Chapter 11, Problem 2MAD

Service yield pricing and differential equations

Cityscape Hotels has 200 rooms available in a major metropolitan city. The hotel is able to attract business customers during the weekdays and leisure customers during the weekend. However, the leisure customers on weekends occupy fewer rooms than do business customers on weekdays. Thus, Cityscape plans to provide special weekend pricing to attract additional leisure customers. A hotel room is priced at $180 per room night. The cost of a hotel room night includes the following:

The special weekend price is proposed for $120 per room night. At this price, it is anticipated that average occupancy for the weekend (Friday, Saturday, and Sunday) will increase from 30% to 50% of available rooms.

1. a. What is the contribution margin for a room night under the normal pricing if only the hotel depreciation and hotel staff (excluding housekeeping) are assumed fixed for all occupancy levels?
2. b. Determine the contribution margin for a room night under the proposed weekend pricing.
3. c. Prepare a differential analysis showing the differential profit for an average weekend between the existing (Alternative 1) and discount (Alternative 2) price plans.
4. d. Should management accept the proposed weekend pricing plan? Explain.

To determine

Calculate the contribution margin for a room night at Hotel C.

Explanation of Solution

Product pricing: Product pricing is the method used for fixing a price for the products sold or the services offered to the consumers. The main aim of product pricing is to calculate the cost and the contribution margin, based on which the price is fixed.

Contribution Margin: Contribution Margin refers to the margin of profit expected by the company. The contribution margin is the difference between the selling price and the cost of the product

Calculate the contribution margin for a room night.

Rate per room night		$180.00
Variable Costs per room night:
Housekeeping service	$23.00
Utilities	$7.00
Amenities	$3.00
Total variable cost per room night		$33.00
Contribution margin per room night		$147.00

Table (1)

Therefore, the contribution margin for a room night at Hotel C is $147.

The contribution margin for a room night at Hotel C is $147. The fixed costs are already distributed among the occupied rooms. Hence the fixed cost is not included in the calculation of the contribution margin for a room night at Hotel C, which is $147.

To determine

Ascertain the contribution margin for a room night at Hotel C, under proposed weekend pricing.

Explanation of Solution

Calculate the contribution margin for a room night.

Rate per room night		$120.00
Variable Costs per room night:
Housekeeping service	$23.00
Utilities	$7.00
Amenities	$3.00
Total variable cost per room night		$33.00
Contribution margin per room night		$87.00

Table (2)

The contribution margin for a room night at Hotel C is $87. The fixed costs are already distributed among the occupied rooms. Hence the fixed cost is not included in the calculation of the contribution margin for a room night at Hotel C, under proposed weekend pricing which is $87.

To determine

Prepare the differential analysis for Hotel C, showing differential income for an average weekend on the given and proposed price plan.

Explanation of Solution

The differential analysis for Hotel C for given alternatives is shown below.

Differential Analysis of Hotel C
	Continue with Existing plan	Execute the Proposed plan	Differential Effect on Income
Revenues per weekend	(1)$32,400	(2)$36,000	$3,600
Variable cost per weekend
Housekeeping Service	(3)(-) $4,410	(4)(-) $6,900	(-) $2,760
Utilities	(5)(-) $1,260	(6)(-) $2,100	(-) $840
Amenities	(7)(-) $540	(8)(-) $900	(-) $360
Total Variable Cost per weekend	(-) $5,940	(-) $9,900	(-) $3,960
Contribution margin per weekend	$26,460	$26,100	(-) $360

Table (3)

The differential analysis of Hotel C shows a fall in income by $360, if the proposed plan is accepted, hence the proposed plan should be rejected.

Working Note:

(1) Calculate the revenue from continuing with existing plan.

  $\begin{array}{c}\text{Revenue = }\left(\begin{array}{l}\text{Actual Price }\times \\ \text{Number of rooms}\end{array}\right)\times \left(\text{30\%}\right)\times \left(\text{3 weekend days}\right)\\ =\left(\text{\$180 }\times \text{ 200 rooms}\right)\times \left(\text{30\%}\right)\times \text{ 3 }\\ =\$36,000\times \left(\text{30\%}\right)\times \text{ 3}\\ =\$10,800\times 3\\ =\text{ \$32,400}\end{array}$

(2) Calculate the revenue from executing the proposed plan.

