Cases 24 & 25 Victoria Chemicals

This week we will be doing a Capital Budgeting case.We will combine Case 24 and 25 into one long case where Victoria Chemicals will be dealing with a Mutually Exclusive Capital Budgeting decision.

You should reread the Principles of Finance textbook chapters (and your notes) dealing with the topic of Capital Budgeting and the decision rules used by companies to determine which projects are acceptable (and profitable).

The PPT files for the relevant chapters have been uploaded to Canvas.

Victoria Chemicals is considering upgrading its ageing plants in Merseyside and Rotterdam.Assume that they can do only one right now.You have to analyze all the given information for both plants and recommend one for updating.

The uploaded spreadsheet will help you with the quantitative analysis.Before you do that, there are some issues you have to deal with (qualitatively) in your case report.

In Case 24, there are sections titled Concerns of the Transport Division, Sales and Marketing Dept., Assistant Plant Manager, and Treasury Staff.Without doing any calculations, you have to discuss how the company should deal with each of these issues.You need to determine what is relevant (and what is not) in Capital Budgeting.Remember that to make the decision, you will be calculating NPV for each project using the given spreadsheet.

On page 354 in Case 24, they list four decision rules used by the company.Two of them are incorrect and should never be used in Capital Budgeting.Identify them, and explain why they should not be used.

In Exhibit 1 on page 355, they give you some data about the competing plants in this industry.What do the numbers tell us?

Exhibit 2 on page 356 should be used for the NPV calculations.For simplicity, you can focus only on the NPV numbers, although IRR is calculated at the same time.Some of the assumptions (and numbers) need to be corrected before you get the right NPV.Remember that NPV should be calculated only with the relevant incremental (or marginal) after-tax cash flows.If the cash flow is not relevant or marginal, it should not be used.Also, only real cash flows should be used, and not accounting numbers.

In Case 25, the only 'issue' you have to deal with is the option on the right-of-way.Think very carefully about this land purchase decision.What should the company do?Make the appropriate adjustments in the NPV calculations.

Exhibit 1 on pages 362-363 should be used for the NPV calculations.The same rules used in Case 24 apply here.Whatever assumptions you make should be used consistently for both cases.

The 'Erosion' numbers given here apply to the Sales Cannibalization effect mentioned in Case 24.If you think it is plausible and relevant, use the same number in both cases to reduce the NPV. Or don't.You can always have alternate scenarios when calculating NPV for Capital Budgeting Projects.

Make a recommendation after you have done all the analysis.What do you recommend the company should do in the long run? Justify your answer with appropriate arguments and data.Are there any additional factors/issues that you think should be considered in the decision making process?

Upload the spreadsheet as a separate document along with your written case report.

For the online discussion, I want you all to post an answer to the following question:

1. Why are the Merseyside and Rotterdam projects mutually exclusive? Justify your answer with appropriate arguments and data.

