3-40
Alternative cost structures, uncertainty, and sensitivity analysis.
1.
Contribution margin assuming fixed rental arrangement = $50 – $30 = $20 per bouquet
Fixed costs = $5,000
Breakeven point = $5,000 ÷ $20 per bouquet = 250 bouquets
Contribution margin assuming $10 per arrangement rental agreement
= $50 – $30 – $10 = $10 per bouquet
Fixed costs = $0
Breakeven point = $0 ÷ $10 per bouquet = 0
(i.e. EB makes a profit no matter how few bouquets it sells)
2.
Let
x
denote the number of bouquets EB must sell for it to be indifferent between the fixed rent and
royalty agreement.
To calculate
x
we solve the following equation.
$50
x
– $30
x
– $5,000 = $50
x
– $40
x
$20
x
– $5,000 = $10
x
$10
x
= $5,000
x
= $5,000 ÷ $10 = 500 bouquets
For sales between 0 to 500 bouquets, EB prefers the royalty agreement because in this range, $10
x
>
$20
x
– $5,000.
For sales greater than 500 bouquets, EB prefers the fixed rent agreement because in this
range, $20
x
– $5,000 > $10
x
.
3.
If we assume the $5 savings in variable costs applies to both options, we solve the
following
equation for
x
.
$50
x
– $25
x
– $5,000 = $50
x
– $35
x
$25
x
– $5,000 = $15
x
$10
x
= $5,000
x
= $5,000 ÷ $10 per bouquet = 500 bouquets
The answer is the same as in Requirement 2, that is, for sales between 0 to 500 bouquets, EB prefers
the royalty agreement because in this range, $15
x
> $25
x
– $5,000.
For sales greater than 500
bouquets, EB prefers the fixed rent agreement because in this range, $25
x
– $5,000 > $15
x
.
4.
Fixed rent agreement:
Bouquets
Sold
(1)
Revenue
(2)
Fixed
Costs
(3)
Variable
Costs
(4)
Operating
Income
(Loss)
(5)=(2)–(3)–(4)
Probability
(6)
Expected
Operating
Income
(7)=(5)
×
(6)
200
200
×
$50=$10,000
$5,000
200
×
$30=$
6,000
$ (1,000)
0.20
$ ( 200)
400
400
×
$50=$20,000
$5,000
400
×
$30=$12,000
$
3,000
0.20
600
600
600
×
$50=$30,000
$5,000
600
×
$30=$18,000
$
7,000
0.20
1,400
800
800
×
$50=$40,000
$5,000
800
×
$30=$24,000
$11,000
0.20
2,200
1,000
1,000
×
$50=$50,000
$5,000
1,000
×
$30=$30,000