Statements of Financial Position of P Ltd and S Ltd as at $30$ June $20$X$8$ are given below:

P Ltd S Ltd

$ $

Property, plant and equipment $15,0009,500$

Investment in S Ltd $5,000-$

Current assets $7,5005,000$

$27,50014,500$

Share capital $10,0005,000$

Retained earnings $12,5007,200$

$22,50012,200$

Non$-$current liabilities $1,000500$

Current liabilities $4,0001,800$

$27,50014,500$

P Ltd acquired $60\%$ of S Ltd on $1$ July $20$X$7$ when the retained earnings of S were $$5,800.$ P paid $$5,000$ in cash and also issued $2$ shares for every $5$ shares acquired in S Ltd$.$ P Ltd further agreed to pay $$2,000$ in $3$ years' time. The market value of P Ltd$\text{'}$s shares at $1$ July $20$X$7$ was $$1\mathrm{.}80.$ P Ltd has only recorded the cash paid in respect of the investment in S Ltd$.$ Current interest rates are $6\%.$

The P Group uses the fair value method to value the non$-$controlling interests. At the date of acquisition, the fair value of the non$-$controlling interest was $$5,750.$

Required:

$($a$)$ Calculate the amount of goodwill implicit in the acquisition of S Ltd$\text{'}$s shares at the acquisition date.

$($b$)$ Calculate the amount of goodwill implicit in the acquisition of S Ltd$\text{'}$s shares at the acquisition date if the proportional interest method is used.