Intro Victoria Chemicals PLC TN This spreadsheet supports INSTRUCTOR analysis of the cases, "Victoria Chemicals PLC (A) & (B)" (Case 24). Copyright (C) 2008 by the Trustees of the University of Virginia Darden School Foundation. Revised 10_10_2009 Page 1 Intro ol Foundation. Page 2 Exhibit 2 VICTORIA CHEMICALS (A) Frank Greystock's DCF Analysis of Merseyside Project (Financial values in millions of British Pounds) Assumptions Annual Output (metric tons) Output Gain/Original Output Price/ton (pounds sterling) Inflation Rate (prices and costs) Gross Margin (ex. Deprec.) Old Gross Margin Energy Savings/Sales Yr. 1-5 Yr. 6-10 Yr. 11-15 Year Now 1. Estimate of Incremental Gross Profit New Output (tons) Lost Output--Construction New Sales (Millions) New Gross Margin New Gross Profit Old Output Old Sales Old Gross Profit Incremental Gross Profit 2. Estimate of Incremental WIP inventory New WIP inventory Old WIP inventory Incremental WIP inventory 3. Estimate of Incremental Depreciation New Depreciation 4. Overhead 5. Prelim. Engineering Costs Pretax Incremental Profit 6. Cash Flow Adjustments Less Capital Expenditur -12.00 Add back Depreciation Less Added WIP inventory 7. Free Cash Flow -12.00 NPV = IRR = 10.57 24.3% 250,000 7.0% 675 0.0% 12.50% 11.5% 1.25% 0.75% 0.0% 1 2008 Discount rate Tax Rate Investment Outlay (mill.) Depreciable Life (years) Salvage Value WIP Inventory/Cost of Goods Months Downtime, Construction Preliminary Engineering Costs Overhead/Investment 10.0% 30% 12.0 15 0 3.0% 1.5 0.5 3.5% 2 2009 3 2010 4 2011 5 2012 6 2013 7 2014 8 2015 9 2016 10 2017 11 2018 12 2019 13 2020 14 2021 15 2022 267,500 267,500 (33,438) 157.99 180.56 13.8% 13.8% 21.72 24.83 267,500 267,500 267,500 267,500 267,500 267,500 267,500 267,500 267,500 267,500 267,500 267,500 267,500 180.56 13.8% 24.83 180.56 13.8% 24.83 180.56 13.8% 24.83 180.56 13.3% 23.92 180.56 13.3% 23.92 180.56 13.3% 23.92 180.56 13.3% 23.92 180.56 13.3% 23.92 180.56 12.5% 22.57 180.56 12.5% 22.57 180.56 12.5% 22.57 180.56 12.5% 22.57 180.56 12.5% 22.57 250,000 168.75 19.41 2.32 250,000 168.75 19.41 5.42 250,000 168.75 19.41 5.42 250,000 168.75 19.41 5.42 250,000 168.75 19.41 5.42 250,000 168.75 19.41 4.52 250,000 168.75 19.41 4.52 250,000 168.75 19.41 4.52 250,000 168.75 19.41 4.52 250,000 168.75 19.41 4.52 250,000 168.75 19.41 3.16 250,000 168.75 19.41 3.16 250,000 168.75 19.41 3.16 250,000 168.75 19.41 3.16 250,000 168.75 19.41 3.16 4.09 4.48 -0.39 4.67 4.48 0.19 4.67 4.48 0.19 4.67 4.48 0.19 4.67 4.48 0.19 4.70 4.48 0.22 4.70 4.48 0.22 4.70 4.48 0.22 4.70 4.48 0.22 4.70 4.48 0.22 4.74 4.48 0.26 4.74 4.48 0.26 4.74 4.48 0.26 4.74 4.48 0.26 4.74 4.48 0.26 1.60 0.42 0.50 -0.20 1.39 0.42 1.20 0.42 1.04 0.42 0.90 0.42 0.78 0.42 0.68 0.42 0.59 0.42 0.55 0.42 0.55 0.42 0.55 0.42 0.55 0.42 0.55 0.42 0.55 0.42 0.55 0.42 3.61 3.80 3.96 4.10 3.32 3.42 3.51 3.55 3.55 2.20 2.20 2.20 2.20 2.20 1.60 0.39 1.85 1.39 -0.58 3.33 1.20 0.00 3.86 1.04 0.00 3.81 0.90 0.00 3.77 0.78 -0.03 3.08 0.68 0.00 3.07 0.59 0.00 3.05 0.55 0.00 3.03 0.55 0.00 3.03 0.55 -0.04 2.04 0.55 0.00 2.08 0.55 0.00 2.08 0.55 0.00 2.08 0.55 0.26 2.34 Exhibit 1 VICTORIA CHEMICALS (B) ANALYSIS OF ROTTERDAM PROJECT (Financial values in millions of British Pounds) Assumptions Annual Output (metric tons) Output Gain Per Year/Prior Year Maximum Possible Output Price/ton (pounds sterling) Inflation (prices and costs) Gross Margin Growth Rate/Year Maximum Possible Gross Margin Gross Margin Tax Rate Investment Outlay (millions Now 2001 2002 2003 250,000 2.0% 267,500 675 0.0% 0.5% 15.0% 11.5% 30.0% 3.5 5 1 1 Discount rate Depreciable Life (years) Overhead/Investment Salvage Value WIP Inventory/Cost of Goods Sold Terminal Value of Right-of-Way Months Downtime, Construction 2001 2002 2003 2004 10.0% 15 3.5% 0 3.0% 40 5 4 3 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Year Now 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 1. Estimate of Incremental Gross Profit New Output 255,000 260,100 265,302 267,500 267,500 267,500 267,500 267,500 267,500 267,500 267,500 267,500 267,500 267,500 267,500 Lost Output--Construction (106,250) (86,700) (66,326) New Sales (Millions) 100.41 117.05 134.31 180.56 180.56 180.56 180.56 180.56 180.56 180.56 180.56 180.56 180.56 180.56 180.56 New Gross Margin 11.5% 12.0% 12.5% 13.0% 13.5% 14.0% 14.5% 15.0% 15.0% 15.0% 15.0% 15.0% 15.0% 15.0% 15.0% New Gross Profit 11.55 14.05 16.79 23.47 24.38 25.28 26.18 27.08 27.08 27.08 27.08 27.08 27.08 27.08 27.08 Old Output 