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![IRR Solution (Try 10%)
$40,000 = $10,000(PVIF10%,1) + $12,000(PVIF10%,2) +
$15,000(PVIF10%,3) + $10,000(PVIF10%,4) + $
7,000(PVIF10%,5)
$40,000 = $10,000(.909) + $12,000(.826) +
$15,000(.751) + $10,000(.683) +
$ 7,000(.621)
$40,000 = $9,090 + $9,912 + $11,265 +
$6,830 + $4,347
= $41,444 [Rate is too low!!]](https://image.slidesharecdn.com/npvirrpi-161105035500/75/Net-Present-Value-IRR-and-Profitability-Index-26-2048.jpg)
![IRR Solution (Try 15%)
$40,000 = $10,000(PVIF15%,1) + $12,000(PVIF15%,2) +
$15,000(PVIF15%,3) + $10,000(PVIF15%,4) + $
7,000(PVIF15%,5)
$40,000 = $10,000(.870) + $12,000(.756) +
$15,000(.658) + $10,000(.572) +
$ 7,000(.497)
$40,000 = $8,700 + $9,072 + $9,870 +
$5,720 + $3,479
= $36,841 [Rate is too high!!]](https://image.slidesharecdn.com/npvirrpi-161105035500/75/Net-Present-Value-IRR-and-Profitability-Index-27-2048.jpg)
![IRR Acceptance Criterion
No! The firm will receive 11.57% for each
dollar invested in this project at a cost of
13%. [ IRR < Hurdle Rate ]
The management of a company has
determined that the hurdle rate is 13% for
projects of this type.
Should this project be accepted?](https://image.slidesharecdn.com/npvirrpi-161105035500/75/Net-Present-Value-IRR-and-Profitability-Index-29-2048.jpg)
![Profitability Index (PI)
PI is the ratio of the present value of a
project’s future net cash flows to the
project’s initial cash outflow.
CF1 CF2 CFn
(1+k)1 (1+k)2 (1+k)n
+ . . . ++ ICOPI =
PI = 1 + [ NPV / ICO ]
<< OR >>](https://image.slidesharecdn.com/npvirrpi-161105035500/75/Net-Present-Value-IRR-and-Profitability-Index-38-2048.jpg)
![PI Acceptance Criterion
This. 1.00less than is PIThe No! means
that the project is not profitable. [Reject as PI <
1.00 ]
PI= $38,572 / $40,000
= .9643 (Method #1, 13-33)
Should this project be accepted?](https://image.slidesharecdn.com/npvirrpi-161105035500/75/Net-Present-Value-IRR-and-Profitability-Index-39-2048.jpg)
Uploaded byWisnu Dewobroto
Net Present Value, IRR and Profitability Index
This document provides an overview of capital budgeting techniques, including net present value (NPV), internal rate of return (IRR), and payback period. It begins with definitions of key terms like present value, future value, and discounting. It then discusses how to calculate NPV and IRR using examples. The strengths and weaknesses of each method are reviewed. The document also demonstrates how to perform the calculations using a financial calculator.
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Net Present Value, IRR and Profitability Index
- 1.
- 2. Sequence • Introduction • Basic terms review •Capital budgeting introduction • Capital budgeting technique • Sensitivity analysis • Scenario analysis
- 3.
- 4. A review of Basics: Present Value, Net Present value and future value • Present value (PV) is the current worth of a future sum of money or stream of cash flows given a specified rate of return. In other words, present value, also known aspresent discounted value, is the value of an expected income stream determined as of the date of valuation • Difference between a project’s value and its cost is its NPV • Future value is the value of an asset at a specific date. It measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate, or more generally, rate of return; it is the present value multiplied by the accumulation function.
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- 6. A review of Basic: Example • a CEO of corporation is looking to invest $ 1 million in project X • He asks from you (FINANCIAL MANAGER) whether to invest or not, and if yes then what should be the grounds Your answer may be: first: forecast the cash flows may be generated by the project Second: determine the appropriate opportunity cost of Capital. That should reflect both; time value of money and Risk factor Third:use the opportunity cost of capital to discount the project's future cash flows Fourth: calculate NPV by subtracting the 1 million investment from present value: (Both formulas are given below) PV= C1/1+r + C2/(1+r)2 . . . + Cn/(1+r)t NPV= C0 +C1/1+r + C2/(1+r)2 . . . + Cn/(1+r)t Note: Invest in Project if its NPV is greater or equal to zero
- 7. Net Present Value • Example: building costs 700,000 it can be sold for $ 800,000. if the discount rate is 10%, calculate: §Present Value § Net Present Value PV= C1/1+r + C2/(1+r)2 . . . + Cn/(1+r)n =800,000/(1+.10) PV= RS. 727273 NPV= C0 +C1/1+r + C2/(1+r)2 . . . + Cn/(1+r)n = 700,000 -727273 NPV= $ +27273
- 8. NPV Strengths and Weaknesses Strengths: • Cash flows assumed to be reinvested at the hurdle rate. • Accounts for TVM. •Considers all cash flows. Weaknesses: • May not include managerial options embedded in the project. See Chapter 14.
