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Chapter 8

Chapter 8. Net Present Value & Other Investment Criteria. We’re starting a NEW SECTION of the course: Section 1 – Overview Ch 1: Intro Section 2 – Financial Statements and CFs Ch 2: Financial Statements and CF definitions Ch 3: Ratios Section 3 – Valuation of future CFs

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Chapter 8

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  1. Chapter 8 Net Present Value & Other Investment Criteria

  2. We’re starting a NEW SECTION of the course: Section 1 – Overview • Ch 1: Intro Section 2 – Financial Statements and CFs • Ch 2: Financial Statements and CF definitions • Ch 3: Ratios Section 3 – Valuation of future CFs • Ch 4: Intro to TVM (Single CFs) • Ch 5: More TVM (Multiple CFs - Annuities) Section 4 – Stocks and Bonds • Ch 6: Bonds • Ch 7: Stocks Section 5 – Capital Budgeting • Ch 8: NPV and other Decision Criteria • Ch 9: Making Cap Budgeting Decisions – Calc CFs

  3. Capital Budgeting is… • Budgeting the firm’s Capital • Capital vs. Working Capital • Spending the big money • Not small, short-term money • The light bill, salaries, office supplies… • But BIG, long-term money • These are called Capital Expenditures • They are recorded on the Balance Sheet • They are depreciated • So if a firms sells stocks, sells bonds, or retains earnings… • What does it do with the money?

  4. Here’s the idea: • The CAPITAL BUDGETING DECISION is about ADDING VALUEto the firm • To pay for capital investments, a firm can sell stocks, sell bonds or retain earnings… • But SHOULDa firm sell stocks, sell bonds or retain earnings? • Does it have something WORTHWILEto do with the money? • Does it have GOOD CAPITAL PROJECTS? • Does the proposed project make ENOUGH MONEY? • Does the proposed project make ADD VALUE? • If the proposed project does not add value… • ThenDON’Tsell stocks, DON’Tsell bonds, DON’Tretain earnings • Instead the firm should PAY DIVIDENS

  5. Net Present Value • How do we know if a proposed project Adds Value? • Or makes Enough Money? • We calculatethe proposed project’s Net Present Value • Called NPV Here’s how NPV analysis works: • The Decision Rule: • If the Net Present Valueis POSITIVE • Then the project Adds Value • It makes Enough Money • So the company should InvesttheCapital • or ”Budget” the Capital

  6. Net Present Value is • The PV of all the project’s future cash flows… • CF1, CF2, CF3,… • Discounted at the Properdiscount rate (R)… • A higher discount rate for riskierprojects • A lower discount rate for less risky projects • Plus the initial (time 0) cash flow... • CF0 is the Initial Cost of the project • CF0 is usually an outflow, so it is usually negative • If the PV of the Future CFsis greater than the Cost: • Then the NPV > 0 and the project Adds Value! • If the company can Spend $100 today • For something Worth$110(in PV terms – so also “today”) • Then do the project!

  7. How to think about NPV • Think about paying $1,000 today for a something long-term: • A bond, an annuity, a truck, a machine… • It will pay net of $400per year for 3 years CF1 = $400, CF2 = $400, CF3 = $400 $400 x 3 = $1,200 > $1,000 so it makes money • But does it make enough money? • Is the PV of $400for three years greater than the cost of $1,000? • How risky is the $400 per year? • In other words: What’s the proper discount rate? • What return do the investors require?

  8. How to think about NPV • Also assume the proper discount rate is 10% • We’ll see where 10% come from later • Pay $1,000 now for $400 at time 1, 2 and 3. • Is it a good investment? • First we have to get all the CFs to the same time period • Use time zero since that is when we make the decison • So take the PV of all the CFs • Since all CFs are the same (an annuity), use the TVM function: N = 3 R = 10% PMT = $400 PV = $995 • So pay $1,000 today To get CFs that are worth only $995 • We would lose $5 in present value terms • NPV = -$5  So don’t do it!

  9. Clicker Question: • A project costs $100,000 today (buy a truck) • The project will have Net CFs of $18,000 per year for 10 years • $18,000 is the net CF. It equals CASH IN (revenues) less CASH OUT (expenses) for each of the next 10 years • The proper discount rate is 10% • Calculate the project’s Net Present Value: Hints: • First calculate the PV of $18k per year for 10 years discounted at 10% • (What is the difference between PV and NPV?) • $10,602 • $80,000 • $100,000 • $110,602 • $180,602

  10. Clicker Answer: • A project costs $100,000 today (buy a truck) and has CFs of $18,000 per year for 10 years • The proper discount rate is 10%. • NPV = Initial CF + PV of Future CFs • PV of Future CFs: N = 10 R = 10% PMT = 18,000 PV = $110,602 • Initial CF = -100,000 • NPV = – $100,000 + $110,602 = $10,602 The Answer is A • So the firm can pay $100,000 for truck that will earn (in PV terms) $110,602 • So the firm can trade $100,000 for $110,602 • This adds $10,602 of value to the firm! • Why don’t firm’s do this all the time? They do.

