Asked by Gavin Pabst on Jul 02, 2024
Verified
Jane Botosan operates a bed and breakfast hotel in a resort area near Lake Michigan. Depreciation on the hotel is $60000 per year. Jane employs a maintenance person at an annual salary of $41000 and a cleaning person at an annual salary of $24000. Real estate taxes are $10000 per year. The rooms rent at an average price of $60 per person per night including breakfast. Other costs are laundry and cleaning service at a cost of $10 per person per night and the cost of food which is $5 per person per night.
Instructions
(a) Determine the number of rentals and the sales revenue Jane needs to break even using the contribution margin technique.
(b) If the current level of rentals is 4000 by what percentage can rentals decrease before Jane has to worry about having a net loss?
(c) Jane is considering upgrading the breakfast service to attract more business and increase prices. This will cost an additional $3 for food costs per person per night. Jane feels she can increase the room rate to $68 per person per night. Determine the number of rentals and the sales revenue Jane needs to break even if the changes are made.
Contribution Margin Technique
A method used in managerial accounting to analyze the profitability of products, segments, or services by calculating revenues minus variable costs.
Depreciation
The systematic allocation of the depreciated cost of an asset over its useful life.
Real Estate Taxes
Taxes levied on property by the local government, based on the assessed value of the property.
- Figure out the break-even points and margins of safety measured in units and by monetary value.
- Determine appropriate pricing strategies to enhance profitability.
Verified Answer
ZK
Zybrea KnightJul 03, 2024
Final Answer :
(a)
Variable costs per person per night: Fixed costs: Laundry and cleaning $10 Depreciation $60,000 Breakfast 5‾ Maintenance 41,000 Total variable $15‾ Cleaning 24,000 Real estate tax 10,000 Total fixed $135,000\begin{array}{crlr}\text { Variable costs per person per night: } && \text { Fixed costs: } \\\text { Laundry and cleaning } & \$ 10 & \text { Depreciation } & \$ 60,000 \\\text { Breakfast } & \underline{5} & \text { Maintenance } & 41,000 \\\text { Total variable } & \underline{\$ 15} & \text { Cleaning } & 24,000 \\& & \text { Real estate tax } & 10,000 \\&& \text { Total fixed } & \$ 135,000\end{array} Variable costs per person per night: Laundry and cleaning Breakfast Total variable $105$15 Fixed costs: Depreciation Maintenance Cleaning Real estate tax Total fixed $60,00041,00024,00010,000$135,000 Break-even number of persons per night rentals: \text { Break-even number of persons per night rentals: } Break-even number of persons per night rentals:
Fixed costs Contribution margin per person per night =$135,000$45∗=3,000 rentals \frac{\text { Fixed costs }}{\text { Contribution margin per person per night }}=\frac{\$ 135,000}{\$ 45^{*}}=3,000 \text { rentals } Contribution margin per person per night Fixed costs =$45∗$135,000=3,000 rentals
∗ Sales price per unit $60 Variable cost per unit 15 Unit contribution margin $45‾\begin{array}{lr}{ }^{*} \text { Sales price per unit } & \$ 60 \\\text { Variable cost per unit } & 15 \\\text { Unit contribution margin } & \underline{\$ 45}\end{array}∗ Sales price per unit Variable cost per unit Unit contribution margin $6015$45
Fixed costs Contribution margin ratio =$135,00075%⋆⋆=$180,000\frac{\text { Fixed costs }}{\text { Contribution margin ratio }}=\frac{\$ 135,000}{75 \%^{\star \star}}=\$ 180,000 Contribution margin ratio Fixed costs =75%⋆⋆$135,000=$180,000
*Unit contribution margin (a) Sales price per unit (b) Contribution margin ratio (a)÷(b)=75%\begin{array}{l}\text { *Unit contribution margin (a) } \\\text { Sales price per unit (b) } \\\text { Contribution margin ratio }(\mathrm{a}) \div(\mathrm{b})=75 \%\end{array} *Unit contribution margin (a) Sales price per unit (b) Contribution margin ratio (a)÷(b)=75%
(b) Margin of safety: \text { Margin of safety: } Margin of safety:
Actual rentals - Break-even rentals Actual rentals =(4,000−3,000)4,000=25%\frac{\text { Actual rentals - Break-even rentals }}{\text { Actual rentals }}=\frac{(4,000-3,000)}{4,000}=25 \% Actual rentals Actual rentals - Break-even rentals =4,000(4,000−3,000)=25%
(c) Variable costs per person per night: Fixed costs: Laundry and cleaning $10.00 Depreciation $60,000 Breakfast 8.00‾ Maintenance 41,000 Total variable $18.00‾ Cleaning 24,000 Real estate tax 10,000 Total fixed $135,000\begin{array}{crlr}\text { Variable costs per person per night: } && \text { Fixed costs: } \\\text { Laundry and cleaning } & \$ 10.00 & \text { Depreciation } & \$ 60,000 \\\text { Breakfast } & \underline{8.00} & \text { Maintenance } & 41,000 \\\text { Total variable } & \underline{\$ 18.00} & \text { Cleaning } & 24,000 \\& & \text { Real estate tax } & 10,000 \\&& \text { Total fixed } & \$ 135,000\end{array} Variable costs per person per night: Laundry and cleaning Breakfast Total variable $10.008.00$18.00 Fixed costs: Depreciation Maintenance Cleaning Real estate tax Total fixed $60,00041,00024,00010,000$135,000 Break-even number of persons per night rentals: \text { Break-even number of persons per night rentals: } Break-even number of persons per night rentals:
