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Unformatted text preview: or, or trial and error to find the root of the equation, we find that: IRR = 16.80% c. The correct decision rule for an investingtype project is to accept the project if the discount rate is below the IRR. Since there is one IRR, a decision can be made. At a point in the future, the cash flows from stream A will be greater than those from stream B. Therefore, although there are many cash flows, there will be only one change in sign. When the sign of the cash flows change more than once over the life of the project, there may be multiple internal rates of return. In such cases, there is no correct decision rule for accepting and rejecting projects using the internal rate of return. 27. To answer this question, we need to examine the incremental cash flows. To make the projects equally attractive, Project Billion must have a larger initial investment. We know this because the subsequent cash flows from Project Billion are larger than the subsequent cash flows from Project Million. So, subtracting the Project Million cash flows from the Project Billion cash flows, we find the incremental cash flows are: Year 0 1 2 3 Incremental cash flows –Io + $1,200 240 240 400 Now we can find the present value of the subsequent incremental cash flows at the discount rate, 12 percent. The present value of the incremental cash flows is: PV = $1,200 + $240 / 1.12 + $240 / 1.122 + $400 / 1.123 PV = $1,890.32 So, if I0 is greater than $1,890.32, the incremental cash flows will be negative. Since we are subtracting Project Million from Project Billion, this implies that for any value over $1,890.32 the NPV of Project Billion will be less than that of Project Million, so I0 must be less than $1,890.32. 133 28. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR of the project is: 0 = $20,000 – $26,000 / (1 + IRR) + $13,000 / (1 + IRR)2 Even though it appears there are two IRRs, a spreadsheet, financial calculator, or trial and error will not give an answer. The reason is that there is no real IRR for this set of cash flows. If you examine the IRR equation, what we are really doing is solving for the roots of the equation. Going back to high school algebra, in this problem we are solving a quadratic equation. In case you don’t remember, the quadratic equation is:
2 x = − b ± b − 4ac 2a In this case, the equation is: x=
− (−26 ,000) ± ( −26 ,000) 2 − 4( 20 ,000)(13,000) 2( 26 ,000) The square root term works out to be: 676,000,000 – 1,040,000,000 = –364,000,000 The square root of a negative number is a complex number, so there is no real number solution, meaning the project has no real IRR. 134 Calculator Solutions 1. b. Project A CFo C01 F01 C02 F02 C03 F03 I = 15% NPV CPT –$139.72 CFo C01 F01 C02 F02 C03 F03 IRR CPT 7.46% 6. Project A CFo C01 F01 C02 F02 C03 F03 IRR CPT 33.37% –$10,000 $6,500 1 $4,000 1 $1,800 1 CFo C01 F01 C02 F02 C03 F03 I = 15% NPV CPT $399.11 –$12,000 $7,000 1 $4,000 1 $5,000 1 5. –$11,000 $5,500 1 $4,000 1 $3,000 1 –$3,500 $1,800 1 $2,400 1 $1,900 1 Project B CFo C01 F01 C02 F02 C03 F03 IRR CPT 29.32% –$2,300 $900 1 $1,600 1 $1,400 1 135 7. CFo 0 C01 $65,000 F01 7 I = 15% NPV CPT $270,427.28 PI = $270,427.28 / $190,000 = 1.423 10. CFo C01 F01 C02 F02 C03 F03 C04 F04 IRR CPT 14.81% $8,000 –$4,400 1 –$2,700 1 –$1,900 1 –$1,500 1 CFo C01 F01 C02 F02 C03 F03 C04 F04 I = 10% NPV CPT –$683.42 11. a. $8,000 –$4,400 1 –$2,700 1 –$1,900 1 –$1,500 1 CFo C01 F01 C02 F02 C03 F03 C04 F04 I = 20% NPV CPT $635.42 $8,000 –$4,400 1 –$2,700 1 –$1,900 1 –$1,500 1 Deepwater fishing CFo –$750,000 C01 $310,000 F01 1 C02 $430,000 F02 1 C03 $330,000 F03 1 IRR CPT 19.83% Submarine ride CFo –$2,100,000 C01 $1,200,000 F01 1 C02 $760,000 F02 1 C03 $850,000 F03 1 IRR CPT 17.36% 136 b. CFo C01 F01 C02 F02 C03 F03 IRR CPT 15.78% c. –$1,350,000 $890,000 1 $330,000 1 $520,000 1 Deepwater fishing CFo –$750,000 C01 $310,000 F01 1 C02 $430,000 F02 1 C03 $330,000 F03 1 I = 14% NPV CPT $75,541.46 Project I CFo C01 F01 I = 10% NPV CPT $52,223.89 $0 $21,000 3 Submarine ride CFo –$2,100,000 C01 $1,200,000 F01 1 C02 $760,000 F02 1 C03 $850,000 F03 1 I = 14% NPV CPT $111,152.69 CFo C01 F01 I = 10% NPV CPT $12,223.89 –$40,000 $21,000 3 12. PI = $52,223.89 / $40,000 = 1.306 Project II CFo C01 F01 I = 10% NPV CPT $21,138.24 $0 $8,500 3 CFo C01 F01 I = 10% NPV CPT $6,138.24 –$15,000 $8,500 3 PI = $21,138.24 / $15,000 = 1.409 137 13. CFo –$32,000,000 C01 $57,000,000 F01 1 C02 –$9,000,000 F02 1 I = 10% NPV CPT $12,380,165.29 CFo C01 F01 C02 F02 IRR CPT 60.61% –$32,000,000 $57,000,000 1 –$9,000,000 1 Financial calculators will only give you one IRR, even if there are multiple IRRs. Using trial and error, or a root solving calculator, the other IRR is –82.49%. 14. b. Board game CFo C01 F01 C02 F02 C03 F03 I = 10% NPV CPT $235.46 Board game CFo C01 F01 C02 F02 C03 F03 IRR CPT 42.43% CFo C01 F01 C02 F02 C03 F03 IRR CPT 18.78% –$600 $700 1 $...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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