  11. Chapter Outline: • Net Present Value • How to CALCULATE NPV • How to INTERPRETNPV • Rules: • NPV Rule • Payback Period Rule • Internal Rate of Return (IRR) • Profitability Index • Average Accounting Return • Modified Internal Rate of Return (We’ll skip these) • Why the other rules flawed: • But why people still use them • Look at the Positive Cash Flowrule • Used mostly for start-ups • Similar to Debt Service Rules: Will the firm generate enough revenue to pay interest expense? • The “Positive CF Rule” is not in the text

  12. 8.1 Net Present Value An NPV Example: A new product line will cost $165k today • Buy a machine for $165k • This is a cash OUTFLOW (“cost”); CF0 = -$165,000 • Earn CF1= $63,120; CF2 = $70,800; CF3 = $91,080 • The proper discount rate is 12% • Why 12%? Because of the project’s risk. So should we do the project? • Does the project add value to the firm? • Does it make enough money? • Is the PV of all the projects future CFs greater than its cost? • Does the project have positive NPV? These are synonyms!

  13. Example Continued: CF0 = -$165,000; CF1= $63,120; CF2 = $70,800; CF3 = $91,080 R= 12% NPV = CF0 + CF1/(1 + R) + CF2/(1 + R)2 + CF3/(1 + R)3 = -$165 + $63.12/(1.12) + $70.80/(1.12)2 + $91.08 /(1.12)3 = -$165 + $177.63 = $12.63 • NPV > 0 so Do the Project(or commit the firm’s capital) • Why? • Because the present value of the project’s future cash flows is greater than it’s cost ($165 < $177.63) • Firm trades $165 today for future CFs worth $177.63 • In today’s terms • So the project increases the firm’s value by $12.63 • CFs in today’s terms are called Discounted Cash Flows or DCFs

  14. New Example: • A new product line will cost $30k today • Revenues will be $20k per year for 8 years • Costs will be $14k per year for 8 years • At the end of year 8, we can sell the machine for $2k • The machine’s “Salvage Value” is $2k • The proper discount rate is 15% • Should we do the project? • In other words: • Does it have positive NPV? • Is the PV of all the future CFs greater than the cost? • Are the DCFs greater then the cost? • Does it add value to the firm? • Does it earn enough to compensate our investors?

  15. Cash Flow Diagram: CF0= -$30; CF1 to CF7 = $6; CF8 = $8; R = 15% NPV = CF0 + PV(CF1 through CF8) NPV = CF0 + CF1/(1+R) + CF2/(1+R)2 + CF3/(1+R)3 + … + CF8/(1+R)8 NPV = -$30 + $27.58 = -$2.42 NPV < 0 so don’t do the project Don’t trade $30k for $27.58k Let’s see how to do this on your calculator 

  16. How to do NPV on your calculator: Recall: CF0 = -$30; CF1 to CF7 = $6; CF8 = $8; R = 15% First Way: Use the TVM Function: • N = 8; R = 15%; PMT = 6; FV = 2; PV = -27.58 (Why does FV = 2?) • Press +/-, then add -$30 • NPV = $27.58 – $30 = -$2.42 (We can only use TVM function since CF1 through CF7 are $6 and CF8 is $6 + $2) Second Way: Use the Cash Flow Register Function: • HP: Use CFj and Nj buttons to input cash flows • CFj is the amount of the CF, Njis the number of times it occurs • Use I/YR to input rate • Use NPV button to calculate NPV • TI: Use {CF} register, the down arrow {¯}, {Enter}, {NPV} and {CPT} buttons to input cash flows and compute NPV

  17. The Cash Flow Register Function - Part 1 First Some Notation: Our subscripts denote the timingof the CF: • CF0 = -$30 occurs at time zero • CF1 through CF7 = $6 occurs at times 1 through 7 • CF8 = $8 occurs at time 8 Calculator’s subscripts change when the CFs changes: • CF0 = -$30 occurs at time 0 • CF1 = $6 and it occurs 7 times so N1 = 7 • CF2 = $8 and it occurs 1 time so N2 = 1 • The calculator knows that CF2 occurs after CF1 is finished • So CF2 must occur at time 8 • Since N2 = 1, the calculator knows the $8 CF occurs once at time 8