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 Old Sales 168.75 168.75 168.75 168.75 168.75 168.75 168.75 168.75 168.75 168.75 168.75 168.75 168.75 168.75 168.75 Old Gross Profit 19.41 19.41 19.41 19.41 19.41 19.41 19.41 19.41 19.41 19.41 19.41 19.41 19.41 19.41 19.41 Incremental Gross Profit (7.86) (5.36) (2.62) 4.07 4.97 5.87 6.78 7.68 7.68 7.68 7.68 7.68 7.68 7.68 7.68 2. Estimate of Incremental Depreciation Yr. 1 Outlays 0.67 0.58 0.50 0.43 0.38 0.33 0.28 0.24 0.23 0.23 0.23 0.23 0.23 0.23 0.23 Yr. 2 Outlays 0.14 0.12 0.10 0.09 0.08 0.07 0.06 0.05 0.05 0.05 0.05 0.05 0.05 0.05 Yr. 3 Outlays 0.15 0.13 0.11 0.09 0.08 0.07 0.06 0.05 0.05 0.05 0.05 0.05 0.05 Total, New Depreciation 0.67 0.72 0.78 0.67 0.58 0.50 0.43 0.37 0.33 0.33 0.33 0.33 0.33 0.33 0.33 3. Overhead 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4. Pretax Incremental Profit (8.53) (6.08) (3.39) 3.40 4.39 5.38 6.35 7.31 7.35 7.35 7.35 7.35 7.35 7.35 7.35 5. Tax Expense (2.56) (1.82) (1.02) 1.02 1.32 1.61 1.90 2.19 2.20 2.21 2.21 2.21 2.21 2.21 2.21 6. After-tax Profit (5.97) (4.26) (2.38) 2.38 3.08 3.76 4.44 5.12 5.14 5.15 5.15 5.15 5.15 5.15 5.15 7. Cash Flow Adjustments Add back Depreciation 0.67 0.72 0.78 0.67 0.58 0.50 0.43 0.37 0.33 0.33 0.33 0.33 0.33 0.33 0.33 Less added WIP inventory 1.81 (0.42) (0.44) (1.19) 0.03 0.03 0.03 0.03 0.12 Capital Spending 3.50 5.00 1.00 1.00 Terminal Value, land 40.00 8. Free Cash Flow (3.50) (12.12) (4.11) (2.16) 4.23 3.62 4.23 4.84 5.46 5.47 5.47 5.47 5.47 5.47 5.47 45.60 DCF, Rotterdam = IRR, Rotterdam = 15.06 17.3% 9. Adjustment for erosion in Merseyside volume: Lost Merseyside Output Lost Merseyside Revenue Lost Merseyside Gross Profits Lost Gross Profits after Taxes Change in Merseyside Inventory Total Effect on Free Cash Flow DCF, Erosion Merseyside -3.05 Cash flows after erosion (3.50) (12.12) DCF, Rotterdam Adjusted for Full Erosion at Merseyside = 12.01 - - (4.11) (2.16) 17,500 11.81 1.36 0.95 0.35 (0.60) 17,500 11.81 1.36 0.95 0.35 (0.60) 17,500 11.81 1.36 0.95 0.35 (0.60) 17,500 11.81 1.36 0.95 0.35 (0.60) 17,500 11.81 1.36 0.95 0.35 (0.60) 17,500 11.81 1.36 0.95 0.35 (0.60) 17,500 11.81 1.36 0.95 0.35 (0.60) 17,500 11.81 1.36 0.95 0.35 (0.60) 17,500 11.81 1.36 0.95 0.35 (0.60) 17,500 11.81 1.36 0.95 0.35 (0.60) 17,500 11.81 1.36 0.95 0.35 (0.60) 17,500 11.81 1.36 0.95 0.35 (0.60) 3.64 3.03 3.64 4.25 4.86 4.88 4.88 4.88 4.88 4.88 4.88 45.00 CHAPTER 11 Cash Flow Estimation and Risk Analysis 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 1 Topics Estimating cash flows: Risk analysis: Relevant cash flows Working capital treatment Sensitivity analysis Scenario analysis Simulation analysis Real options 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 2 The Big Picture: Project Risk Analysis Project's Cash Flows (CFt) CF NPV = (1 1+ r )1 Initial cost Market interest rates Market risk aversion CF + (1 2+ r)2 CF + + N (1 + r)N Project's risk-adjusted cost of capital (r) Project's debt/equity capacity Project's business risk 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Proposed Project Data $200,000 cost + $10,000 shipping + $30,000 installation. Economic life = 4 years. Salvage value = $25,000. MACRS 3-year class. Continued... 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 4 Project Data Annual unit sales = 1,250. Unit sales price = $200. Unit costs = $100. Net working capital: (Continued) NWCt = 12%(Salest+1) Tax rate = 40%. Project cost of capital = 10%. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 5 Incremental Cash Flow for a Project Project's incremental cash flow is: Corporate cash flow with the project Minus Corporate cash flow without the project. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 6 Treatment of Financing Costs Should you subtract interest expense or dividends when calculating CF? NO. We discount project cash flows with a cost of capital that is the rate of return required by all investors (not just debtholders or stockholders), and so we should discount the total amount of cash flow available to all investors. They are part of the costs of capital. If we subtracted them from cash flows, we would be double counting capital costs. 7 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Sunk Costs Suppose $100,000 had been spent last year to improve the production line site. Should this cost be included in the analysis? NO. This is a sunk cost. Focus on incremental investment and operating cash flows. