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          underpayment which the taxpayer establishes is not attributable             
          to fraud.  Secs. 6653(b)(2), 6663(b).                                       
               A.  Underpayment                                                       
               The Commissioner has the burden of proving by clear and                
          convincing evidence that an underpayment exists in each of the              
          years in issue.  The Commissioner is not required to prove the              
          exact amount of the underpayment.  DiLeo v. Commissioner, 96 T.C.           
          at 873.  On the other hand, the Commissioner does not satisfy his           
          burden of proof by merely relying on the taxpayer’s failure to              
          prove error in the determination.  Id.  On the basis of the                 
          evidence presented and our analysis supra, we find that                     
          respondent has clearly and convincingly established that                    
          petitioner had underpayments of tax in 1988, 1989, and 1990.                
               B.  Underpayment Due to Fraud                                          
               Fraud has been defined as an “intentional wrongdoing on the            
          part of a taxpayer motivated by a specific purpose to evade a tax           
          known or believed to be owing.”  Stoltzfus v. United States, 398            
          F.2d 1002, 1004 (3d Cir. 1968); see also Langworthy v.                      
          Commissioner, T.C. Memo. 1998-218.  Courts consider a taxpayer’s            
          entire course of conduct in determining fraudulent intent.  DiLeo           
          v. Commissioner, supra at 874; Petzoldt v. Commissioner, 92 T.C.            
          661, 699 (1989).  Because direct evidence is rarely available,              
          fraud may be proven by circumstantial evidence.  DiLeo v.                   
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