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![Compute IRR and NPV in Microsoft Excel
1.IRR Function
Description:
The Microsoft Excel IRR function returns the internal rate of
return for a series of cash flows. The cash
flows must occur at regular intervals, but do not have to be the
same amounts for each interval.
Syntax
The syntax for the IRR function in Microsoft Excel is:
IRR(range, [estimated_irr] )
Parameters or Arguments
range
A range of cells that represent the series of cash flows.
estimated_irr
Optional. It is your guess at the internal rate of return. If this
parameter is omitted, it
assumes an estimated_irr of 0.1 or 10%
Example (as Worksheet Function)
Let's look at some Excel IRR function examples and explore](https://image.slidesharecdn.com/computeirrandnpvinmicrosoftexcel1-221028224510-3822b722/85/Compute-IRR-and-NPV-in-Microsoft-Excel-1-IRR-Function-docx-1-320.jpg)
![The syntax for the NPV function in Microsoft Excel is:
NPV( discount_rate, value1, [value2, ... value_n] )
Parameters or Arguments
discount_rate
The discount rate for the period.
value1, value2, ... value_n
The future payments and income for the investment (ie: cash
flows). There can be up
to 29 values entered.
Note
Microsoft Excel's NPV function does not account for the intial
cash outlay, or may account for
it improperly depending on the version of Excel. However, there
is a workaround.
This workaround requires that you NOT include the initial
investment in the future
payments/income for the investment (ie: value1, value2, ...
value_n), but instead, you need to
subtract from the result of the NPV function, the amount of the
initial investment.
The workaround formula is also different depending on whether
the cash flows occur at the
end of the period (EOP) or at the beginning of the period
(BOP).
If the cash flows occur at the end of the period (EOP), you](https://image.slidesharecdn.com/computeirrandnpvinmicrosoftexcel1-221028224510-3822b722/85/Compute-IRR-and-NPV-in-Microsoft-Excel-1-IRR-Function-docx-3-320.jpg)
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Compute IRR and NPV in Microsoft Excel 1.IRR Function .docx
- 1. Compute IRR andNPV in Microsoft Excel 1.IRR Function Description: The Microsoft Excel IRR function returns the internal rate of return for a series of cash flows. The cash flows must occur at regular intervals, but do not have to be the same amounts for each interval. Syntax The syntax for the IRR function in Microsoft Excel is: IRR(range, [estimated_irr] ) Parameters or Arguments range A range of cells that represent the series of cash flows. estimated_irr Optional. It is your guess at the internal rate of return. If this parameter is omitted, it assumes an estimated_irr of 0.1 or 10% Example (as Worksheet Function) Let's look at some Excel IRR function examples and explore
- 2. how to usethe IRR function as a worksheet function in Microsoft Excel: Based on the Excel spreadsheet above: This first example returns an internal rate of return of 28%. It assumes that you start a business at a cost of $7,500. You net the following income for the first four years: $3,000, $5,000, $1,200, and $4,000. This next example returns an internal rate of return of 5%. It assumes that you start a business at a cost of $10,000. You net the following income for the first three years: $3,400, $6,500, and $1,000. =IRR(B1:B4) Result: 5% 2.NPV Function Description The Microsoft Excel NPV function returns the net present value of an investment. Syntax
- 3. The syntax forthe NPV function in Microsoft Excel is: NPV( discount_rate, value1, [value2, ... value_n] ) Parameters or Arguments discount_rate The discount rate for the period. value1, value2, ... value_n The future payments and income for the investment (ie: cash flows). There can be up to 29 values entered. Note Microsoft Excel's NPV function does not account for the intial cash outlay, or may account for it improperly depending on the version of Excel. However, there is a workaround. This workaround requires that you NOT include the initial investment in the future payments/income for the investment (ie: value1, value2, ... value_n), but instead, you need to subtract from the result of the NPV function, the amount of the initial investment. The workaround formula is also different depending on whether the cash flows occur at the end of the period (EOP) or at the beginning of the period (BOP). If the cash flows occur at the end of the period (EOP), you