Fixed costs Contribution margin per person per night =$135,000$50∗=2,700 rentals \frac{\text { Fixed costs }}{\text { Contribution margin per person per night }}=\frac{\$ 135,000}{\$ 50^{*}}=2,700 \text { rentals } Contribution margin per person per night Fixed costs =$50∗$135,000=2,700 rentals
"Sales price per unit $68 Variable cost per unit 18 Unit contribution margin $50\begin{array}{ll}\text { "Sales price per unit } & \$ 68 \\\text { Variable cost per unit } & 18 \\\text { Unit contribution margin } & \$ 50\end{array} "Sales price per unit Variable cost per unit Unit contribution margin $6818$50 Break-even point in sales dollars: 2700 × $68 = $183600
Variable costs per person per night: Fixed costs: Laundry and cleaning $10 Depreciation $60,000 Breakfast 5‾ Maintenance 41,000 Total variable $15‾ Cleaning 24,000 Real estate tax 10,000 Total fixed $135,000\begin{array}{crlr}\text { Variable costs per person per night: } && \text { Fixed costs: } \\\text { Laundry and cleaning } & \$ 10 & \text { Depreciation } & \$ 60,000 \\\text { Breakfast } & \underline{5} & \text { Maintenance } & 41,000 \\\text { Total variable } & \underline{\$ 15} & \text { Cleaning } & 24,000 \\& & \text { Real estate tax } & 10,000 \\&& \text { Total fixed } & \$ 135,000\end{array} Variable costs per person per night: Laundry and cleaning Breakfast Total variable $105$15 Fixed costs: Depreciation Maintenance Cleaning Real estate tax Total fixed $60,00041,00024,00010,000$135,000 Break-even number of persons per night rentals: \text { Break-even number of persons per night rentals: } Break-even number of persons per night rentals:
Fixed costs Contribution margin per person per night =$135,000$45∗=3,000 rentals \frac{\text { Fixed costs }}{\text { Contribution margin per person per night }}=\frac{\$ 135,000}{\$ 45^{*}}=3,000 \text { rentals } Contribution margin per person per night Fixed costs =$45∗$135,000=3,000 rentals
∗ Sales price per unit $60 Variable cost per unit 15 Unit contribution margin $45‾\begin{array}{lr}{ }^{*} \text { Sales price per unit } & \$ 60 \\\text { Variable cost per unit } & 15 \\\text { Unit contribution margin } & \underline{\$ 45}\end{array}∗ Sales price per unit Variable cost per unit Unit contribution margin $6015$45
Fixed costs Contribution margin ratio =$135,00075%⋆⋆=$180,000\frac{\text { Fixed costs }}{\text { Contribution margin ratio }}=\frac{\$ 135,000}{75 \%^{\star \star}}=\$ 180,000 Contribution margin ratio Fixed costs =75%⋆⋆$135,000=$180,000
*Unit contribution margin (a) Sales price per unit (b) Contribution margin ratio (a)÷(b)=75%\begin{array}{l}\text { *Unit contribution margin (a) } \\\text { Sales price per unit (b) } \\\text { Contribution margin ratio }(\mathrm{a}) \div(\mathrm{b})=75 \%\end{array} *Unit contribution margin (a) Sales price per unit (b) Contribution margin ratio (a)÷(b)=75%
(b) Margin of safety: \text { Margin of safety: } Margin of safety:
Actual rentals - Break-even rentals Actual rentals =(4,000−3,000)4,000=25%\frac{\text { Actual rentals - Break-even rentals }}{\text { Actual rentals }}=\frac{(4,000-3,000)}{4,000}=25 \% Actual rentals Actual rentals - Break-even rentals =4,000(4,000−3,000)=25%
(c) Variable costs per person per night: Fixed costs: Laundry and cleaning $10.00 Depreciation $60,000 Breakfast 8.00‾ Maintenance 41,000 Total variable $18.00‾ Cleaning 24,000 Real estate tax 10,000 Total fixed $135,000\begin{array}{crlr}\text { Variable costs per person per night: } && \text { Fixed costs: } \\\text { Laundry and cleaning } & \$ 10.00 & \text { Depreciation } & \$ 60,000 \\\text { Breakfast } & \underline{8.00} & \text { Maintenance } & 41,000 \\\text { Total variable } & \underline{\$ 18.00} & \text { Cleaning } & 24,000 \\& & \text { Real estate tax } & 10,000 \\&& \text { Total fixed } & \$ 135,000\end{array} Variable costs per person per night: Laundry and cleaning Breakfast Total variable $10.008.00$18.00 Fixed costs: Depreciation Maintenance Cleaning Real estate tax Total fixed $60,00041,00024,00010,000$135,000 Break-even number of persons per night rentals: \text { Break-even number of persons per night rentals: } Break-even number of persons per night rentals:
Fixed costs Contribution margin per person per night =$135,000$50∗=2,700 rentals \frac{\text { Fixed costs }}{\text { Contribution margin per person per night }}=\frac{\$ 135,000}{\$ 50^{*}}=2,700 \text { rentals } Contribution margin per person per night Fixed costs =$50∗$135,000=2,700 rentals
"Sales price per unit $68 Variable cost per unit 18 Unit contribution margin $50\begin{array}{ll}\text { "Sales price per unit } & \$ 68 \\\text { Variable cost per unit } & 18 \\\text { Unit contribution margin } & \$ 50\end{array} "Sales price per unit Variable cost per unit Unit contribution margin $6818$50 Break-even point in sales dollars: 2700 × $68 = $183600
Learning Objectives
- Figure out the break-even points and margins of safety measured in units and by monetary value.
- Determine appropriate pricing strategies to enhance profitability.