Question

the road feast has two restaurants that are open 24 hours a day. fixed costs for the two restaurants together total $456,000 per year. service varies from a cup of coffee to full meals. the average sales bill per customer is $9.50. the average cost of food and other variable costs for each customer is $3.80. the income tax rate is 30%. target net income is $159,600.required1. compute the revenue needed to earn the target net income.2. how many customers are needed to earn net income of $159,600? how many customers are needed to break even?3. compute net income if the number of customers is 145,000.

Explanation:

Step1: Calculate unit contribution margin

Unit contribution margin = Average sales bill - Average variable cost
$\$9.50 - \$3.80 = \$5.70$

Step2: Calculate target operating income

First, find pre-tax income: Target net income / (1 - tax rate)
$\frac{\$159,600}{1 - 0.30} = \frac{\$159,600}{0.70} = \$228,000$

Step3: Solve Q1: Revenue for target net income

First, find total customers needed: (Fixed costs + Target operating income) / Unit contribution margin
$\frac{\$456,000 + \$228,000}{\$5.70} = \frac{\$684,000}{\$5.70} = 120,000$ customers
Revenue = Number of customers × Average sales bill
$120,000 \times \$9.50 = \$1,140,000$

Step4: Solve Q2a: Customers for target net income

From Step3, the number of customers is already calculated as:
$\frac{\$456,000 + \$228,000}{\$5.70} = 120,000$ customers

Step5: Solve Q2b: Break-even customers

Break-even customers = Fixed costs / Unit contribution margin
$\frac{\$456,000}{\$5.70} = 80,000$ customers

Step6: Solve Q3: Net income with 145,000 customers

Total contribution margin = Number of customers × Unit contribution margin
$145,000 \times \$5.70 = \$826,500$
Operating income = Total contribution margin - Fixed costs
$\$826,500 - \$456,000 = \$370,500$
Net income = Operating income × (1 - tax rate)
$\$370,500 \times (1 - 0.30) = \$370,500 \times 0.70 = \$259,350$

Answer:

1. Revenue needed to earn target net income: $\$1,140,000$
2. Customers needed for target net income: 120,000; Break-even customers: 80,000
3. Net income with 145,000 customers: $\$259,350$