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 8 Incremental Costs Suppose the plant space could be leased out for $25,000 a year. Would this affect the analysis? Yes. Accepting the project means we will not receive the $25,000. This is an opportunity cost and it should be charged to the project. A.T. opportunity cost = $25,000 (1 - T) = $15,000 annual cost. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 9 Externalities If the new product line would decrease sales of the firm's other products by $50,000 per year, would this affect the analysis? Yes. The effects on the other projects' CFs are \"externalities.\" Net CF loss per year on other lines would be a cost to this project. Externalities will be positive if new projects are complements to existing assets, negative if substitutes. 10 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. What is an asset's depreciable basis? Basis = Cost + Shipping + Installation $240,000 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 11 Annual Depreciation Expense (Thousands of Dollars) Year % X (Initial Basis) $240 = Deprec. $80.0 1 0.3333 2 0.4445 106.7 3 0.1481 35.5 4 0.0741 17.8 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 12 Annual Sales and Costs Units Unit Price Unit Cost Sales Costs Year 1 Year 2 Year 3 Year 4 1,250 1,250 1,250 1,250 $200 $206 $212.18 $218.55 $100 $103 $106.09 $109.27 $250,00 0 $125,00 0 $257,50 $265,22 $273,18 0 5 8 $128,75 $132,61 $136,58 0 3 8 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 13 Why is it important to include inflation when estimating cash flows? Nominal r > real r. The cost of capital, r, includes a premium for inflation. Nominal CF > real CF. This is because nominal cash flows incorporate inflation. If you discount real CF with the higher nominal r, then your NPV estimate is too low. Continued... 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 14 Inflation (Continued) Nominal CF should be discounted with nominal r, and real CF should be discounted with real r. It is more realistic to find the nominal CF (i.e., increase cash flow estimates with inflation) than it is to reduce the nominal r to a real r. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 15 Operating Cash Flows (Years 1 and 2) Sales Costs Deprec. EBIT Taxes (40%) EBIT(1 - T) + Deprec. Net Op. CF Year 1 $250,000 125,000 79,992 $ 45,008 18,003 $ 27,005 79,992 $106,997 Year 2 $257,500 128,750 106,680 $ 22,070 8,828 $ 13,242 106,680 $119,922 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 16 Operating Cash Flows (Years 3 and 4) Sales Costs Deprec. EBIT Taxes (40%) EBIT(1 - T) + Deprec. Net Op. CF Year 3 $265,225 132,613 35,544 $ 97,069 38,827 $ 58,241 35,544 $ 93,785 Year 4 $273,188 136,591 17,784 $118,807 47,523 $ 71,284 17,784 $ 89,068 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 17 Cash Flows Due to Investments in Net Working Capital (NWC) CF Due to NWC Sales Investment (% of sales) in NWC Year Year Year Year Year 0 1 $250,000 2 257,500 3 265,225 4 273,188 $30,000 30,900 31,827 32,783 0 -$30,000 -900 -927 -956 32,783 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 18 Salvage Cash Flow at t = 4 (000s) Salvage Value Book Value Gain or loss Tax on SV Net Terminal CF $25 0 $25 10 $15 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 19 What if you terminate a project before the asset is fully depreciated? Basis = Original basis - Accum. deprec. Taxes are based on difference between sales price and tax basis. Cash flow = Sale - Taxe from sale proceed s s paid 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 20 Example: If Sold After 3 Years for $25 ($ thousands) Original basis = $240. After 3 years, basis = $17.8 remaining. Sales price = $25. Gain or loss = $25 - $17.8 = $7.2. Tax on sale = 0.4($7.2) = $2.88. Cash flow = $25 - $2.88 = $22.12. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 21 Example: If Sold After 3 Years for $10 ($ thousands) Original basis = $240. After 3 years, basis = $17.8 remaining. Sales price = $10. Gain or loss = $10 - $17.8 = -$7.8. Tax on sale = 0.4(-$7.8) = -$3.12. Cash flow = $10 - (-$3.12) = $13.12. Sale at a loss provides a tax credit, so cash flow is larger than sales price! 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 22 Net Cash Flows for Years 1-2 Init. Cost Op. CF NWC CF Salvage CF Net CF Year 0 Year 1 Year 2 0 0 $240,000 0 $106,997 $119,922 -$30,000 -$900 -$927 0 0 0 - $106,097 $118,995 $270,000 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 23 Net Cash Flows for Years 3-4 Init. Cost Op. CF NWC CF Salvage CF Net CF Year 3 Year 4 0 0 $93,785 $89,068 -$955 $32,782 0 $15,000 $92,830 $136,850 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 24 Project Net CFs Time Line 0 1 2 (270,000)106,097 118,995 3 4 92,830 136,850 Enter CFs in CFLO register and I/YR = 10. NPV = $88,010. IRR = 23.9%. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 25 What is the project's MIRR? 0 10% 1 2 (270,000)106,097 118,995 3 92,830 4 136,850 102,113 143,984 141,215 (270,000) MIRR = ? 524,162 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 26 Calculator Solution Enter positive CFs in CFLO. Enter I/YR = 10. Solve for NPV = $358,009.72. Now use TVM keys: PV = -358,009.72, N = 4, I/YR = 10; PMT = 0; Solve for FV = 524,162.03. (This is TV of inflows) Use TVM keys: N = 4; FV = 524,162.03; PV = -270,000; PMT= 0; Solve for I/YR = 18.0%. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 27 What is the project's payback? ($ thousands) 0 1 2 3 4 (270) 106 119 93 137 (45) 48 185 Cumulative: (270) (164) Payback = 2 + $45/$93 = 2.5 years. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 28 What does \"risk\" mean in capital budgeting? Uncertainty about a project's future profitability. Measured by NPV, IRR, beta. Will taking on the project increase the firm's and stockholders' risk? 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 29 Is risk analysis based on historical data or subjective judgment? Can sometimes use historical data, but generally cannot. So risk analysis in capital budgeting is usually based on subjective judgments. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 30 What three types of risk are relevant in capital budgeting? Stand-alone risk Corporate risk Market (or beta) risk 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 31 Stand-Alone Risk The project's risk if it were the firm's only asset and there were no shareholders. Ignores both firm and shareholder diversification. Measured by the or CV of NPV, IRR, or MIRR. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 32 Probability Density Flatter distribution, larger , larger stand-alone risk. 0 E(NPV) NPV 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 33 Corporate Risk Reflects the project's effect on corporate earnings stability. Considers firm's other assets (diversification within firm). Depends on project's , and its correlation, , with returns on firm's other assets. Measured by the project's corporate beta. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 34 Project X is negatively correlated to firm's other assets, so has big diversification benefits Profitability If r = 1.0, no diversification benefits. If r 0 CV 685 94 -$166,208 $163 $84,551 86.9% 0.93 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 52 Interpreting the Results Inputs are consistent with specified distributions. Units: Mean = 1,252; St. Dev. = 199. Price: Mean = $200; St. Dev. = $30. Mean NPV = $88,808. Low probability of negative NPV (100% - 87% = 13%). 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 53 Histogram of Results 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 54 What are the advantages of simulation analysis? Reflects the probability distributions of each input. Shows range of NPVs, the expected NPV, NPV, and CVNPV. Gives an intuitive graph of the risk situation. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 55 What are the disadvantages of simulation? Difficult to specify probability distributions and correlations. If inputs are bad, output will be bad: \"Garbage in, garbage out.\" (More...) 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 56 What are the disadvantages of simulation? Sensitivity, scenario, and simulation analyses do not provide a decision rule. They do not indicate whether a project's expected return is sufficient to compensate for its risk. Sensitivity, scenario, and simulation analyses all ignore diversification. Thus they measure only stand-alone risk, which may not be the most relevant risk in capital budgeting. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 57 If the firm's average project has a CV of 0.2 to 0.4, is this a high-risk project? What type of risk is being measured? CV from scenarios = 1.15, CV from simulation = 0.93. Both are > 0.4, this project has high risk. CV measures a project's standalone risk. High stand-alone risk usually indicates high corporate and market risks. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 58 With a 3% risk adjustment, should our project be accepted? Project r = 10% + 3% = 13%. That's 30% above base r. NPV = $65,350. Project remains acceptable after accounting for differential (higher) risk. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 59 Should subjective risk factors be considered? Yes. A numerical analysis may not capture all of the risk factors inherent in the project. For example, if the project has the potential for bringing on harmful lawsuits, then it might be riskier than a standard analysis would indicate. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 60 What is a real option? Real options exist when managers can influence the size and risk of a project's cash flows by taking different actions during the project's life in response to changing market conditions. Alert managers always look for real options in projects. Smarter managers try to create real options. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 61 What are some types of real options? Investment timing options Growth options Expansion of existing product line New products New geographic markets 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 62 Types of real options (Continued) Abandonment options Contraction Temporary suspension Flexibility options 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 63 Chapter 10 The Basics of Capital Budgeting: Evaluating Cash Flows 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 1 Topics Overview and \"vocabulary\" Methods NPV IRR, MIRR Profitability Index Payback, discounted payback Unequal lives Economic life Optimal capital budget 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 2 The Big Picture: The Net Present Value of a Project Project's Cash Flows (CFt) CF NPV = (1 1+ r )1 Initial cost Market interest rates Market risk aversion CF + (1 2+ r)2 CF + + N (1 + r)N Project's risk-adjusted cost of capital (r) Project's debt/equity capacity Project's business risk 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. What is capital budgeting? Analysis of potential projects. Long-term decisions; involve large expenditures. Very important to firm's future. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 4 Steps in Capital Budgeting Estimate cash flows (inflows & outflows). Assess risk of cash flows. Determine r = WACC for project. Evaluate cash flows. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 5 Capital Budgeting Project Categories 1. Replacement to continue profitable operations 2. Replacement to reduce costs 3. Expansion of existing products or markets 4. Expansion into new products/markets 5. Contraction decisions 6. Safety and/or environmental projects 7. Mergers 6 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Independent versus Mutually Exclusive Projects Projects are: independent, if the cash flows of one are unaffected by the acceptance of the other. mutually exclusive, if the cash flows of one can be adversely impacted by the acceptance of the other. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 7 Cash Flows for Franchises L and S 0 1 2 3 -100.00 10 60 80 0 1 2 3 70 50 20 L's CFs: S's CFs: -100.00 10% 10% 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 8 NPV: Sum of the PVs of All Cash Flows N CFt NPV = (1 + t= t r) 0 Cost often is CF0 and is negative. N NPV = t= 1 CFt - CF 0 t (1 + r) 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 9 What's Franchise L's NPV? 0 L's CFs: -100.00 1 2 3 10 60 80 10% 9.09 49.59 60.11 18.79 = NPVL NPVS = $19.98. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 10 Calculator Solution: Enter Values in CFLO Register for L -100 CF0 10 CF1 60 CF2 80 CF3 10 I/YR NPV = 18.78 = NPVL 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 11 Rationale for the NPV Method NPV = PV inflows - Cost This is net gain in wealth, so accept project if NPV > 0. Choose between mutually exclusive projects on basis of higher positive NPV. Adds most value. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 12 Using the NPV measure, which franchise(s) should be accepted? If Franchises S and L are mutually exclusive, accept S because NPVs > NPVL. If S & L are independent, accept both; NPV > 0. NPV is dependent on cost of capital. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 13 Internal Rate of Return: IRR 0 1 2 3 CF0 Cost CF1 CF2 Inflows CF3 IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = 0. