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Question & Answer: Consider the following two mutually exclusive projects Year Cash FlowCash Flow 19,500 8,725 8,850 8,675 19,500 9,850 7,6…..

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Answer 1. | ||||||

The formula for IRR is: | ||||||

0 = P_{0} + P_{1}/(1+IRR) + P_{2}/(1+IRR)_{2} + P_{3}/(1+IRR)_{3} + . . . +P_{n}/(1+IRR)_{n} |
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By Using the above formula, we caluclate IRR: | ||||||

Year | Project X1 | Project X2 | ||||

Intial Investment | 0 | (19,500) | (19,500) | |||

Expcted Net Cash inflow | 1 | 8,725 | 9,850 | |||

2 | 8,850 | 7,675 | ||||

3 | 8,675 | 8,575 | ||||

Internal Rate of Return | 16.49% | 16.61% | ||||

Answer 2. | ||||||

Year | Project X1 | Project X2 | Differnce | |||

Intial Investment | 0 | (19,500) | (19,500) | – | ||

Expcted Net Cash inflow | 1 | 8,725 | 9,850 | (1,125) | ||

2 | 8,850 | 7,675 | 1,175 | |||

3 | 8,675 | 8,575 | 100 | |||

Crossover Rate | 12.36% | |||||

Answer 3. | ||||||

Calculation of NPV | ||||||

Particulars | Year | 0% Factor | Project X1 | Project X2 | ||

Cash Inflow | Present value | Cash Inflow | Present value | |||

Cash Inflow | ||||||

Net Cash Inflow | 1 | 1.00000 | 8,725.00 | 8,725.00 | 9,850.00 | 9,850.00 |

2 | 1.00000 | 8,850.00 | 8,850.00 | 7,675.00 | 7,675.00 | |

3 | 1.00000 | 8,675.00 | 8,675.00 | 8,575.00 | 8,575.00 | |

A. Total Cash Inflow – PV | 26,250.00 | 26,100.00 | ||||

Cash Outflow | ||||||

Cost | 0 | 1 | 19,500.00 | 19,500.00 | 19,500 | 19,500 |

B. Total Cash Outflow – PV | 19,500.00 | 19,500.00 | ||||

NPV (A – B) | 6,750.00 | 6,600.00 | ||||

Calculation of NPV | ||||||

Particulars | Year | 15% Factor | Project X1 | Project X2 | ||

Cash Inflow | Present value | Cash Inflow | Present value | |||

Cash Inflow | ||||||

Net Cash Inflow | 1 | 0.86957 | 8,725.00 | 7,587 | 9,850.00 | 8,565 |

2 | 0.75614 | 8,850.00 | 6,692 | 7,675.00 | 5,803 | |

3 | 0.65752 | 8,675.00 | 5,704 | 8,575.00 | 5,638 | |

A. Total Cash Inflow – PV | 19,983 | 20,007 | ||||

Cash Outflow | ||||||

Cost | 0 | 1 | 19,500.00 | 19,500 | 19,500.00 | 19,500 |

B. Total Cash Outflow – PV | 19,500 | 19,500 | ||||

NPV (A – B) | 483 | 507 | ||||

Calculation of NPV | ||||||

Particulars | Year | 25% Factor | Project X1 | Project X2 | ||

Cash Inflow | Present value | Cash Inflow | Present value | |||

Cash Inflow | ||||||

Net Cash Inflow | 1 | 0.80000 | 8,725.00 | 6,980 | 9,850.00 | 7,880 |

2 | 0.64000 | 8,850.00 | 5,664 | 7,675.00 | 4,912 | |

3 | 0.51200 | 8,675.00 | 4,442 | 8,575.00 | 4,390 | |

A. Total Cash Inflow – PV | 17,086 | 17,182 | ||||

Cash Outflow | ||||||

Cost | 0 | 1 | 19,500.00 | 19,500 | 19,500.00 | 19,500 |

B. Total Cash Outflow – PV | 19,500 | 19,500 | ||||

NPV (A – B) | (2,414) | (2,318) |