Company "A" is being pushed by activist investors to break up or spin out a chronically underperforming division.
 
Company A Balance Sheet (data from public sources)  
shares outstanding:           2.26 B 
total assets ($B):           34.8     ($15.40/share)   
cash on hand ($B):          8.61    ($3.81/share)
total debt ($B):              4.32    ($1.91/share)
revenue ($B):               36.6     ($16.20/share)
market cap ($B):           20.2     ($8.94/share)
 
Breaking into two companies (B & C) along business lines as suggested (splitting the balance sheet 50:50) along with data for separate divisions assembled from Co. A's Qtrly Earning Press Releases:
 
                                   B            C     
TTM Sales ($B)            17.7        19.0      (TTM = Trailing Twelve Months) 
5yr Ann. Sales Growth   11.4%     11.7%    (calculated) 
TTM Net Margin            11.9%      -5.4%
5 yr Avg Qtrly Margin    11.7%       5.9%
5 yr Tot Net/Tot Sales    11.9%       6.3%
 
debt ($B)                    2.16        2.16
cash ($B)                    4.30        4.31
total assets ($B)          17.40      17.40
hyp. shares                  2.26        2.26       
 
For Co. B alone, with more cash than debt and low double-digit revenue growth and steady margin, what Price-to-Earnings or Price-to-Sales should it have?
 
P/E=15 implies market cap of $31.6B (= 15 * [TTM_Sales * TTM_Net Margin]) or $13.98/share
P/S=2.0 implies market cap of $35.4B or $15.56/share
 
The liquidation value (at fire sale pricing) of Co.C assets would seem to be at least $8-10B ($3.54-4.42/share).
So the combined (or break-up) value would appear to be in the range of $17.52-$19.98.