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 14 NPV: Enter r, solve for NPV. N CFt (1 + t=0 t r) = NPV 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 15 IRR: Enter NPV = 0, Solve for IRR N t= 0 CFt =0 (1 + IRR)t IRR is an estimate of the project's rate of return, so it is comparable to the YTM on a bond. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 16 What's Franchise L's IRR? 0 IRR = ? 1 2 3 -100.00 10 60 80 PV1 PV2 PV3 0 = NPV Enter CFs in CFLO, then press IRR: IRRL = 18.13%. IRRS = 23.56%. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 17 Finding IRR if CFs are Constant 0 1 2 3 -100 40 40 40 INPUTS3 -100 N 40 I/YR 0 PV PMT FV OUTPUT 9.70% Or, with CFLO, enter CFs and press IRR = 9.70%. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 18 Rationale for the IRR Method If IRR > r, then the project's rate of return is greater than its cost-some return is left over to boost stockholders' returns. Example: r= 10%, IRR = 15%. So this project adds extra return to shareholders. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 19 Decisions on Franchises S and L per IRR If S and L are independent, accept both: IRRS > r and IRRL > r. If S and L are mutually exclusive, accept S because IRRS > IRRL. IRR is not dependent on the cost of capital used. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 20 Construct NPV Profiles Enter CFs in CFLO and find NPVL and NPVS at different discount NPVL NPVS rates: r 0 5 10 15 20 50 33 19 7 (4) 40 29 20 12 5 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 21 NPV Profile L Crossover Point = 8.7% S IRRS = 23.6% IRRL = 18.1% 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. NPV and IRR: No conflict for independent projects. NPV ($) IRR > r and NPV > 0 Accept. r > IRR and NPV NPVS , IRRS > IRRL CONFLICT r > 8.7%: NPVS> NPVL , IRRS > IRRL NO CONFLICT S 8.7 IRRL IRRS r (%) 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 24 To Find the Crossover Rate Find cash flow differences between the projects. See data at beginning of the case. Enter these differences in CFLO register, then press IRR. Crossover rate = 8.68%, rounded to 8.7%. Can subtract S from L or vice versa and consistently, but easier to have first CF negative. If profiles don't cross, one project dominates the other. 25 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Two Reasons NPV Profiles Cross Size (scale) differences. Smaller project frees up funds at t = 0 for investment. The higher the opportunity cost, the more valuable these funds, so high r favors small projects. Timing differences. Project with faster payback provides more CF in early years for reinvestment. If r is high, early CF especially good, NPVS > NPVL. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 26 Modified Internal Rate of Return (MIRR) MIRR is the discount rate that causes the PV of a project's terminal value (TV) to equal the PV of costs. TV is found by compounding inflows at WACC. Thus, MIRR assumes cash inflows are reinvested at WACC. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 27 MIRR for Franchise L: First, find PV and TV (r = 10%). 0 10% -100.0 1 2 3 10.0 60.0 80.0 10% 10% 100.0 PV outflows 66.0 12.1 158.1 TV inflows 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 28 Second, find discount rate that equates PV and TV. 0 -100.0 1 2 MIRR = 16.5% PV outflows 3 158.1 TV inflows $100 = MIRRL = 16.5% $158.1 (1+MIRRL)3 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 29 To find TV with financial calculator: Step 1, Find PV of inflows. First, enter cash inflows in CFLO register: CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80 Second, enter I/YR = 10. Third, find PV of inflows: Press NPV = 118.78 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 30 Step 2, Find TV of inflows. Enter PV = -118.78, N = 3, I/YR = 10, PMT = 0. Press FV = 158.10 = FV of inflows. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 31 Step 3, Find PV of outflows. For this problem, there is only one outflow, CF0 = -100, so the PV of outflows is -100. For other problems there may be negative cash flows for several years, and you must find the present value for all negative cash flows. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 32 Step 4, Find \"IRR\" of TV of inflows and PV of outflows. Enter FV = 158.10, PV = -100, PMT = 0, N = 3. Press I/YR = 16.50% = MIRR. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 33 Profitability Index The profitability index (PI) is the present value of future cash flows divided by the initial cost. It measures the \"bang for the buck.