Break-Even Analysis and Profit Planning

This solved assignment focuses on break-even analysis for two products, A and B. It calculates the break-even point in units and dollars for each product separately. The assignment then explores the break-even point when manufacturing both products in a 3:1 ratio, determining the required production volume for both products to achieve a specific profit target. Finally, it calculates the Earnings Before Interest and Taxes (EBIT) and net earnings considering a tax rate of 30 cents per dollar.

Decision Support Tools

TABLE OF CONTENTS
QUESTION 1: DECISION ANALYSIS.........................................................................................4
A. Assessing the utility function as well as standard gamble which helps in determining utility
value.............................................................................................................................................4
B. Investing primarily in share market........................................................................................4
1...................................................................................................................................................4
2...................................................................................................................................................5
3...................................................................................................................................................5
4...................................................................................................................................................5
5...................................................................................................................................................5
6...................................................................................................................................................5
QUESTION 2: VALUE OF INFORMATION................................................................................6
a....................................................................................................................................................6
B. Analyzing the prior probability...............................................................................................6
C. Posterior probability................................................................................................................7
D. Expected net gain and loss after conducting the market research..........................................7
QUESTION 3 MONTE CARLO SIMULATION...........................................................................7
a....................................................................................................................................................7
b...................................................................................................................................................7
QUESTION 4 REGRESSION ANALYSIS....................................................................................8
a....................................................................................................................................................8
b...................................................................................................................................................8
c..................................................................................................................................................12
d.................................................................................................................................................12
QUESTION 5: CVP ANALYSIS..................................................................................................13

a..................................................................................................................................................13
b.................................................................................................................................................13
c..................................................................................................................................................14
d.................................................................................................................................................14
D (i)............................................................................................................................................14
D (ii)...........................................................................................................................................14

QUESTION 1: DECISION ANALYSIS
A. Assessing the utility function as well as standard gamble which helps in determining utility
value
In utility assessment, it consists of identifying bad and best utility to be used in process.
Thus, where 0 represents a bad, while 1 for good quality of a utility. This assessment helps in
ranking the commodities which will be helpful in identifying no. of better and worst articles are
stated in a study. In context with implicating this theory which determines that, monetary value
will not be a reliable indication in judging over all outcomes and make decision. Here,
economists have to assume that significant individual makes decision to enhance their utilities.
Standard Gamble:
In consideration with this approach the standard gamble techniques had been used in
analyzing the values of utilities. It assists that when the variables are indifferent the utility values
are equal.
B. Investing primarily in share market
1.
Decision Matrix
Investment
10000 Shares
Government
Bonds
Monetary
Gain/loss
Action States
%
Return
Yearly
return in
Amount % Return
Yearly
return in
Amount Amount
Full Investment in shares 14.00% 1400 9.00% 900 Gain of 500
Full Investment in shares 8.00% 800 9.00% 900 Loss of 100
Full Investment in shares 0.00% 0 9.00% 900 Loss of 900
Half Investment is shares 14.00% 700 9.00% 450 Gain of 250
Half Investment is shares 8.00% 400 9.00% 450 Loss of 50
Half Investment is shares 0.00% 0 9.00% 450 Loss of 450
All the comparisons done with the returns on the Government Bonds as it is minimum
returns that can be achieved.

2.
Alternative that an optimist will choose which is providing higher rate of returns and they
are risk takers.
3.
Alternative that a pessimist will choose is where the returns are fixed they think the world
is bad.
4.
Criterion of Regret
There has been influences of two criterion of regret such as Maximin and Minimax
Maximin: It benefits in analyzing a minimum payoff for each variable. Similarly, it
selects the variable with the highest minimum payoff.
Minimax: It analyzed the possible regret for variables under each state of nature. It also
demonstrated the maximum possible regret for such variables as well as selects the alternative
with smallest maximum regret.
5.
Probability Investment
%
Return
Government
Bonds
%
Return
Total
Returns
Good Market 0.4 4000 14.00% 6000 9.00% 1100
Fair Market 0.4 4000 8.00% 6000 9.00% 860
Bad Market 0.2 2000 0.00% 8000 9.00% 720
Optimum action will be as probability of having good market is there than the investment
should be done in that way as it will provide maximum return on investments
6.
The expected value of perfect information % is:
Stock 880
Government Bonds 900

As the maximum of expectation is in Government Bonds. As not knowing the directions
where will be the market go we expect the most of returns from government bonds thus EMV
=900
QUESTION 2: VALUE OF INFORMATION
a.
B. Analyzing the prior probability
In analyzing outcomes based on favorable and unfavorable probabilities of variables. The
prior probability be analyses as:
P(F)= 0.70 P(A ǀ F)= 70% (There are $3500 cost to the favorable market predictions)
P(U)= 0.20 P(Aǀ U)= 20% (There are $1000 cost to the unfavorable market predictions)

C. Posterior probability
P(A) = P(A ǀ F) P(F) + P(A ǀ U) P(U)
P(F ǀ A) = P(F ∩ A)/P(A) = P(A ǀ F) P(F)/P(A ǀ F) P(M) + P(A ǀ U) P(U)
= 3500*0.7 / (3500*0.7) + (1000*0.2)
= 0.924
P(U ǀ A) = P(U ∩ A)/ P(A) = P(A ǀ U) P(U)/ P(A ǀ F) P(F) + P(A ǀ U) P(U)
1000* 0.20/ (3500*0.7)+ (1000*0.2)
= 0.075
D. Expected net gain and loss after conducting the market research
Probability of having favorable outcomes = 3500
Probability of having unfavorable outcomes are = 1000
Therefore,
=3500-1000
= 2500
There will be gain of 2500 which insist that the market research will be helpful in bringing the
suitable gains.
QUESTION 3 MONTE CARLO SIMULATION
a.
Average monthly profit to Ajax Tyres over the period of 12 months are as follows:
Ajax Tyres
DATA
Prob Cum
prob Demand Selling Price $160 $180
0.05 0.05 100 Monthly Fixed
cost $2,000

