Question

based on the following information, days cash held is closest to: - revenues = $1,000 - net income = $500 - cgs = $300 - cash holdings = $150 - total assets = $3,000 8.33 days 54.75 days 182.50 days 304.17 days

Explanation:

Step1: Recall the formula for days' cash held

The formula for days' cash held is $ \text{Days' Cash Held} = \frac{\text{Cash Holdings}}{\text{Daily Cash Expenditures}} $. First, we need to find the daily cash expenditures. For daily cash expenditures, we can use the cost of goods sold (CGS) as an approximation of daily cash outflows related to operations. The daily cash expenditure is calculated as $ \frac{\text{CGS}}{\text{Number of days in a year}} $. Assuming a 365 - day year, the daily cash expenditure is $ \frac{300}{365} $.

Step2: Calculate daily cash expenditure

Daily cash expenditure $ = \frac{300}{365} \approx 0.8219 $ (rounded to four decimal places).

Step3: Calculate days' cash held

Now, use the formula for days' cash held: $ \text{Days' Cash Held} = \frac{\text{Cash Holdings}}{\text{Daily Cash Expenditure}}=\frac{150}{\frac{300}{365}} $. We can rewrite this as $ 150\times\frac{365}{300} $.

Simplify the expression: $ \frac{150\times365}{300}=\frac{365}{2} = 182.5 $? Wait, no, that's a mistake. Wait, actually, the correct approach is that days' cash held can also be calculated as $ \text{Days' Cash Held}=\frac{\text{Cash}}{\text{Average Daily Cash Expenses}} $, and if we consider that the cash expenditure related to operations is often approximated by CGS (since CGS is the direct cost of producing goods, which is a cash - outlay in most cases). But another way: The formula for days' cash on hand (which is similar to days' cash held) is $ \text{Days' Cash on Hand}=\frac{\text{Cash}+\text{Short - Term Investments}}{\text{Daily Operating Expenses}} $. But in this case, we can use the formula $ \text{Days' Cash Held}=\frac{\text{Cash}}{\frac{\text{CGS}}{365}} $ (assuming CGS is the operating cash outflow).

Wait, let's recalculate:

$ \text{Daily CGS}=\frac{300}{365}\approx0.8219 $

$ \text{Days' Cash Held}=\frac{150}{\frac{300}{365}}=150\times\frac{365}{300}=\frac{365}{2} = 182.5 $? But that's one of the options (182.50 days). Wait, but let's check again.

Wait, maybe the formula is $ \text{Days' Cash Held}=\frac{\text{Cash}}{\frac{\text{Operating Expenses}}{365}} $, and operating expenses here can be approximated by CGS. So:

$ \text{Days' Cash Held}=\frac{150}{\frac{300}{365}}=\frac{150\times365}{300}=\frac{365}{2}=182.5 $ days.

Wait, but let's check the answer options. 182.50 days is one of the options. Wait, but let's re - examine the formula.

Alternatively, the formula for days' cash held is $ \text{Days' Cash Held}=\frac{\text{Cash}}{\text{Daily Cash Expenditures}} $, where daily cash expenditures are calculated as $ \frac{\text{Total Cash Expenditures}}{\text{365}} $. If we consider that the cash expenditures for the year are equal to CGS (since CGS is a major cash outflow), then total cash expenditures for the year = 300. Then daily cash expenditures = 300/365. Then days' cash held = 150/(300/365)=150×365/300 = 182.5 days.

Answer:

182.50 days