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- 12. Important Points to be remembered about Net Present Value • First: NPV rule recognizes that a $ today is worth more than a $ tomorrow (time value of money). • Second: NPV depends on the forecasted cash flows from the project and the opportunity cost of capital •Third: PV measures in todays money, therefore we add them up. • NPV depends on Cash flows, not on book returns. Book returns are the accounting record rather than cash as: Book rate of Returns= book income/book assets
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- 17. Payback method • Payback period in capital budgeting refers to theperiod of time required to recoup the funds expended in an investment, or to reach the break-even point. For example, a $1000 investment which returned $500 per year would have a two-year payback period. The time value of money is not taken into account.
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- 20. Why payback can give misleading answers • Payback rule ignores all cash flows after the cutoff date. • Its rule gives equal weight to all cash flows before the cutoff date •Companies still frequently use it because it is the simplest way to communicate the idea. • Everyone can understand it • Manager like it as it tell short span period; good for their promotion
- 21. PBP Strengths and Weaknesses Strengths: • Easy to use and understand • Can be used as a measure of liquidity •Easier to forecast ST than LT flows Weaknesses: • Does not account for TVM • Does not consider cash flows beyond the PBP •
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- 24. Independent Project • Independent --A project whose acceptance (or rejection) does not prevent the acceptance of other projects under consideration. ◆ For this project, assume that it is independent of any other potential projects.
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- 26. IRR Solution (Try 10%) $40,000 = $10,000(PVIF10%,1) + $12,000(PVIF10%,2) + $15,000(PVIF10%,3) + $10,000(PVIF10%,4) + $ 7,000(PVIF10%,5) $40,000 = $10,000(.909) + $12,000(.826) + $15,000(.751) + $10,000(.683) + $ 7,000(.621) $40,000 = $9,090 + $9,912 + $11,265 + $6,830 + $4,347 = $41,444 [Rate is too low!!]
- 27. IRR Solution (Try 15%) $40,000 = $10,000(PVIF15%,1) + $12,000(PVIF15%,2) + $15,000(PVIF15%,3) + $10,000(PVIF15%,4) + $ 7,000(PVIF15%,5) $40,000 = $10,000(.870) + $12,000(.756) + $15,000(.658) + $10,000(.572) + $ 7,000(.497) $40,000 = $8,700 + $9,072 + $9,870 + $5,720 + $3,479 = $36,841 [Rate is too high!!]
- 28. .10 $41,444 .05 IRR$40,000 $4,603 .15 $36,841 ($1,444)(0.05) $4,603 IRR Solution (Interpolate) $1,444X X = X = .0157 IRR = .10 + .0157 = .1157 or 11.57%
- 29. IRR Acceptance Criterion No! The firm will receive 11.57% for each dollar invested in this project at a cost of 13%. [ IRR < Hurdle Rate ] The management of a companyhas determined that the hurdle rate is 13% for projects of this type. Should this project be accepted?
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- 31. Actual IRR Solution Using Your Financial Calculator Steps in the Process Step 1: Press CFkey Step 2: Press 2nd CLR Work keys Step 3: For CF0 Press -40000 Enter ¯ keys Step 4: For C01 Press 10000 Enter ¯ keys Step 5: For F01 Press 1 Enter ¯ keys Step 6: For C02 Press 12000 Enter ¯ keys Step 7: For F02 Press 1 Enter ¯ keys Step 8: For C03 Press 15000 Enter ¯ keys Step 9: For F03 Press 1 Enter ¯ keys
- 32. Actual IRR Solution Using Your Financial Calculator Steps in the Process (Part II) Step 10:For C04 Press 10000Enter ¯ keys Step 11:For F04 Press 1 Enter ¯ keys Step 12:For C05 Press 7000 Enter ¯ keys Step 13:For F05 Press 1 Enter ¯ keys Step 14: Press ¯ ¯ keys Step 15: Press IRR key Step 16: Press CPT key Result: Internal Rate of Return = 11.47%
- 33. IRR Strengths and Weaknesses Strengths: • Accounts for TVM • Considers all cash flows •Less subjectivity Weaknesses: • Assumes all cash flows reinvested at the IRR • Difficulties with project rankings and Multiple IRRs
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- 38. Profitability Index (PI) PI is the ratio of the present value of a project’s future net cash flows to the project’s initial cash outflow. CF1 CF2 CFn (1+k)1(1+k)2 (1+k)n + . . . ++ ICOPI = PI = 1 + [ NPV / ICO ] << OR >>
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- 41. Other Project Relationships • Mutually Exclusive --A project whose acceptance precludes the acceptance of one or more alternative projects. ◆ Dependent -- A project whose acceptance depends on the acceptance of one or more other projects.
