Question

Sharon is making an investment of $80,000 today and expects to receive $2,000 each year for the next five years. At the end of the fifth year, a sum of $100,000 will be returned. What is the internal rate of return compounded annually on this investment?

a) 6.84% b) 6.86% c) 6.88% d) 7.02%

Answer #1

6% | 7% | ||||

Period | Cash Flow | Discountig
Factor [1/(1.06^period)] |
PV of cash
flows (cash flow*discounting factor) |
Discountig
Factor [1/(1.07^period)] |
PV of cash
flows (cash flow*discounting factor) |

0 | -80000 | 1 | -80000 | 1 | -80000 |

1 | 2000 | 0.9433962 | 1886.79245 | 0.9345794 | 1869.158879 |

2 | 2000 | 0.8899964 | 1779.99288 | 0.8734387 | 1746.877457 |

3 | 2000 | 0.8396193 | 1679.23857 | 0.8162979 | 1632.595754 |

4 | 2000 | 0.7920937 | 1584.18733 | 0.7628952 | 1525.790424 |

5 | 102000 | 0.7472582 | 76220.3336 | 0.7129862 | 72724.59031 |

NPV = | 3150.54486 | NPV = | -500.98718 |

IRR is the rate of return at which NPV=0

Here, NPV@6% is positive and @7% is negative.

Therefore, IRR is between 6% and 7%

IRR = Rate at which positive NPV + [Positive NPV/(Positive NPV-Negative NPV)]

= 6% + [3150.54/(3150.54-(-500.99)]

= 6% + [3150.54/3651.53]

= 6% + 0.86% = **6.86%**

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