- 4. would use thefollowing formula: =NPV( discount_rate, value1, value2, ... value_n ) - Initial Investment If the cash flows occur at the beginning of the period (BOP), ou would use the following formula: =NPV( discount_rate, value2, ... value_n ) - Initial Investment + value1 Example (as Worksheet Function) Let's look at some NPV examples and explore how to use the NPV function as a worksheet function in Microsoft Excel: This first example returns a net present value of $3,457.19. It assumes that you pay $7,500 as an initial investment . You then receive the following income for the first four years (EOP): $3,000, $5,000, $1,200, and $4,000. An annual discount rate of 8% is used. =NPV(8%, 3000, 5000, 1200, 4000) - 7500 This next example returns a net present value of $8,660.77. It assumes that you pay $10,000 as an initial investment. You then receive the following income for the first three years (BOP): $3,400, $6,500, and $10,000. An annual discount rate of 5% is used. =NPV(5%, 6500, 10000) - 10000 + 3400
- 5. Below is theexample used in Chapter 10 PPT. Chapter 12. Cash Flow Estimation 1
- 6. Net Present Valueanalysis, IRR, and PI methods provide very sophisticated measures of shareholder value generated by potential capital investments. If cash flow estimates are bad, any analytical technique for assessing project value will lead to poor investment decisions. Capital Budgeting and Cash Flows 2 Capital budgeting concerned with cash flows, not accounting profit. To evaluate a capital investment, we must know: Incremental cash outflows of the investment (marginal cost of investment), and Incremental cash inflows of the investment (marginal benefit of investment) The timing and magnitude of cash flows and accounting profits
- 7. can differ dramatically. CashFlows Versus Accounting Profit 3 Financing costs should be excluded when evaluating a project’s cash flow. Ask the following: Is the project’s existence dependent on financing? NO!!!-- you must separate financing and investment decisions Both interest expense from debt financing and dividend payments to equity investors should be excluded. Financing costs are captured in the discounting future cash flows to present. Financing Costs
- 8. 4 Land, Buildings, Equipment,etc. Asset purchases represent negative cash flows (Accounts don’t show purchase as a deduction from earnings-use depreciation instead). Shipping and installation costs should be included in the purchase price. Full initial cost becomes the depreciable basis. Costs of fixed assets
- 9. 5 Accountants subtract depreciationfrom revenues to obtain net income. Depreciation shelters income from tax – which impacts cash flows – so it is relevant. Depreciation must be added to net income when estimating the project’s cash flow. Non-cash Charges 6
- 10. Working capital= Currentassets – current liabilities Usually inventory, accounts receivable, and accounts payable Usually, working capital = Inv + AR – AP New investment projects typically increase net working capital: cash outflow. Most of the increase comes from additional inventories and receivables. Typically an outflow at the beginning of a project and an inflow at the end. Changes in Net Working capital 7 Relevant Cash flows (not accounting earnings) Depreciation