  18. General Procedure for Entering CFs into Your Calculator • Enter CF0 • Enter the 1st distinct future CF Enter the number of times it occurs • Enter the 2nd distinct future CF Enter the number of times it occurs • Enter the 3nd distinct future CF Enter the number of times it occurs… For this example there are 2 distinct futureCFs(after CF0): • The first is $6 and it occurs 7 times • The second is $8 and it occurs 1 time

  19. Using the Calculator to Calculate NPV

  20. Now Calculate NPV for the First Example: Recall: • CF0= -$165,000 • CF1= $63,120 • CF2= $70,800 • CF3= $91,080 • R = 12% Note: • Three distinct CFs after CF0. • Each occurs one time. • Since each CF occurs only one time • So you do not have to enter the number of times in to the calculator • Since one time is the default! • So note for the TI the “Double Arrow” {¯} {¯} on the next page

  21. Using the Calculator to Calculate NPV for the First Example: CF0= -$165,000 CF1= $63,120 CF2= $70,800 CF3= $91,080 R= 12%

  22. Another Example: A Project has the following Net CFs: • Cost of the project (at time 0) is $200 • It has a net inflow of $100 in years 1 and 2 • It has a net outflow of $100 in year 3 • It has a net inflow of $200 in year 4 Must pay more in year 3. Why? Maybe to Refurbish the machines? Should the firm go ahead with the project? • Does the project add value? • Does it earn enough to compensate the investors? • Is the NPV >0? First write down the CFs for the project:

  23. Calculate NPV: CF0 = -200, CF1 = 100 2 times, CF2 = -100, CF3 = 200

  24. Example Continued: What if the discount rate is 20% instead of 10%. • The cash flows are already entered so just change R: Now the project’s NPV < 0, so the project does not add value at R = 20% • Why would the discount rate (R) be 20% instead of 10%? • Because it costs the firm more to raise capital. • In other words: The investors demand a greater return. (Why? ) • Possible reasons: • It is a riskier project: Before Toilet Paper CFs (10%), Now Yacht CFs (20%) • The general cost of capital in the economy is higher: • More perceived risk in the overall (macro) economy • Less money available to be invested (lower supply of money  higher price of money) • So what happens when the Fed Eases? Tightens?

  25. Clicker Question: • A project costs $3,000 today • It will have positive CFs of $600 per year for 10 years. • In addition, it will cost $200 to clean up the mess caused by the project at time 10 • The proper discount rate is 10%. • Calculate the project’s NPV: • $609.63 • $2,800.00 • $3,000.00 • $3,400.77 • $4,207.25

  26. Clicker Answer: Time Subscripts: CF0 = -$3,000, CF1 through CF9 = $600, CF10 = $400 Calc Subscripts: CF0= -$3,000, CF1= $600 nine times, CF2= $400 The Answer is A. So pay $3,000 today for DCFs worth $3,609.63 So the NET Present Value (or NPV) = $609.63 Extra Question: What if the discount rate increases to 15%? The new NPV is -$38.18 < 0

  27. Calculating NPV with EXCEL VERY IMPORTANT: • The Excel NPV() function does NOT calculate NPV!!!! • It calculates PV of the CFs ! • Also called the Discounted Cash Flows (or DCFs) • Example on page 242shows how to calculate NPV in Excel Make sure you can do this! • See if you can use Excel to calculate the NPV for the previous examples in the slides.

  28. Consider NPV as a Decision Rule: • NPV accounts for the Time Valueof money • Later CFs are discounted more • $100 discounted by 10% in 2 years = $100/1.12 = $83 • $100 discounted by 10% in 10years = $100/1.110= $39 • NPV accounts for Risk of the cash flows • Greater the risk, greater the cost of the company’s capital • Greater return is required by investors • You want to make yachts? Give me 20% on my investment. • You want to make toilet paper? I’ll take 10% on my investment. • The Cost of the Firm’s Capitalis the discount rate (R) • The greater the R, the smaller the NPV • NPV measures the Increase in Value from undertaking the project • If we have two mutually exclusive projects • Select the one with the higher NPV • Since it adds more value to the firm

