Calculate percentages by excluding negative values

Question

i am not sure where my basics are being messed up while calculating percentages.

Let me give the scenario

Suppose i have assets on My Name

Cash = 12000
Real Estate  = 30000
Stocks = 7000
Outstanding loan = -23000

Assets1 = 12000+ 30000 + 7000 - 23000=  26000

Assets on my partners name

Furniture  = 8000
Jewelry = 17000

Assets2 = 8000 + 17000 =  25000

Total assets = 26000 + 25000 = 51000

I want to represent all my assets excluding loan as a percentage. I add absolute value of my loan so that all my positive asset percentages can add up to 100

Cash         = (12000 * 100)/74000 = 16.22
Real Estate  = (30000 * 100)/74000 = 40.54 
Stocks       = (7000  * 100)/74000 = 09.46
Furniture    = (8000  * 100)/74000 = 10.81
Jewelry      = (17000 * 100)/74000 = 22.97

if we see the sum of percentages

Asset1
16.22 + 40.54 + 9.46 = 66.22

Asset2
10.81 + 22.97 = 33.78 

66.22 + 33.78 = 100

But if i calculate the Asset1 net percentage using total-->

26000*100/51000 = 50.98

and Asset2 net percentage using total-->

25000*100/51000 = 49.02

Why are the individual percentages adding up to 66.22 and 33.78 respectively

Answer 1

The individual percentages are adding up to 66.22% and 33.78% because when calculating these you are not deducting the outstanding loan amount from your assets. When you are calculating the percentages with the totals of the two partners, you are dividing with a total asset value with the outstanding loan deducted already. $\frac{26,000}{51,000} \neq \frac{49,000}{74,000}$.

If you want to exclude the outstanding loan from the calculation (as if it does not exist) use the first calculation. If you want to use your assets accounting the outstanding loan use the second calculation. If you want to use the first method of calculation (finding the percents of each asset) while accounting for the outstanding loan, you can do:

Cash: $(\frac{12,000}{51,000})\times 100 = 23.53\%$

Real Estate: $(\frac{30,000}{51,000})\times 100 = 58.82\%$

Stocks: $(\frac{7,000}{51,000})\times 100 = 13.73\%$

Outstanding Loan: $(\frac{-23.000}{51,000})\times 100 = -45.10\%$

Your Assets out of Total: $23.53\%+58.82\%+13.73\%-45.10\%=50.98\%$

Answer 2

All your arithmetic is correct. What changes is what you want to compute.

In your first calculation you are ignoring the loan. When you do that, you have about $2/3$ of the total assets. That is a well defined calculation. Whether it is useful is another matter. In the second calculation you are computing each person's share of the net worth, where the loan is considered. That is also a well defined calculation.

One way to look at what is useful is to ask what happens if one of you takes out a $1,000,000$ loan and keeps it in cash. The person that does that has almost all of your joint assets if you ignore the loan. Your net assets and percentages of them have not changed. Does it make sense to ignore the loan?