Decomposition with time shifting

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

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