  29. Other Rules: • Are there other ways to determine if we should do a project? • NO! • But we’ll look at some other common rules anyway • To see how they work • And try to see why they are flawed. • The Payback Period Rule • Yes, you are responsible for this rule • Internal Rate of Return • Yes, you are responsible for this rule • Profitability Index • Yes, you are responsible for this rule • Average Accounting Return • Modified Internal Rate of Return • No, you are not responsible for these rules

  30. 8.4 Internal Rate of Return (IRR) • IRR is the R that that makes the NPV = 0 • NPV = CF0 + CF1/(1 + R) + CF2/(1 + R)2 + … + CFN/(1 + R)N • What R do I plug in to make NPV = 0: • 0 = NPV = CF0 + CF1/(1 + IRR) + CF2/(1 + IRR)2 + … + CFN/(1 + IRR)N Example: CF0 = -$100; CF1 = $60; CF2 = $60 • So this project costs $100 and pays $60 twice • Calculate the IRR for the project: • First we’ll estimate the IRR: • NPV = CF0 + CF1/(1 + R) + CF2/(1 + R)2 • R = 12%  NPV = -$100 + $60/1.12 + $60/1.122 = $1.40 • R = 14%  NPV = -$100 + $60/1.14 + $60/1.142 = -$1.20 • So the IRR must be between 12% and 14% • R = 13%  NPV = -$100 + $60/1.13 + $60/1.132 = +$0.09 • So IRR is close to 13%

  31. Use the Calculator to Calculate IRR: Time Subscripts:CF0= -$100; CF1 = $60;CF2 = $60 Calc Subscripts:CF0= -$100; CF1 = $60 two times • IRR = 13.07% • So what does this mean? • How do we interpret IRR?

  32. The IRR “Decision Rule” • Or How to Interpret IRR • The IRR is what the project earns • So does it earn ENOUGH? Does it earn more than REQUIRED? • If the IRR is Greater than the Required Return, the NPV is Positive • So Accept the Project IRR > R NPV > 0Accept • If the IRR is Less than the Required Return, the NPV is Negative • So Rejectthe Project IRR<R NPV<0Reject For this Example, IRR = 13.07%: • If R = 12%IRR > R NPV > 0Accept the project • Since it adds value • If R = 14%IRR<R NPV<0Reject the project • Since it does not add value • Where does R come from? It is the return required by the investors • For now it is given (but we will calculate it later)

  33. Graph of NPV and R: • When NPV = 0, R = IRR. This happens at R = 13.07% • If the Required Rate (the Hurdle Rate) < IRR, then Accept the project since NPV > 0 • If the Required rate for this project is 12%, accept. If it is 14%, reject.

  34. Clicker Question: • A project costs $5,000 today • It will have positive CFs of $800 per year for 10 years. • Calculate the project’s IRR • 5.0105% • 6.0105% • 7.0105% • 8.0105% • 9.6059%

  35. Clicker Answer: CF0 = -$5,000, CF1 through CF10 = $800 CF0 = -$5,000, CF1$800 ten times The Answer is E. Bonus Question: What is the NPV of these CF at 9.6059%? • The NPV is $0.00! • The IRR is the discount rate that makes the NPV = 0

  36. Problems with IRR: Cash Flows that Change Signs: • A mining project costs $90 • It pays $132 in year 1 and $100 in year 2 • Clean up costs in year 3 are $150 • CF0 = -$90, CF1 = $132, CF2 = $100, CF3 = -$150 • R = 5%  NPV = -$90 + $132/1.05 + $100/1.052- $150/1.053 = -$3.16 • R = 25%  NPV = -$90 + $132/1.25 + $100/1.252- $150/1.253 = $2.80 • R = 50%  NPV = -$90 + $132/1.50 + $100/1.502- $150/1.503= -$2.00 • At very low discount rates (5%): $132 + $100 = $232 inflows do not compensate for the $90 + $150 = $240 outflows • At very high discount rates (50%): $150 outflow year 3 is not as important relative to the inflows at times 1 and 2 If the CFs change signs, the IRR rule may not work 

  37. Use the Calculator to Compute IRR: • For a project when the CFs change signs… • CF0 = -$90, CF1 = $132, CF2 = $100, CF3 = -$150 What does the NPV, R graph look like for this project? 

  38. Graph of NPV and R: When NPV = 0, R = IRR. This happens at R = 10.11% and 42.66% If Required Rate < 42.66%, accept, but less than 10.11%, reject The IRR rule (if the required rate is less than IRR, accept) does not work!

