I didn't quite understand the decomposition with time shifting that we did in class on Monday. So, i did the birthday cake example in excel.

***Note: There doesn't seem to be any way to paste excel in here easily, i just found out. So if you click 'edit' the tabular info lines up much better and is easier to ready. **

Then after i got the birthday cake figured out i did a slightly more complicated one for practice.

**Birthday Cake example (i=10%)**

Year | Asset | = | Constant 1 | + | Constant 2 | + | Constant 3 | + | Constant 4 |
---|---|---|---|---|---|---|---|---|---|

0 | 0 | = | 0 | + | 0 | + | 0 | + | 0 |

1 | 1 | = | 1 | + | 0 | + | 0 | + | 0 |

2 | 2 | = | 1 | + | 1 | + | 0 | + | 0 |

3 | 3 | = | 1 | + | 1 | + | 1 | + | 0 |

4 | 4 | = | 1 | + | 1 | + | 1 | + | 1 |

5 | 4 | = | 1 | + | 1 | + | 1 | + | 1 |

6 | 4 | = | 1 | + | 1 | + | 1 | + | 1 |

7 | 4 | = | 1 | + | 1 | + | 1 | + | 1 |

8 | 3 | = | 1 | + | 1 | + | 1 | + | 0 |

9 | 2 | = | 1 | + | 1 | + | 0 | + | 0 |

10 | 1 | = | 1 | + | 0 | + | 0 | + | 0 |

A=1 | A=1 | A=1 | A=1 | ||||||

N=10 | N=8 | N=6 | N=4 |

Constant1 P=(P/A, i=10%, N=10) P=1(6.1446) 6.1446

Constant2 P=(P/A, i=10%, N=8)/(1+i)^1 P=1(5.3349)/(1+.1)^1 4.849909

Constant3 P=(P/A, i=10%, N=6)/(1+i)^2 P=1(4.3553)/(1+.1)^2 3.599421

Constant4 P=(P/A, i=10%, N=4)/(1+i)^3 P=1(3.1699)/(1+.1)^3 2.381593

Ptotal 16.97552

Here is practice problem i made up.

Year | Asset | = | Constant 1 | + | Constant 2 | + | Constant 3 | + | Constant 4 | + | Constant 5 |
---|---|---|---|---|---|---|---|---|---|---|---|

0 | 0 | = | 0 | + | 0 | + | 0 | + | 0 | + | 0 |

1 | 20 | = | 20 | + | 0 | + | 0 | + | 0 | + | 0 |

2 | 35 | = | 20 | + | 15 | + | 0 | + | 0 | + | 0 |

3 | 45 | = | 20 | + | 15 | + | 10 | + | 0 | + | 0 |

4 | 50 | = | 20 | + | 15 | + | 10 | + | 5 | + | 0 |

5 | 51 | = | 20 | + | 15 | + | 10 | + | 5 | + | 1 |

6 | 50 | = | 20 | + | 15 | + | 10 | + | 5 | + | 0 |

7 | 45 | = | 20 | + | 15 | + | 10 | + | 0 | + | 0 |

8 | 35 | = | 20 | + | 15 | + | 0 | + | 0 | + | 0 |

9 | 20 | = | 20 | + | 0 | + | 0 | + | 0 | + | 0 |

10 | 0 | = | 0 | + | 0 | + | 0 | + | 0 | + | 0 |

A=20 | A=15 | A=10 | A=5 | A=1 | |||||||

N=9 | N=7 | N=5 | N=3 | N=1 |

Constant1 P=(P/A, i=11%, N=9) P=20(5.5370) 110.74

Constant2 P=(P/A, i=11%, N=7)/(1+i)^1 P=15(4.7122)/(1+.11)^1 63.67837838

Constant3 P=(P/A, i=11%, N=5)/(1+i)^2 P=10(3.6959)/(1+.11)^2 29.99675351

Constant4 P=(P/A, i=11%, N=3)/(1+i)^3 P=5(2.4437)/(1+.11)^3 8.934061892

Constant5 P=(P/A, i=11%, N=1)/(1+i)^4 P=1(.9009)/(1+.11)^4 0.593450735

Ptotal 213.943