Set Bound Attr in `didInitAttrs`

components.my-component.js

import Ember from 'ember';

export default Ember.Component.extend({  
  didInitAttrs() {
    this._super(...arguments);
    
    var value = this.get('value');
    
    if (value) {
      console.log('initial value');
    	this.doSomeStuff(value);
    }
  },

  doSomeStuff: function (value) {
    console.log('update value');
    this.set('value', '+1' + value);
  }
});

controllers.application.js

import Ember from 'ember';

export default Ember.Controller.extend({
  appName:'Ember Twiddle',
  appValue: '000'
});

templates.application.hbs

{{my-component value=appValue}}

templates.components.my-component.hbs

<p>{{value}}</p>

twiddle.json

{
  "version": "0.4.8",
  "dependencies": {
    "jquery": "https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.3/jquery.js",
    "ember": "https://cdnjs.cloudflare.com/ajax/libs/ember.js/1.13.8/ember.js",
    "ember-template-compiler": "https://cdnjs.cloudflare.com/ajax/libs/ember.js/1.13.8/ember-template-compiler.js"
  }
}