AngularJS how to force an input to be re-rendered on blur

I have some custom validation code, which includes a $formatter. (I store currency in pence for correctness, but display in pounds.pence.)

If the user types '10' into the input (which is a valid value), the input remains displaying '10' after they move to the next field.

I would like it to display 10.00 for consistency.

If the model changed the value to 1000, then the formatter would make the field display '10.00'.

I would like the formatter to run on field.blur() (so long as the input is valid).

My problem is that if I change the model value from 10 to 10, there is understandably no change, and so the field is not re-rendered.

code:

var CURRENCY_REGEXP = /^\-?\d+(\.?\d?\d?)?$/;
app.directive('currency', function() {
  return {
    require: 'ngModel',
    link: function(scope, elm, attrs, ctrl) {
      ctrl.$parsers.unshift(function(viewValue) {
        if (CURRENCY_REGEXP.test(viewValue)) {
          // it is valid
          ctrl.$setValidity('currency', true);
          console.log("valid");
          return viewValue * 100;
        } else if (viewValue === '') {
          return 0;
        } else {
          // it is invalid, return undefined (no model update)
          ctrl.$setValidity('currency', false);
          console.log("invalid");
          return undefined;
        }
      });
      ctrl.$formatters.push(function(modelValue) {
         if (modelValue === 0) { // we're using integer pence, so this is safe
             return '';
         }
         return (modelValue / 100).toFixed(2); 
      });
    }
  };
});

P.S. This has nothing to do with Angular's built-in 'currency'.

Update: I've added a 'renderOnBlur' directive, as per Andy's answer. It gets called, but calling the render method does not re-render the input. i.e. '10' stays as '10', rather than changing to '10.00' as desired.

(When the model value changes in these fields, they are correctly rendered with the 2 decimal places.)

The page which Andy mentions http://docs.angularjs.org/api/ng.directive:ngModel.NgModelController says that you have to implement $render yourself. This seems odd, as the inputs are already rendered correctly when the model value changes.

app.directive('renderOnBlur', function() {
    return {
        require: 'ngModel',
        restrict: 'A',
        link: function(scope, elm, attrs, ctrl) {
            elm.bind('blur', function() {
                console.log('rendering ctrl', ctrl);
                ctrl.$render();
            });
        }
    };  
});

P.S. I have no idea what restrict: 'A', does - it's true cargo-cult programming at its worst. The require: 'ngModel', seems necessary to populate the ctrl parameter.

Inspired by the answer from @Dan Doyen, I rewrote it as:

app.directive('renderOnBlur', function() {
    return {
        require: 'ngModel',
        restrict: 'A',
        link: function(scope, elm, attrs, ctrl) {
            elm.bind('blur', function() {
                var viewValue = ctrl.$modelValue;
                for (var i in ctrl.$formatters) {
                    viewValue = ctrl.$formatters[i](viewValue);
                }
                ctrl.$viewValue = viewValue;
                ctrl.$render();
            });
        }
    };  
});

This has the benefit of being generic for any $formatter, rather than repeating the formatter code as in Dan's answer.