VAT – Decision with respect to Voluntary registration

BPP question:-

On 1 January 2016, Flick commenced in partnership with Art running a small cinema. The partnership voluntarily registered for value added tax (VAT) on 1 January 2016, and immediately began using the flat rate scheme to calculate the amount of VAT payable. The relevant flat rate scheme percentage for the partnership’s trade is 12%. For the quarter ended 31 March 2016 the partnership had standard rated sales of £59,700, and these were all made to members of the general public. For the same period standard rated expenses amounted to £27,300. Both figures are stated inclusive of VAT.

Explain whether or not it was financially beneficial for the partnership to have voluntarily registered for VAT from 1 January 2016.

Solution given:-

The partnership’s sales are all to members of the general public, who cannot recover the input VAT. It may not therefore be possible to pass the output VAT on to customers in the prices charged. To the extent this is not possible the partnership would have had to absorb all or some of this amount itself as a cost. It was therefore not beneficial for the partnership to have voluntarily registered for VAT from 1 January 2016. For the quarter ended 31 March 2016 voluntary registration reduced the partnership’s profits by a maximum of £7,164 (£5,400 if the normal basis had been used).

My concern:- I agree going for Voulntary basis with FLAT SCHEME is not beneficial, but If he is going with the normal vat, why it is not beneficial as follows:-

With out VAT Registaion :- 49750-27300= 22450
With VAT (Normal scheme) – 49750-27300-4550 (INPUT VAT) = 17900

Saving :- 4550

Any thing went wrong ???