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Why is the NAV for direct funds more than regular funds?

The NAV of a scheme is derived from the summation of several factors or variables which is known as the profitability metric. It's derived using the below formula:

Interest income + Dividend income Realized capital gains Valuation gains - (Realized capital losses) - (Valuation losses) - (Scheme expenses)

As you can see the scheme expenses is a subtraction, so basically, the NAV would be lesser if scheme expenses are higher. 

The expense ratio is nothing but the scheme expenses. The expense ratio is generally denoted as a percentage which is specified as per annum. For the calculation of the NAV, the scheme expense is calculated and deducted on daily basis.

Now, for a regular plan of a particular mutual fund scheme, the expense ratio is higher than that of a direct plan of the same scheme which means that the scheme expenses is higher for a regular plan. 

Thus, the NAV of a direct plan will always be higher than that of a regular plan. This means that the returns generated for a direct plan is essentially much higher than that of a regular plan.

Refer this post on tradingqna for more information.