- 11. Incremental cash flows Opportunitycosts: The return on the best alternative use of an asset. Must be included. (Example: land previously owned.) Side effects (externalities): Effects of a project on cash flows in other parts of the firm. (E.g. cannibalism or synergy) Taxes Irrelevant Sunk costs: Outlays that have already occurred. Cash Flows 8 Opportunity Costs: Currently own land or have to purchase land Sunk costs: Bought a cell phone, now want new I- Phone…should original price of phone be included? (1) Cash Flows from Operations Operating Cash Flow = EBIT – Taxes + Depreciation Other Methods for Computing OCF Bottom-Up Approach Works only when there is no interest expense
- 12. OCF = NI+ depreciation Top-Down Approach OCF = Sales – Costs – Taxes Don’t subtract non-cash deductions Tax Shield Approach OCF = (Sales – Costs)(1 – tc) + Depreciation* tc Estimating Cash Flows 9 Capital Spending: Changes to fixed assets (2) Cash Flows from Investments Part I: Net Capital Spending Usually up front and at the end Remember salvage value (after tax) Part II: Changes in Net Working Capital Part III: Opportunity Costs (3) Cash Flows from Side Effects cannibalism or synergy Estimating Cash Flows
- 13. 10 Speedo has decidedto introduce the LZR-2. An improved version of the LZR that Phelps and others wore. Speedo spent 250k developing an improved “Pulse” fabric Speedo spent 100k test marketing it with Olympic hopeful swimmers Test market was successful Example: Speedo LZR-2
- 14. 11 Details Speedo is assumingthree years for the project. They assume that at the end of three years the technology will be essentially obsolete. Cost of equipment to support the new swimsuit: $200,000 (depreciated according to MACRS 3-year life) Increase in net working capital (mainly fabric materials): $20,000. This will be recovered at the end of the project. Inflation has been built into financial statements already. Operating costs are about 90% of revenues. The equipment can be sold at the end of the project for an estimated $20,000. Speedo has estimated the appropriate discount rate to be 10%. Example: Speedo LZR-2
- 15. 12 See the textfor the details of the case. Relevant or not? 250k developing fabric? 100k test marketing swimsuits? Example: Speedo LZR-2 13 Starting point: Year 0 outflows
- 16. Equipment -200 NWC -20 Total-220 Example: Speedo LZR-2 14 Depreciation Why do we care about depreciation? Taxes Tax shield = depreciation * tax rate Now, do you want tax shields sooner or later? Tax law allows accelerated depreciation (Modified Accelerated Cost Recovery System or MACRS) Example: Speedo LZR-2
- 17. 15 Tax Shield comingsooner implies that the Present Value of the tax shield will be larger Example: Speedo LZR-2 16
- 18. Example: Speedo LZR-2 MACRSincreases the present value of an investment’s tax benefits. Speedo (rounded):Year Investment%Depr1200.3366.002200.4590.003200.1530.004200. 0714.00 17 Example: Speedo LZR-2Year 1Year 2Year 3Revenues4,000.003,000.002,000.00Oper costs-3,600.00- 2,700.00-1,800.00Depreciation-66.00-90.00-30.00Inc before tax334.00210.00170.00Tax (40%)-133.60-84.00-68.00Net Inc200.40126.00102.00+ Depreciation+66.00+90.00+30.00Oper CF266.40216.00132.00
- 19. 18 Equipment can besold at end of year 3 for 20,000. So, additional CF: Book value: 14 Capital gain: 20 – 14 = 6 Taxes: 6 * .4 = 2.4 CF: 20 – 2.4 = 17.6 Put it all together! Capital investment Change in NWC Operating CFs (need depreciation) CF from Salvage Evaluate! Example: LZR-2
- 20. 19 200 – 186= BV of 14 Example: LZR-2Year 0Year 1Year 2Year 3Capital Inv-200.00D in NWC-20.000.000.00+20.00Oper CF+266.40+216.00+132.00Salvage CF+17.60Net CFs- 220.00266.40216.00169.60 Find NPV, IRR. 20 Discount rate of 10% Year(s)3-Year5-Year7-Year10-Year15-Year20-Year