\" 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 34 Franchise L's PV of Future Cash Flows Project L: 0 10% 1 2 3 10 60 80 9.09 49.59 60.11 118.79 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 35 Franchise L's Profitability Index PIL = PV future CF Initial cost = $118.79 $100 PIL = 1.1879 PIS = 1.1998 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 36 What is the payback period? The number of years required to recover a project's cost, or how long does it take to get the business's money back? 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 37 Payback for Franchise L 0 CFt -100 Cumulative -100 PaybackL 1 10 -90 2 2.4 60 -30 0 3 80 50 = 2 + $30/$80 = 2.375 years 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 38 Payback for Franchise S 0 CFt 1 1.6 2 3 -100 70 50 20 Cumulative -100 -30 0 20 40 PaybackS = 1 + $30/$50 = 1.6 years 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 39 Strengths and Weaknesses of Payback Strengths: Provides an indication of a project's risk and liquidity. Easy to calculate and understand. Weaknesses: Ignores the TVM. Ignores CFs occurring after the payback period. No specification of acceptable payback. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 40 Discounted Payback: Uses Discounted CFs 0 10% 1 2 3 10 60 80 CFt -100 PVCFt -100 9.09 49.59 60.11 Cumulative -100 -90.91 -41.32 18.79 Discounted =2 + $41.32/$60.11 = 2.7 yrs payback Recover investment + capital costs in 2.7 yrs. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 41 Normal vs. Nonnormal Cash Flows Normal Cash Flow Project: Cost (negative CF) followed by a series of positive cash inflows. One change of signs. Nonnormal Cash Flow Project: Two or more changes of signs. Most common: Cost (negative CF), then string of positive CFs, then cost to close project. For example, nuclear power plant or strip mine. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 42 Inflow (+) or Outflow (-) in Year 0 1 2 3 4 5 N - + + + + + N - + + + + - - - - + + + N + + + - - - N - + + - + - NN NN 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. NN 43 Pavilion Project: NPV and IRR? 0 r = 10% -800,000 1 2 5,000,000 -5,000,000 Enter CFs in CFLO, enter I/YR = 10. NPV = -386,777 IRR = ERROR. Why? 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 44 Nonnormal CFsTwo Sign Changes, Two IRRs NPV Profile NPV ($) IRR2 = 400% 450 0 -800 100 400 r (%) IRR1 = 25% 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 45 Logic of Multiple IRRs At very low discount rates, the PV of CF2 is large & negative, so NPV 0. Result: 2 IRRs. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 46 Finding Multiple IRRs with Calculator 1. Enter CFs as before. 2. Enter a \"guess\" as to IRR by storing the guess. Try 10%: 10 STO IRR = 25% = lower IRR (See next slide for upper IRR) 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 47 Finding Upper IRR with Calculator Now guess large IRR, say, 200: 200 STO IRR = 400% = upper IRR 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 48 When there are nonnormal CFs and more than one IRR, use MIRR. 0 1 2 -800,000 5,000,000 -5,000,000 PV outflows @ 10% = -4,932,231.40. TV inflows @ 10% = 5,500,000.00. MIRR = 5.6% 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 49 Accept Project P? NO. Reject because MIRR = 5.6% NPVT, but which is better? T can be repeated! CF0 T -100 F -100 CF1 60 33.5 2 4 I/YR 10 10 NPV 4.132 6.190 NJ 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 52 Equivalent Annual Annuity Approach (EAA) Convert the PV into a stream of annuity payments with the same PV. T: N=2, I/YR=10, PV=-4.132, FV = 0. Solve for PMT = EAAT = $2.38. F: N=4, I/YR=10, PV=-6.190, FV = 0. Solve for PMT = EAAF = $1.95. T has higher EAA, so it is a better project. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 53 Replacement Chain Note that Project T could be repeated after 2 years to generate additional profits. Use replacement chain to put on common life. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 54 Replacement Chain Approach: F with Replication ($ thousands) 0 1 2 3 4 T: -100 60 60 -100 -40 60 60 60 60 -100 60 NPV = $7.547. 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 55 Or, Use NPVs 0 4.132 3.415 7.547 1 10% 2 3 4 4.132 The repeated NPV of Project T is bigger than F's NPV ($7.514 > $6.190). 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 56 Suppose the cost to repeat T in two years rises to $105,000? 0 T: -100 10% 1 2 3 4 60 60 -105 -45 60 60 NPVT = $3.415