  39. Another Problem with IRR: Mutually Exclusive Projects: • Both projects require the same factory or land or HR or… • Assume a 10% required return for either project • Calculate the IRR for Each Project (using calculator) • IRRA = 19.43% • IRR Rule: 19.43% > 10% so IRR > R so Accept Project A • IRRB = 22.18% • IRR Rule: 22.18% > 10% so IRR > R so Accept Project B

  40. IRR and Mutually Exclusive Projects The Required Rate = 10% • IRRA= 19.43% • IRRB= 22.18% • So both have IRR > R. • So which do we accept? Must calculate the NPV of each project at 10%: • NPVA = $64.05 • NPVB = $60.74 NPVA > NPVB so accept A What if the required rate is 15%? Calculate NPV of each project at 15%: • NPVA = $28.36 • NPVB = $33.84 NPVB > NPVA so accept B What do the graphs of these two projects look like? 

  41. Graph of Projects A and B: At 15%, Project B is better. At 10%, Project A is better.

  42. How to find Crossover Point: Calculate the IRR of the differences in the CFs: This also works for B – A as well. Try it!

  43. 8.5 The Profitability Index (PI) Profitability Index = PV/Cost For Project A at 15%: • PV = $325/1.15 + $325/1.152 = $528.36 • Cost = $500 • PI = $528.36/$500 = 1.06 Rule: If PI > 1 then accept the project IF PI > 1, then PV > Cost so it must mean the NPV > 0 For Project A at 25%: • PV = $325/1.25 + $325/1.252 = $468.00 • Cost = $500 • PI = $468.00/$500 = 0.94 Rule: If PI < 1 then reject the project IF PI < 1, then PV < Cost so it must mean the NPV < 0 Almost identical decisions to NPV The problem is with mutually exclusive projects 

  44. Problem with PI: Mutually Exclusive Projects: • Consider projects A and B again: • Now look at the NPV and PI for each project at different discount rates: At 5% and 10% • A adds more value since NPVA> NPVB, so choose A • But since PIB> PIA, the PI rule leads to the wrong decision.

  45. 8.2 The Payback Period Rule • Count the number of years it takes to recoup the initial investment • If the number of years is fewer than the required years, accept. Example: • CF0 = -$165,000; CF1 = $63,120; CF2 = $70,800; CF3 = $91,080 • Year 1: $165,000– $63,120= $101,880 (cost not yet recovered) • Year 2: $101,880 – $70,800= $31,080 (cost not yet recovered) • Year 3: $31,080 – $91,080= -$60,000 (recovered during year 3) • Payback Period = 2 yrs + Portion of next year needed to get the rest 2 + $31,080 / $91,080 = 2 + 0.34 = 2.34 years • If required payback period is 2 years, reject the project. • If required payback period is 3 years, accept the project.

  46. More Payback Period Examples: • Compare the Payback Period to the NPV • Assume we require our investment back in 2 years • Which projects do we accept? The Payback Rule Suggests: • Incorrectly Reject Project A (since Payback > 2 but NPV > 0) • Incorrectly Accept Project E (since Payback < 2 but NPV < 0)

  47. One More Payback Period Example (Similar to table 8.2 on page 245) • We can see that the “Long” Project is best • “Long” adds the most value – it has the highest NPV • The Payback rule does not distinguish between Short 1 and Short 2 • Also, according to the Payback Rule, Short 2 is better than Long

  48. Clicker Question: Calculate the payback period for each project: • 2.50, 2.67, 3.25 • 2.50, 3.00, 3.50 • 3.00, 3.00, 4.00 • 3.00, 3.00, 4.25 • 3.67, 3.67, 3.25

  49. Clicker Answer: Project 1: $500 = $200 + $200 + .5($200)  2.50 Years Project 2: $500 = $100 + $200 + .67($300)  2.67 Years Project 3: $500 = $0 + $0 + $0 + .25($2,000)  3.25 Years The Answer is A. Bonus Question: Which Project is Best is R = 10%? Must Calculate the NPV at 10%! Project 3 is best since it has the greatest NPV at 10%

  50. Consider Payback Period as a Decision Rule: • The Payback rule does not account for the time value of money • With a 2 year rule, CF1 and CF2 are the same. • The Payback rule does not account for the risk of the cash flows • High risk projects and low risk projects are the same. • Payback rule gives no indication of the project’s value. • If we have two mutually exclusive projects • Select the one with the shorter payback period • Since it adds more value to the firm • Consider “Long” and Short 2 from the previous page: • Long adds more value but has the longer Payback period Implicitly, the payback rule ASSUMES: • R = 0 for any CFs prior to the payback period • R = infinity for any CFs after (since they are not considered) • CF

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