Question

What is the present value of a stream of cash flows expected to grow at a 10 percent rate per year for 5 years and then remain constant thereafter until the final payment in 30 years. The payment at the end of the first year is $1,000 and the discount rate is 5.00 percent.

Answer #1

The first stream is a growing annuity. The PV of a growing | |

annuity is given by the formula: | |

PVGA = [P/(r-g)]*[1-((1+g)/(1+r))^n] | |

Where | |

P = First payment | |

r = rate per period | |

g = growth rate | |

n = number of periods | |

Substituting values, the PV of the first 5 year's cash flow = ((1000/(0.05-0.10))*((1-(1.1/1.05)^5)) = | $ 5,237.53 |

PV of the cash flows from 6th year = 1000*1.1^5*(1.05^25-1)/(0.05*1.05^25*1.05^5) = | $ 17,784.82 |

PV of the cash flows for 30 years |
$ 23,022.36 |

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