Why is such complex code emitted for dividing a signed integer by a power of two?

When I compile this code with VC++10:

DWORD ran = rand();
return ran / 4096;

I get this disassembly:

299: {
300:    DWORD ran = rand();
  00403940  call        dword ptr [__imp__rand (4050C0h)]  
301:    return ran / 4096;
  00403946  shr         eax,0Ch  
302: }
  00403949  ret

which is clean and concise and replaced a division by a power of two with a logical right shift.

Yet when I compile this code:

int ran = rand();
return ran / 4096;

I get this disassembly:

299: {
300:    int ran = rand();
  00403940  call        dword ptr [__imp__rand (4050C0h)]  
301:    return ran / 4096;
  00403946  cdq  
  00403947  and         edx,0FFFh  
  0040394D  add         eax,edx  
  0040394F  sar         eax,0Ch  
302: }
  00403952  ret

that performs some manipulations before doing a right arithmetic shift.

What's the need for those extra manipulations? Why is an arithmetic shift not enough?