Using a combination of salesforce Read metadata and listMetadata to get an csv export of access information of report folders. used jsforce for all the necessary calls.

jsforce_reportaccess_download.js

var jsforce = require('jsforce');
var fs = require('fs');
var conn = new jsforce.Connection({
   // use loginUrl : 'https://login.salesforce.com' for production
   loginUrl : 'https://test.salesforce.com'
});
conn.login('yourusername', 'yourpassword+securitytoken', function(err, userInfo) {
  if (err) { return console.error(err); }
  // Now you can get the access token and instance URL information.
  // Save them to establish connection next time.
  console.log(conn.accessToken);
  console.log(conn.instanceUrl);
  // logged in user property
  console.log("User ID: " + userInfo.id);
  console.log("Org ID: " + userInfo.organizationId);
  // ...
  var reportfolders=[];
  var csvstring=[];
  fs.writeFile('oldModel.csv','"fullName","accessType","publicFolderAccess","Name","sharedToType"\n',function(err){});

  conn.metadata.list([{type:'ReportFolder'}],'30.0',function(err,result){
  for(var i=0;i<result.length;i++)
  {
    reportfolders.push(result[i].fullName);
    if(reportfolders.length==10){
        conn.metadata.read('ReportFolder', reportfolders, function(err, metadata) {
          if (err) { console.error(err); }
          if(metadata!=undefined && metadata.hasOwnProperty('length')){
          for (var j=0; j < metadata.length; j++) {
            var meta = metadata[j];
            if(meta!=undefined && meta.hasOwnProperty('accessType'))
            {
              var resultstr='';
              if(meta.hasOwnProperty('sharedTo'))
              {
                if(meta.sharedTo.hasOwnProperty('group'))
                  resultstr+=['"'+meta.fullName+'"','"'+meta.accessType+'"','"'+meta.publicFolderAccess+'"','"'+meta.name+'"',"group",'"'+meta.sharedTo.group+'"'].join(',')+'\n';
                if(meta.sharedTo.hasOwnProperty('portalRole'))
                  resultstr+=['"'+meta.fullName+'"','"'+meta.accessType+'"','"'+meta.publicFolderAccess+'"','"'+meta.name+'"',"portalRole",'"'+meta.sharedTo.portalRole+'"'].join(',')+'\n';
                if(meta.sharedTo.hasOwnProperty('portalRoleAndSubordinates'))
                  resultstr+=['"'+meta.fullName+'"','"'+meta.accessType+'"','"'+meta.publicFolderAccess+'"','"'+meta.name+'"',"portalRoleAndSubordinates",'"'+meta.sharedTo.portalRoleAndSubordinates+'"'].join(',')+'\n';
                if(meta.sharedTo.hasOwnProperty('role'))
                  resultstr+=['"'+meta.fullName+'"','"'+meta.accessType+'"','"'+meta.publicFolderAccess+'"','"'+meta.name+'"',"role",'"'+meta.sharedTo.role+'"'].join(',')+'\n';
                if(meta.sharedTo.hasOwnProperty('roleAndSubordinates'))
                  resultstr+=['"'+meta.fullName+'"','"'+meta.accessType+'"','"'+meta.publicFolderAccess+'"','"'+meta.name+'"',"roleAndSubordinates",'"'+meta.sharedTo.roleAndSubordinates+'"'].join(',')+'\n';
                if(meta.sharedTo.hasOwnProperty('roleAndSubordinatesInternal'))
                  resultstr+=['"'+meta.fullName+'"','"'+meta.accessType+'"','"'+meta.publicFolderAccess+'"','"'+meta.name+'"',"roleAndSubordinatesInternal",'"'+meta.sharedTo.roleAndSubordinatesInternal+'"'].join(',')+'\n';
              }
              fs.appendFile('oldModel.csv', resultstr, function (err) {});
            }
          }
      }
      });
    reportfolders=[];
    }
  }
  });
});