How much is Enough??

A big part of our financial life keeps revolving around a simple looking equation-

A= P * (1+r)^n

The compound interest equation. No wonder, it's called the Eighth wonder of the world.

Investors' keep trying to improve r.... the CAGR.. by looking to benefit from volatility that equity markets' possesses.
Financial advisers, on the other hand, keep asking us to ignore r & focus on n.. the time period.

So, let me ignore both & focus on A.. the final amount, The Target.

Was listening to Mr Subra's lecture on personal finance (See here), and in the first part of the video he says, A = 20 crore for a 30 year old with monthly expense of 50,000.
Looked really high to me, having believed Basant's figure of 50 times annual expense to be the final target (he used 2% dividend yield to calculate the amount).

So, the question came again- How much is Enough??

So, here is my calculation-

Assumptions-

• Remaining Life = 60 years (better to be conservative here; so a 30 year old to live till 90)
• Inflation= 10% (better to be conservative here also)
• Cagr= 12% (better to be conservative here also)
• Money withdrawn at year start (& not equally throughout) & return comes at year end (& not equally throughout) .. (better to be conservative here also)

Lets say I withdraw 1 lakh (from portfolio) in Year 1 to pay for annual expense & that annual expense keeps on rising at 10% every year, so in Year 2, I will need 1.1 lakh & so on & so in Year 60, I will need 277 lakh.

Now, this withdrawn amount will reduce the portfolio by same amount & then have applied r (12% growth) on year ending fund. Calculation below- 

Year starting fund withdrawn ending fund 1 37.0 1.0 36.0 2 40.3 1.1 39.2 3 43.9 1.2 42.7 4 47.8 1.3 46.5 5 52.1 1.5 50.6 6 56.7 1.6 55.1 7 61.7 1.8 59.9 8 67.1 1.9 65.2 9 73.0 2.1 70.9 10 79.4 2.4 77.0 11 86.3 2.6 83.7 12 93.7 2.9 90.8 13 101.7 3.1 98.6 14 110.4 3.5 107.0 15 119.8 3.8 116.0 16 129.9 4.2 125.8 17 140.9 4.6 136.3 18 152.6 5.1 147.6 19 165.3 5.6 159.7 20 178.9 6.1 172.8 21 193.5 6.7 186.8 22 209.2 7.4 201.8 23 226.0 8.1 217.9 24 244.0 9.0 235.0 25 263.2 9.8 253.4 26 283.8 10.8 273.0 27 305.7 11.9 293.8 28 329.1 13.1 316.0 29 353.9 14.4 339.5 30 380.2 15.9 364.3 31 408.0 17.4 390.6 32 437.5 19.2 418.3 33 468.5 21.1 447.3 34 501.0 23.2 477.8 35 535.1 25.5 509.6 36 570.7 28.1 542.6 37 607.8 30.9 576.8 38 646.1 34.0 612.1 39 685.5 37.4 648.1 40 725.9 41.1 684.7 41 766.9 45.3 721.6 42 808.2 49.8 758.5 43 849.5 54.8 794.7 44 890.1 60.2 829.8 45 929.4 66.3 863.1 46 966.7 72.9 893.8 47 1001.1 80.2 920.9 48 1031.4 88.2 943.2 49 1056.4 97.0 959.4 50 1074.5 106.7 967.8 51 1083.9 117.4 966.5 52 1082.5 129.1 953.4 53 1067.8 142.0 925.8 54 1036.9 156.2 880.6 55 986.3 171.9 814.4 56 912.1 189.1 723.1 57 809.8 208.0 601.9 58 674.1 228.8 445.3 59 498.8 251.6 247.1 60 276.8 276.8 0.0

Then using the Goal seek function (to make Year 60 ending fund value = 0), we get Starting fund value at Year 1 = 37.0 lakhs 

i.e 37 times annual expense.

So, the magical number for a 30 year old with annual expense of 6 lakh is 2.22 cr (assuming he continues to cover medical, leisure expense etc in this annual expense only).

For a remaining life of 70 years, we need 40 times expense & for 80 years remaining, we need around 43 times.

So, 37-40 times annual expense is enough!

However, since equity returns will be lumpy, a negative return in early years will hurt. Hence, we need to build some Margin of safety into the formula.
Hence, 50 times annual expense should be enough! (except in extreme situations)

And that's not impossible provided we take care of P, r and n of the Compounding equation.