- 21. 133.332014.291053.75 244.453224.49189.57.22 314.8119.217.4914.48.556.68 47.4111.5212.4911.527.76.18 511.528.939.226.935.71 65.768.927.376.235.28 7 8.936.555.94.89 8 4.456.555.94.52 96.565.94.46 10 6.555.94.46 11 3.295.94.46 12 5.94.46 13 5.914.46 14 5.94.46 15 5.914.46 16 2.994.46 17-20 4.46 21 2.23 Tax Depreciation Schedules by Recovery-Period Class Table 6.1Period012345671Capital Investment10,000(1,949)2Accumulated depreciation1,5833,1674,7506,3337,9179,500- 03Year-end book value10,0008,4176,8335,2503,6672,083500- 04Working capital5501,2893,2614,8903,5832,002- 05Total book value (3+4)10,0008,9678,1228,5118,5575,6662,502- 06Sales52312,88732,61048,90135,83419,7177Cost of goods sold8377,72919,55229,34521,49211,8308Other Costs4,0002,2001,2101,3311,4641,6111,7729Depreciation1,583 1,5831,5831,5831,5831,58310Pretax profit (6-7-8- 9)(4,000)(4,097)2,36510,14416,50911,1484,5321,44911Tax at 35%(1,400)(1,434)8283,5505,7783,9021,58650712Profit after tax (10-11)2,600(2,663)1,5376,59510,7317,2462,946942 Table 6.2Period012345671Sales52312,88732,61048,90135,83419,7172 Cost of goods sold8377,72919,55229,34521,49211,8303Other costs4,0002,2001,2101,3311,4641,6111,7724Tax on
- 22. operations(1,400)(1,434)8283,5505,7783,9021,5865Cash flow from operations(1-2-3- 4)(2,600)(1,080)3,1208,17712,3148,8294,5296Change in working capital(550)(739)(1,972)(1,629)1,3071,5812,0027Capital investment and disposal(10,000)1,4428Net cash flow (5+6+7)(12,600)(1,630)2,3816,20510,68510,1366,1103,4449Pre sent value at 20%(12,600)(1,358)1,6543,5915,1534,0742,046961Net Present value= +3520 (sum of 9) Table 6.4Tax Depreciation Schedules by Recovery-Period ClassYear(s)3-Year5-Year7-Year10-Year15-Year20- Year133.332014.291053.75244.453224.49189.57.22314.8119.21 7.4914.48.556.6847.4111.5212.4911.527.76.18511.528.939.226. 935.7165.768.927.376.235.2878.936.555.94.8984.456.555.94.52 96.565.94.46106.555.94.46113.295.94.46125.94.46135.914.461 45.94.46155.914.46162.994.4617-204.46212.23 Table 6.5Period012345671Sales52312887326104890135834197172Co st of goods sold8377729195522934521492118303Other Costs40002200121013311464161117724Tax depreciation20003200192011525765Pretax profit (1-2-3-4)- 4000-451474898071694011579553919496Taxes at 35%-1400- 15802623432592940531939682 Table 6.6Period012345671Sales52312887326104890135834197172Co st of goods sold8377729195522934521492118303Other costs40002200121013311464161117724Tax-1400- 158026234325929405319396825Cash flow from operations (1- 2-3-4)-2600-934368682951216386784176-6826Change in working capital-550-739-1972-16291307158120027Capital investment and disposal-1000019498Net cash flow (5+6+7)- 12600-148429476323105349985575732699Present Value= +3802 (sum of 9)-12600-123720473659508040131928912Net present value= +3802 (sum of 9) 7.1Plotting data Fig
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- 28. 6.2%199134.2%19929.0%199311.3%1994- 0.1%199536.5%199621.2%199731.3%199823.4%199923.6%200 0-10.9%2001-11.0%2002-20.9% Chapter 11. CapitalBudgeting 1 Capital budgeting deals with investment decisions where
- 29. Time is animportant element of the decision Cash flows of investment can be measured But, there may be some uncertainties Classification of decisions Accept or reject Choose best of a set (mutually exclusive) Ranking (projects are independent and cash is limited) Capital budgeting Independent vs. mutually exclusive projects Independent projects: if the cash flows of one are unaffected by the acceptance of the other. Multiple projects can be chosen. Mutually exclusive projects: if the cash flows of one can be adversely impacted by the acceptance of the other. Only ONE of several potential projects can be chosen
- 30. 3 Financial managers shouldaccept a project when its perceived benefits exceed perceived costs. In general, value is created when benefits exceed costs. NPV = Total PV of future CFs - Initial Investment When firms accept all positive Net Present Value investments, they maximize the value of their shareholders. Net Present Value (NPV)
- 31. Net Present Value(NPV) Sum of the PVs of all cash inflows and outflows of a project: Estimating NPV: 1. Estimate future cash flows: how much? and when? 2. Estimate discount rate 3. Estimate initial costs Reinvestment assumption Assumes all cash flows are reinvested at discount rate Rule Accept if NPV > 0 Reject if NPV < 0. Ranking Criteria Choose the highest NPV
- 32. What is ProjectS’ NPV? WACC = 10% Year CFt PV of CFt 0 - 100 - $100.00 1 70 63.64 2 50 41.32 3 20 15.02 NPVS = $ 19.98 Excel: =NPV(rate,CF1:CFn) + CF0 Here, CF0 is negative, rate is discount rate or WACC.