  $\begin{array}{c}\text{Revenue = }\left(\begin{array}{l}\text{Proposed Price }\times \\ \text{Number of rooms}\end{array}\right)\times \left(\text{50\%}\right)\times \left(\text{3 weekend days}\right)\\ =\left(\text{\$120 }\times \text{ 200 rooms}\right)\times \left(\text{50\%}\right)\times \text{ 3 }\\ =\$24,000\times \left(\text{50\%}\right)\times \text{ 3}\\ =\$12,000\times 3\\ =\text{ \$36,000}\end{array}$

(3) Calculate the cost of housekeepingservice for continuing with existing plan.

  $\begin{array}{c}\begin{array}{l}\text{Housekeeping}\\ \text{Services}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Actual Cost }\times \\ \text{Number of rooms}\end{array}\right)\times \left(\text{30\%}\right)\times \left(\text{3 weekend days}\right)\\ =\left(\text{\$23 }\times \text{ 200 rooms}\right)\times \left(\text{30\%}\right)\times \text{ 3 }\\ =\$4,600\times \left(\text{30\%}\right)\times \text{ 3}\\ =\$1,380\times 3\\ =\text{ \$4,140}\end{array}$

(4) Calculate the cost of housekeeping service for executing the proposed plan.

  $\begin{array}{c}\begin{array}{l}\text{Housekeeping}\\ \text{Services}\end{array}\}\text{= }\left(\begin{array}{l}\text{Proposed Cost }\times \\ \text{Number of rooms}\end{array}\right)\times \left(\text{50\%}\right)\times \left(\text{3 weekend days}\right)\\ =\left(\text{\$23 }\times \text{ 200 rooms}\right)\times \left(\text{50\%}\right)\times \text{ 3 }\\ =\$4,600\times \left(\text{50\%}\right)\times \text{ 3}\\ =\$2,300\times 3\\ =\text{ \$6,900}\end{array}$

(5) Calculate the cost of utilities for continuing with existing plan.

  $\begin{array}{c}\text{Utilities = }\left(\begin{array}{l}\text{Actual Cost }\times \\ \text{Number of rooms}\end{array}\right)\times \left(\text{30\%}\right)\times \left(\text{3 weekend days}\right)\\ =\left(\text{\$7 }\times \text{ 200 rooms}\right)\times \left(\text{30\%}\right)\times \text{ 3 }\\ =\$1,400\times \left(\text{30\%}\right)\times \text{ 3}\\ =\$420\times 3\\ =\text{ \$1,260}\end{array}$

(6) Calculate the cost of utilities for executing the proposed plan.

  $\begin{array}{c}\text{Utilities = }\left(\begin{array}{l}\text{Proposed Cost }\times \\ \text{Number of rooms}\end{array}\right)\times \left(\text{50\%}\right)\times \left(\text{3 weekend days}\right)\\ =\left(\text{\$7 }\times \text{ 200 rooms}\right)\times \left(\text{50\%}\right)\times \text{ 3 }\\ =\$1,400\times \left(\text{50\%}\right)\times \text{ 3}\\ =\$700\times 3\\ =\text{ \$2,100}\end{array}$

(7) Calculate the cost of amenities for continuing with existing plan.

  $\begin{array}{c}\text{Amenities = }\left(\begin{array}{l}\text{Actual Cost }\times \\ \text{Number of rooms}\end{array}\right)\times \left(\text{30\%}\right)\times \left(\text{3 weekend days}\right)\\ =\left(\text{\$3 }\times \text{ 200 rooms}\right)\times \left(\text{30\%}\right)\times \text{ 3 }\\ =\$600\times \left(\text{30\%}\right)\times \text{ 3}\\ =\$180\times 3\\ =\text{ \$540}\end{array}$

(8) Calculate the cost of amenities for executing the proposed plan.

  $\begin{array}{c}\text{Amenities = }\left(\begin{array}{l}\text{Proposed Cost }\times \\ \text{Number of rooms}\end{array}\right)\times \left(\text{50\%}\right)\times \left(\text{3 weekend days}\right)\\ =\left(\text{\$3 }\times \text{ 200 rooms}\right)\times \left(\text{50\%}\right)\times \text{ 3 }\\ =\$600\times \left(\text{50\%}\right)\times \text{ 3}\\ =\$300\times 3\\ =\text{ \$900}\end{array}$

To determine

Explain whether the management of Hotel C, should accept the proposed weekend pricing plan.

Explanation of Solution

The management of Hotel C should not accept the proposed weekend pricing plan. The proposed plan results in the decrease in income by $360. However, if there is a greater demand and more number of rooms get filled up then the proposed plan shall bring in greater revenue.