It is the middle of June $2024,$ and Alpha Ltd$.$ is reviewing its working capital management for July $2024.$

Forecast financial information at the start of July $2024$ is as follows:

$$ Inventory: P$185,000$

$$ Trade receivables: P$160,500$

$$ Trade payables: P$35,200$

$$ Overdraft: P$80,000$

All sales are on credit, and they are expected to be $1\mathrm{.}4$ million for $2024.$ Monthly sales are as follows:

$$ May $2024($actual$)$: P$110,250$

$$ June $2024($forecast$)$: P$120,000$

$$ July $2024($forecast$)$: P$140,000$

Alpha Ltd$.$ has a gross profit margin of $35\%.$ Although Alpha Ltd$.$ offers $30$ days' credit, only $55\%$ of customers pay in the month following purchase, while the remaining customers take an additional month of credit.

Inventory is expected to increase by P$2,000$ during July $2024.$

Alpha Ltd$.$ plans to pay $60\%$ of trade payables in July $2024$ and defer paying the remaining $40\%$ until the end of August $2024.$ All suppliers of the company require payment within $30$ days. Credit purchases from suppliers during July $2024$ are expected to be P$100,000.$

Interest of P$25,000$ is due to be paid in July $2024$ on fixed$-$rate bank debt. Operating cash outflows are expected to be $60,000$ in July $2024.$ Alpha Ltd$.$ has no cash and relies on its overdraft to finance daily operations. The company has no plans to raise long$-$term finance during July $2024.$

Assume that each year has $365$ days.

Required:

a$)$

i$)$ Calculate the cash operating cycle of Alpha Ltd$.$ at the start of July $2024.(4$ marks$)$

ii$)$ Calculate the overdraft expected at the end of July $2024.(5$ marks$)$

iii$)$ Calculate the current ratios at the start and end of July $2024.(6$ marks$)$

$($b$)$ Discuss five techniques that Alpha Ltd$.$ could use in managing trade receivables. $(10$ marks$)$