Question

Lemon Ltd. offers executive training seminars using, in part, recorded lectures of a well-known speaker. The agreement calls for Lemon to pay a royalty for the use of the lectures. The lecturer's agent offers Lemon two options. The first option is revenue-based and Lemon agrees to pay 25 percent of its revenues to the speaker. The second option is a flat rate of $358,800 annually for the use of the lectures in these seminars. The royalty agreement will run one year and the royalty option chosen cannot be changed during the agreement. All other royalty terms are the same.

Lemon charges $1,600 for the seminar and the variable costs for the seminar (excluding any royalty) is $400. Annual fixed costs (excluding any royalties) are $538,200.

Required:

a. What is the annual break-even level assuming:

1. 1. The revenue-based royalty agreement?
2. 2. The flat-rate royalty agreement?

b. At what annual volume would the operating profit be the same regardless of the royalty option chosen?

c. Assume an annual volume of 1,500 seminars. What is the operating leverage assuming:

1. 1. The revenue-based royalty agreement?
2. 2. The flat-rate royalty agreement?

d. Assume an annual volume of 1,500 seminars. What is the margin of safety assuming:

1. 1. The revenue-based royalty agreement?
2. 2. The flat-rate royalty agreement?

Answer 1

A) 1) Total annual fixed cost = $ 538,200

variable cost if the revenue based loyalty agreement considered = $ 400+ [ $ 1,600 X 25%] = $ 800

Contributions margin = revenues - variable costs = $ 1,600 - $ 800 = $ 800

PV ratio = [contribution / revenue] X 100% = [$ 800/ $ 1,600 ] X 100% = 50%

Annual break even level = fixed cost / PV ratio

Annual break even level = $ 538,200/50% = $ 538,200 X 100/50 = $ 1,076,400

2) Fixed annual cost = $ 538,200 +$ 358,800 = $ 897,000

Revenue per seminar = $ 1,600 variable cost = $ 400

Contribution per seminar = $ 1,600.- $ 400 = $ 1,200

PV ratio = [contributions / revenues ] X 100% = [ $ 1,200/ $ 1,600] X 100% = 75%

Annual break even level = $ 897,000/ 75% = $ 897,000 X 100/75 = $ 1,196,000

B) $ 358,800 / [ $ 1,600 X 25%] = 897 seminars

Annual revenues for 897 seminar = $ 897 X $ 1,600 = $ 1,435,200. At $ 1,435,200 revenue volume and 897 annual seminar total operating profit in both the options will remain same.

Particulars	Revenue based loyalty agreement	Flat rate royalty agreement
Revenue [ 897 X $ 1,600]	$ 1,435,200	$ 1,435,200
varible cost for revenue based loyalty 897 X $( 400+ 400)	$ ( 717,600)
Variable cost for flat rate 897 X $ 400		$( 358,800)
Contribution	$ 717,600	$ 1,076,400
Fixed cost
Under royalty based	$ (538,200)
Under flat rate ( $ 538,200 + $ 358,800)		$( 897,000)
Operating profit	$ 179,400	$ 179,400

C) calculation for operating leverage

Particulars	revenue based on royalty agreement	flat rate royalty agreement
Revenue ( $ 1,600 X 1,500)	$ 2,400,000	$ 2,400,000
Less:variable costs	$ 1,200,000	$ 600,000
Contributions	$ 1,200,000	$ 1,800,000
Less: Fixed cost	$ 538,200	$ 897,000
Operating profit	$ 661,800	$ 903,000

Operating leverage under revenue based on royalty agreement = [change in operating profits / change in revenue ] = [ $ 661,800/ $ 2,400,000] = 0.27575 or 27.575%

Operating leverage under flat royalty agreement = [ $ 903,000/$ 2,400,000] = 0.37625 or 37.625%

Note: There was no actual previous sales or revenue so calculated operating profits considered as change in operating profits. [ previous year operating profits was $ 0, due to lack of information ]

D) margin of safety = actual sales or revenue - BEP sales or revenue

Margin of safety under revenue based loyalty agreement in 1,500 seminars volume = $ 2,400,000 - $ 1,076,400 = $ 1,323,600

Margin of safety under flat rate royalty agreement in 1,500 seminars volume = $ 2,400,000 - $ 1,196,000 = $ 1,204,000