Buying companies - math of a problem

Three companies are up for grabs but you have money to buy two only. The management has given instructions for you to only consider companies which give a high "Return on Capital Employed" ratio. All three companies are equally priced. Here are the specs -

1. Company A earns a profit of Rs. 80 from a capital employed of Rs. 100
2. Company B earns Rs. 20 from a capital emp of Rs. 100
3. Company C earns Re. 1 from a capital emp of Rs. 20

Thus company A has an ROCE of 80%, company B has an ROCE of 20% while company C has an ROCE of only 5%.

You might be tempted to buy companies A and B as they definitely have a much higher ROCE as compared to company C. Lets do some further math here -

Case 1: You drop A and pick B, C
Your total profit would be 21 (20+1) while your cumulative cap. emp. will total 120 (100+20) .. giving you a total ROCE of 21/120 = 17.5%

Case 2: You drop B and pick A, C
Now your cumulative ROCE jumps up to 67.5% (81/120)

Case 3: You drop C and pick B, A
A total profit of 100 (80+20) and total CE of 200 (100+100) means, a combined ROCE of 50%

So while dropping company C may seem a good choice, it'll not be too appreciated by your management.

Implications - Such situations also come to light in corporate quarters. E.g. an increase in homeloan rates may lead to lowered demand for housing and hence the share price of banks would come down. The larger part of the puzzle is "what is the contribution of home loans to the bank's total asset disbursements". In a previous blog I had explained the same situation w.r.t. HLL and it's price war with P&G on the detergents front.