Question $2$: $(30$ points$)$ Pizza Piatta$$s $2023$ financial statements are below. Assume that the firm is beginning to forecast and plan for $2024$ and needs to know the answers to the questions below.

a$.(15$ points$)$ What is the fastest that Pizza Piatta can grow next year $($i$.$e$.,$ the $$growth speed limit$$ that I discussed in class$)$ assuming that the firm does not want to access external capital $($of any type$)$ and that it does not want to change its dividend payout policy?

b$.(15$ points$)$ Assume that Pizza Piatta is operating at full capacity. Also assume that assets, costs, and current liabilities vary directly with sales. The dividend payout ratio is constant. What is the external financing needed if sales increase by $13\%?$

$2023$ income statement

Net sales $$2,015$

COGS $$679$

Depreciation $$203$

EBIT $$1,133$

Interest paid $$0$

Taxable income $$1,133$

Taxes paid $($@ $40\%)$ $$453$

Net income $$680$

Dividends paid $$272$

$2023$ balance sheet

Assets Liabilities

Cash $$1,040$ Accounts payable $$1,250$

Accounts receivable $$650$ Long$-$term debt $$2,300$

Inventory $$525$ Paid in capital $($common equity$)$ $$2,000$

Total current assets $$2,215$ Retained earnings $$2,450$

Net fixed assets $$5,785$

Total assets $$8,000$ Total liabilities and equity $$8,000$