- 33. 6 Rationale for theNPV Method NPV = PV of inflows – Cost = Net gain in wealth If projects are independent, accept if NPV > 0. If projects are mutually exclusive, accept projects with the highest positive NPV, those that add the most value.
- 34. 7 IRR is thediscount rate that forces PV of inflows equal to cost, and the NPV = 0: Reinvestment assumption: All future cash flows assumed reinvested at the IRR Solving for IRR with a financial calculator: Enter CFs in Cash Flow register. Press IRR. Solving for IRR with Excel: =IRR(CF0:CFn) Internal Rate of Return (IRR)
- 35. 8 How is aproject’s IRR similar to a bond’s YTM? They are the same thing. Think of a bond as a project. The YTM on the bond would be the IRR of the “bond” project. EXAMPLE: Suppose a 10-year bond with a 9% annual coupon and $1,000 par value sells for $1,134.20. Solve for IRR = YTM = 7.08%, the annual return for this project/bond. 9 Rules for the IRR Method For independent projects: Take all projects with IRR>r* r*=the opportunity cost of capital or required rate of return For mutually exclusive projects:
- 36. Take the projectwith the highest IRR, if IRR>r* 10 What is the IRR of the following project? The IRR does not always exist! Potential problems with IRRYear012Project A100-200150
- 37. Lending or Borrowing? Potentialproblems with IRR 12 Potential problems with IRR The following cash flow generates NPV=$ 3.3 million at 10%. It has IRRs of (-44%) and +11.6%.
- 38. Cash Flows (millionsof Australian dollars) 13 When the sign of the cash flows changes more than once, you get multiple rates of return The IRR does not always unique! Potential problems with IRR
- 39. 600 NPV 300 0 -30 -600 Discount Rate IRR=11.6% IRR=-44% 14 For cashflows that alternate in sign (i.e. negative, positive, negative), it is not clear whether you are a net borrower or a net lender. Thus, it is not clear whether you would prefer a high or low IRR.
- 40. If cash flowshave the traditional pattern (one or several negative cash flows followed by only positive cash flows), then the NPV is positive whenever the IRR is greater than the opportunity cost of capital – Thus, the IRR rule usually works. Potential problems with IRR FlowsNumber of IRRsIRR criterionNPV criterionFirst cash flow is (-) and all remaining cash flows are (+)1Accept if IRR>R Reject if IRR<RAccept if NPV>0 Reject if NPV<0 First cash flows is (+) and all remaining cash flows are (- )1Accept if IRR<R Reject if IRR>R Accept if NPV>0 Reject if NPV<0 Some cash flows after first are (+) and some cash flows after first are (-)Maybe more than 1No valid IRRAccept if NPV>0 Reject if NPV<0 General rules
- 41. Potential problems withIRR: scale issue Mutually Exclusive Projects Mutually exclusive Only ONE of several potential projects can be chosen Independent: Accepting/rejecting one project does not affect the decision of the other projects Scale issues IRR sometimes ignores the magnitude of the project.
- 42. 17 Potential problems withIRR: scale issue In this case, can IRR be salvaged? Look at smaller project Acceptable? Yes. So, should you invest extra $$$ for larger project. Look at incremental CFs: INCREMENTAL IRR Now, which project is better? 18 Timing Issues
- 43. Preferred project dependson the discount rate, not the IRR (mutually exclusive projects) Potential problems with IRR: timing issue 0 1 2 3 $10,000 $1,000 $1,000 -$10,000 Project A 0 1 2 3 $1,000 $1,000 $12,000 -$10,000 Project B
- 44. 19 Potential problems withIRR: timing issue 20 20 Potential problems with IRR: timing issue 10.55% = IRR To find crossover rate: Find INCREMENTAL IRR!
