Question

The Typhoon Resort, which has 100 rooms, has currently been experiencing an occupancy dip to a 60.00% level. The current rack rate is $80.00 with a marginal cost of $20.00 per room. The management of this resort would like to see the options when they apply $10.00 and 10.00% discounts from the current rack rate separately. Based on these two discount situations, what equivalent occupancy percentages must be achieved to maintain the same levels of contribution margin for both $10.00 and 10.00% discounts from the current rack rate? Also, what is the increase in #of rooms sold over the current #of rooms sold when the management applies $10.00 discount (assume that marginal cost will remain the same for all of the discount situations)?

Options:

A. 72.00% at $10 discount and 69.23% at 10% discount

B. 72.00% at $10 discount and 65.50% at 10% discount

C. 71.00% at $10 discount and 70.40% at 10% discount

D. 69.40% at $10 discount and 70.94% at 10% discount

Answer 1

Current occupancy of the Typhoon Resort = 60% of 100 rooms = 60 rooms

Contribution per room = Current rack rate less marginal cost = 80-20 = $60 per room

Therefore, total contribution margin = 60 rooms * $60 per room = $3,600

Now,

		figures in $
Particulars	$10 discount on rack rate	10% discount on rack rate
Rack rate	80	80
Discount	10	8
Discounted rack rate	70	72
Marginal cost	20	20
Contribution margin per room occupancy (a)	50	52
Total Contribution margin to be maintained (b)	3,600	3,600
No. of rooms to be occupied (b/a)	72	69.23
Equivalent occupancy percentage (on 100 rooms)	72.00%	69.23%

Note: Formula for equivalent occupancy percentage:

(Current Occupancy % * Current contribution margin / New contribution margin)

Hence, option A is correct. Other options are incorrect.

Also, the increase in number of rooms sold over the current no. of rooms sold when the management applies $10 discount = 72-60 = 12 rooms