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- 45. B. Cash Flow Pattern Let us compare a decreasing cash-flow (D) project and an increasing cash-flow (I) project. NET CASH FLOWS Project DProject IEND OF YEAR 0 -$1,200 -$1,200 1 1,000 100 2 500 600 3 100 1,080
- 46. D 23% $198 1.17 I17% $198 1.17 Cash Flow Pattern Calculate the IRR, NPV@10%, and PI@10%. Which project is preferred? Project IRR NPV PI
- 47.
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- 49. Another Way to Look at Things 1. Adjust cash flows to a common terminal year if project “Y” will NOT be replaced. Compound Project Y, Year 1 @10% for 2 years. Year 0 1 2 3 CF -$1,000$0 $0 $2,420 Results: IRR* = 34.26% NPV = $818 *Lower IRR from adjusted cash-flow stream. X is still Best.
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- 52. Available Projects for BW Project ICO IRR NPV PI A $ 500 18% $ 50 1.10 B 5,000 25 6,500 2.30 C 5,000 37 5,500 2.10 D 7,500 20 5,000 1.67 E 12,500 26 500 1.04 F 15,000 28 21,000 2.40 G 17,500 19 7,500 1.43 H 25,000 15 6,000 1.24
- 53. Choosing by IRRs for BW Project ICO IRR NPV PI C $ 5,00037% $ 5,500 2.10 F 15,000 28 21,000 2.40 E 12,500 26 500 1.04 B 5,000 25 6,500 2.30 Projects C, F, and E have the three largest IRRs. The resulting increase in shareholder wealth is $27,000 with a $32,500 outlay.
- 54. Choosing by NPVs for BW Project ICO IRR NPV PI F $15,000 28% $21,000 2.40 G 17,500 19 7,500 1.43 B 5,000 25 6,500 2.30 Projects F and G have the two largest NPVs. The resulting increase in shareholder wealth is $28,500 with a $32,500 outlay.
- 55. Choosing by PIs for BW Project ICO IRR NPV PI F $15,000 28%$21,000 2.40 B 5,000 25 6,500 2.30 C 5,000 37 5,500 2.10 D 7,500 20 5,000 1.67 G 17,500 19 7,500 1.43 Projects F, B, C, and D have the four largest PIs. The resulting increase in shareholder wealth is $38,000 with a $32,500 outlay.
- 56. Summary of Comparison Method Projects Accepted Value Added PIF, B, C, and D $38,000 NPV F and G $28,500 IRR C, F, and E $27,000 PI generates the greatest increase in shareholder wealth when a limited capital budget exists for a single period.
- 57. Post-Completion Audit Post-completion Audit A formal comparison of the actual costs and benefits of a project with original estimates. • Identify any project weaknesses • Develop a possible set of corrective actions •Provide appropriate feedback Result: Making better future decisions!
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- 59. Project analysis • Investment process starts with the preparation of an annual capital budget. • Project authorization and problem of biased forecasts •Post audits • Identification of problems • Accuracy of forecast Any suggestion
- 60. Sensitivity analysis • Uncertainty means more things can happen than will happen. • Example A company is introducing new scooters for city use with Rs. 15 b Net investment for 10 years, producing NCF of Rs. 3 B in ten years. Staff have prepared the forecasts at 10% NPV. =(-15)+3/(1.1)10 = Rs. +3.43 billions Production department estimated cost per unit is Rs. 300,000 and 100,00 scooter can be made in the year. If calculated the revenue as the firm has 1% market share, it will be: Unit sales= new product share in market*size of scooter market 37.5 billions(Revenue) = 100,000*375,000 Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be apportioned to different sources of uncertainty in its inputs.
- 61.
- 62. Sensitivity analysis… • Value Information • Suppose that production department is worried about the machine which will not work properly and the firm has to purchase another method which incure per unit cost an extra Rs. 20,000: units sales*additional unit cost*(1-tax rate) Rs.1 Billion= 100,000*20,000*.50 It will reduce the NPV by: 1/(1.10)10 • Limits of sensitivity analysis • Giving ambiguous results
- 63. Scenario analysis • Scenario analysis is a process of analyzing possible future events by considering alternative possible outcomes (sometimes called "alternative worlds"). •Thus, the scenario analysis, which is a main method of projections, does not try to show one exact picture of the future.