- 45. 21 The number ofyears required to recover a project’s cost, or “How long does it take to get our money back?” Calculated by adding project’s cash inflows to its cost until the cumulative cash flow for the project turns positive. Payback period
- 46. The payback periodis the number of years, t*, such that For independent projects Accept all projects for which t*<K (where K is the cutoff) For mutually exclusive projects: Accept the project with the lowest t* as long as t*<K (where K is the cutoff) Mutually exclusive: Only ONE of several potential projects can be chosen Payback period
- 47. Payback period PaybackL =2 + / = 2.375 years 30 80 CFt Cumulative 0 1 2 3 -30 Project L’s Payback Calculation -100 50 -90 80 -100 60 10
- 48. 24 Examine the threeprojects and note the mistake we would make if we insisted on only taking projects with a payback period of 2 years or less. Payback period 25 Strengths and Weaknesses of Payback Strengths Provides an indication of a project’s risk and liquidity. Easy to calculate and understand.
- 49. Weaknesses Ignores the timevalue of money. Ignores CFs occurring after the payback period. 26 The discounted payback period is the number of years, t*, such that For non-mutually excusive projects Accept all projects for which t*<K For mutually exclusive projects: Accept the project with the lowest t* as long as t*<K (where K is the cutoff) Discounted payback period
- 50. Discounted Payback Period Usesdiscounted cash flows rather than raw CFs. Disc PaybackL = 2 + / = 2.7 years; If our cutoff rule was 2 years, this project would be rejected. 41.32 60.11 CFt Cumulative 0 1 2 3
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- 59. E NPV IRR C C ($4,000.00) ($3,000.00) ($2,000.00) ($1,000.00) $0.00 $1,000.00 $2,000.00 $3,000.00 $4,000.00 $5,000.00 0%10%20%30%40% Discount rate NPV Project A ProjectB Chart7000.010.010.020.020.030.030.040.040.050.050.060.060.0 70.070.080.080.090.090.10.10.110.110.120.120.130.130.140.14 0.150.150.160.160.170.170.180.180.190.190.20.20.210.210.220. 220.230.230.240.240.250.250.260.260.270.270.280.280.290.290 .30.30.310.310.320.320.330.330.340.340.350.350.360.360.370.3 70.380.380.390.390.40.4 Project A Project B Discount rate NPV 2000 4000 1833.5408874698 3581.6602321185 1673.934004326 3185.7146594758
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- 62. -1378.2951116924 -3089.7556484446 -1416.0766347355 -3144.5231153686 Sheet10123$ (10,000.00)$ 10,000.00$1,000.00$ 1,000.00A$ (10,000.00)$ 1,000.00$ 1,000.00$ 12,000.00B16.04%IRR A12.94%IRR BDiscount RateProject AProject B0%$2,000.00$4,000.001%$1,833.54$3,581.662%$1,673.93$3, 185.713%$1,520.85$2,810.844%$1,373.98$2,455.825%$1,233.0 3$2,119.496%$1,097.72$1,800.787%$967.79$1,498.688%$842. 99$1,212.279%$723.10$940.6510%$607.88$683.0111%$497.14 $438.5812%$390.67$206.6213%$288.28($13.54)14%$189.80($ 222.53)15%$95.05($420.95)16%$3.89($609.38)17%($83.85)($7 88.32)18%($168.31)($958.29)19%($249.63)($1,119.76)20%($3 27.93)($1,273.15)21%($403.35)($1,418.89)22%($475.99)($1,55 7.36)23%($545.98)($1,688.95)24%($613.41)($1,813.98)25%($6 78.40)($1,932.80)26%($741.04)($2,045.71)27%($801.41)($2,15 3.01)28%($859.62)($2,254.96)29%($915.74)($2,351.84)30%($9 69.85)($2,443.89)31%($1,022.04)($2,531.35)32%($1,072.37)($ 2,614.42)33%($1,120.92)($2,693.34)34%($1,167.75)($2,768.28 )35%($1,212.93)($2,839.45)36%($1,256.51)($2,907.02)37%($1, 298.57)($2,971.15)38%($1,339.14)($3,032.01)39%($1,378.30)( $3,089.76)40%($1,416.08)($3,144.52)Discount RateNPV0%$2,000.004%$1,373.988%$842.9912%$390.6716%$ 3.8920%($327.93)24%($613.41)28%($859.62)32%($1,072.37)3 6%($1,256.51)40%($1,416.08)44%($1,554.45)48%($1,674.48)5 2%($1,778.60)56%($1,868.86)60%($1,947.02)64%($2,014.59)1 7%($83.85)18%($168.31)19%($249.63)20%($327.93)21%($403. 35)22%($475.99)23%($545.98)24%($613.41)25%($678.40)26% ($741.04)27%($801.41)28%($859.62)29%($915.74)30%($969.8 5)31%($1,022.04)32%($1,072.37)33%($1,120.92)34%($1,167.7 5)35%($1,212.93)36%($1,256.51)37%($1,298.57)38%($1,339.1 4)39%($1,378.30)40%($1,416.08) Sheet100000000000000000000000000000000000000000000000 00000000000000000000000000000000000
