D0 (1+g)∞0 1 2 3 ∞
• 128. Constant Growth Dividend Model128P0 = = \$30.501.14(1+.07).11 – .07What is the value of a share of common stock if themost recently paid dividend (D0) was \$1.14 per share anddividends are expected to grow at a rate of 7%?Assume that you require a rate of return of 11%on this investment.P0 = =D0(1+g)ks – gD1ks – g
• 129. Valuing Total Stockholders’ Equity• The Investor’s Cash Flow DCF Model– Investor’s Cash Flow is the amount that is“free” to be distributed to debt holders,preferred stockholders and commonstockholders.– Cash remaining after accounting forexpenses, taxes, capital expenditures andnew net working capital.129
• 130. 130Calculating Intrinsic ValueTata Co. ExampleFor Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org
• 131. 131ECP Homework1. Indicate which of the following bonds seems to be reported incorrectly with respect to discount, premium,or par and explain why. Bond Price Coupon Rate Yield to Maturity A 105 9% 8%B 100 6% 6%C 101 5% 4.5%D 102 0% 5%2. What is the price of a ten-year \$1,000 par-value bond with a 9% annual coupon rate and a 10% annualyield to maturity assuming semi-annual coupon payments?3. You have an issue of preferred stock that is paying a \$3 annual dividend. A fair rate of return on thisinvestment is calculated to be 13.5%. What is the value of this preferred stock issue?4. Total assets of a firm are \$1,000,000 and the total liabilities are \$400,000. 500,000 shares of commonstock have been issued and 250,000 shares are outstanding. The market price of the stock is \$15 and netincome for the past year was \$150,000.a.. Calculate the book value of the firm.b. Calculate the book value per share.c. Calculate the P/E ratio.5. A firm’s common stock is currently selling for \$12.50 per share. The required rate of return is 9% and thecompany will pay an annual dividend of \$.50 per share one year from now which will grow at a constant ratefor the next several years. What is the growth rate? For Deep Study of Cost of Capital, please visitour website : http://www.svtuition.org