- 63. Project A Project B Discountrate NPV 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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- 65. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Sheet2 Sheet3 YearProject AProject BProjectA-B Project B-A 0($10,000)($10,000)$0$0 1$10,000$1,000$9,000($9,000) 2$1,000$1,000$0$0 3$1,000$12,000($11,000)$11,000 ($3,000.00) ($2,000.00) ($1,000.00) $0.00 $1,000.00 $2,000.00 $3,000.00 0%5%10%15%20% Discount rate NPV A-B B-A Sheet1YearProject AProject BProject A-BProject B- A0($10,000)($10,000)$0$01$10,000$1,000$9,000($9,000)2$1,0 00$1,000$0$03$1,000$12,000($11,000)$11,00010.55%Discount
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- 67. 369.2789980449 -217.5573823181 217.5573823181 -75.1314800902 75.1314800902 58.5611836015 -58.5611836015 184.046035506 -184.046035506 301.814145891 -301.814145891 412.3247051606 -412.3247051606 516.0073041477 -516.0073041477 613.2640350865 -613.2640350865 704.4714286726 -704.4714286726 789.9822411827 -789.9822411827 870.1271043316 -870.1271043316 945.2160493827 -945.2160493827 Sheet1YearProject AProject BProjectA-BProject B- A0($10,000)($10,000)$0$01$10,000$1,000$9,000($9,000)2$1,0 00$1,000$0$03$1,000$12,000($11,000)$11,00010.55%Discount rtaeA-BB- A0%($2,000.00)$2,000.001%($1,748.12)$1,748.122%($1,511.7 8)$1,511.783%($1,289.99)$1,289.994%($1,081.84)$1,081.845% ($886.46)$886.466%($703.06)$703.067%($530.90)$530.908%($ 369.28)$369.289%($217.56)$217.5610%($75.13)$75.1311%$58 .56($58.56)12%$184.05($184.05)13%$301.81($301.81)14%$41 2.32($412.32)15%$516.01($516.01)16%$613.26($613.26)17%$ 704.47($704.47)18%$789.98($789.98)19%$870.13($870.13)20
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- 71. 1 What sources ofcapital do firms use? © 2020 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Capital Debt Preferred Stock
- 72. Common Equity Retained Earnings NewCommon Stock Short-Term Debt Long-Term Debt
- 73. Calculating the WeightedAverage Cost of Capital WACC = wdrd(1 – T) + wprp + wcrs The w’s refer to the firm’s capital structure weights: wd=weight of the debt wp=weight of the preferred stock wc=weight of the common equity The r’s refer to the cost of each component: rd=before-tax cost of the debt rp =cost of the preferred stock rs =cost of the common equity
- 74. 3 Before-tax or after-taxcapital costs? Stockholders focus on after-tax CFs. Therefore, we should focus on after-tax capital costs; i.e., use after-tax costs of capital in WACC. Only rd needs adjustment, because interest is tax deductible. After-tax cost of debt=Interest rate on debt - Tax saving © 2020 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Cost of Debt WACC = wdrd(1 – T) + wprp + wcrs rd is the marginal cost of debt capital. The yield to maturity on outstanding long-term debt is often
- 75. used as ameasure of rd. 5 Cost of Preferred Stock WACC = wdrd(1 – T) + wprp + wcrs rp is the marginal cost of preferred stock, which is the return investors require on a firm’s preferred stock. D is the preferred dividend. P is the current price of the preferred stock. Preferred dividends are not tax-deductible, so no tax adjustments necessary.
- 76. 6 The Cost ofCommon Equity Cost of equity is more challenging to estimate than the cost of debt or the cost of preferred stock because common stockholder’s rate of return is not fixed as there is no stated coupon rate or dividend. The costs will vary for two sources of equity: Retained earnings (No flotation costs) Note retained earnings are not a free source of capital. There is an opportunity cost. rs=cost of the retained earning New issue (incurs flotation costs) re=cost of new common stock
- 77. Cost estimation techniques ThreeWays to Determine the Cost of Common Equity, rs The Dividend Growth Model: rs = (D1/P0) + g The Capital Asset Pricing Model: rs = rf + β(rM – rf ) Bond-Yield-Plus-Risk-Premium: rs = Bond yield + risk premium= rd + RP
- 78. The Dividend GrowthModel Investors’ required rate of return (For Retained Earnings): D1 = Dividend expected one year hence P0 = Current price of common stock g = growth rate The Dividend Growth Model Investors’ required rate of return (For new issues) D1 = Dividends expected one year hence NP = Net proceeds per share = Stock price – flotation cost per share F=the percentage flotation cost required to sell the new stock g = growth rate
- 79. The Dividend GrowthModel Example: A company expects dividends this year to be $1.10, based upon the fact that $1 were paid last year. The firm expects dividends to grow 10% next year and into the foreseeable future. Stock is trading at $35 a share. Cost of retained earnings: Cost of new stock (with a $3 floatation cost per share):
- 80. The Capital AssetPricing Model CAPM: rs = rf + β(rM – rf ) rf = Risk Free rate rm =market risk return rm – rf = Market Risk Premium Capital Asset Pricing Model Example: If beta is 1.25, risk-free rate is 1.5% and expected return on market is 10% – rf) = .015 + 1.25(.10 – .015) = 12.125%
- 81. Capital Asset PricingModel Variable estimates CAPM is easy to apply. Also, the estimates for model variables are generally available from public sources. Risk Free Rate: Wide range of US government securities on which to base risk-free rate Beta: Estimates of beta are available from a wide range of services, or can be estimated using regression analysis of historical data. Market risk premium: It can be estimated by looking at history of stock returns and premium earned over risk-free rate.
- 82. Bond-Yield-Plus-Risk-Premium Approach rd =10% and RP = 4%. This RP(risk premium) is not the same as the CAPM RPM. This method produces a ballpark estimate of rs, and can serve as a useful check. rs = rd + RP rs = 10.0% + 4.0% = 14.0% 15 What factors influence a company’s composite WACC? Market conditions. The firm’s capital structure and dividend policy. The firm’s investment policy. Firms with riskier projects generally have a higher WACC.
- 83. 16 Should the companyuse the composite WACC as the hurdle rate for each of its projects? NO! The composite WACC reflects the risk of an average project undertaken by the firm. Therefore, the WACC only represents the “hurdle rate” for a typical project with average risk. Different projects have different risks. The project’s WACC should be adjusted to reflect the project’s risk.
- 84. 17 Divisional Cost ofCapital p r D = P P D r p =