0.1 0.15 120 Profit Margin 20% 30%
0.2 0.35 140
0.3 0.65 160
0.25 0.9 180
0.1 1 200
1
MODE
L
Sellin
g Profit Fixed
Month RN1 Deman
d Price RN2 Margi
n Costs Profit
1 0.2329
7 199 $173 0.2276
3 0.2 $2,00
0 34.6
2 0.822 164 $173 0.1330
7 0.21
$2,00
0
36.902
1
3 0.966 159 $172 0.8388
4 0.28
$2,00
0 48.828
4 0.028 157 $173 0.1857
7 0.22
$2,00
0
37.813
8
5 0.511 104 $164 0.8110
4 0.28
$2,00
0
46.101
1
6 0.810 131 $168 0.8309
2 0.28
$2,00
0
47.559
5
7 0.066 179 $170 0.6692
4 0.27
$2,00
0
45.377
1
8 0.655 175 $177 0.7726
4 0.28
$2,00
0
49.075
8
9 0.943 182 $165 0.0978
2 0.21
$2,00
0 34.614
10 0.635 132 $164 0.2095
4 0.22
$2,00
0
36.236
4
11 0.736 171 $171 0.7680
3 0.28
$2,00
0
47.333
3
12 0.657 196 $161 0.5075
1 0.25
$2,00
0 40.371
Ajax Tyres
DAT
A

Prob Cum
prob Demand Sellin
g Price 160 180
0.05 =+B6 100 Mont
hly Fixed cost 200
0
0.1 =+C6+
B7 120 Profit Margin 0.2 0.3
0.2 =+C7+
B8 140
0.3 =+C8+
B9 160
0.25 =+C9+
B10 180
0.1 =+C10
+B11 200
1
MO
DEL
Selling Profit Fix
ed
Mon
th RN1 Demand Price RN2 Margin Cos
ts Profit
1 0.2329
7
=RANDBETWE
EN(100,200)
=RANDBETWE
EN(160,180)
0.227
625 0.2 =+
H6
=+E17
*G17
2
=RAN
D()
=RANDBETWE
EN(100,200)
=RANDBETWE
EN(160,180) =RA
ND()
=0.2+(0.3-
0.2)*F18
=+
H1
7
=+E18
*G18
3 =RAN
D()
=RANDBETWE
EN(100,200)
=RANDBETWE
EN(160,180) =RA
ND()
=0.2+(0.3-
0.2)*F19
=+
H1
8
=+E19
*G19
4
=RAN
D()
=RANDBETWE
EN(100,200)
=RANDBETWE
EN(160,180) =RA
ND()
=0.2+(0.3-
0.2)*F20
=+
H1
9
=+E20
*G20
5 =RAN
D()
=RANDBETWE
EN(100,200)
=RANDBETWE
EN(160,180) =RA
ND()
=0.2+(0.3-
0.2)*F21
=+
H2
0
=+E21
*G21
6
=RAN
D()
=RANDBETWE
EN(100,200)
=RANDBETWE
EN(160,180) =RA
ND()
=0.2+(0.3-
0.2)*F22
=+
H2
1
=+E22
*G22
7 =RAN
D()
=RANDBETWE
EN(100,200)
=RANDBETWE
EN(160,180) =RA
ND()
=0.2+(0.3-
0.2)*F23
=+
H2
2
=+E23
*G23
8
=RAN
D()
=RANDBETWE
EN(100,200)
=RANDBETWE
EN(160,180) =RA
ND()
=0.2+(0.3-
0.2)*F24
=+
H2
3
=+E24
*G24

9 =RAN
D()
=RANDBETWE
EN(100,200)
=RANDBETWE
EN(160,180) =RA
ND()
=0.2+(0.3-
0.2)*F25
=+
H2
4
=+E25
*G25
10
=RAN
D()
=RANDBETWE
EN(100,200)
=RANDBETWE
EN(160,180) =RA
ND()
=0.2+(0.3-
0.2)*F26
=+
H2
5
=+E26
*G26
11 =RAN
D()
=RANDBETWE
EN(100,200)
=RANDBETWE
EN(160,180) =RA
ND()
=0.2+(0.3-
0.2)*F27
=+
H2
6
=+E27
*G27
12
=RAN
D()
=RANDBETWE
EN(100,200)
=RANDBETWE
EN(160,180) =RA
ND()
=0.2+(0.3-
0.2)*F28
=+
H2
7
=+E28
*G28
b.
Month
Profit
per
unit
1 34.6
2 36.90
3 48.83
4 37.81
5 46.10
6 47.56
7 45.38
8 49.08
9 34.61
10 36.24
11 47.33
12 40.37
average profit per unit 42.07
c.
By doing assessment, it has identified that average profit margin will increase by 22-32%
if selling price inclines by $40. In this case, Ajax Tyres will not lose sales so it is recommended
to the concerned business unit that it should focus on doing changes in selling price. This in turn
positively contributes in the profit margin of an organization.

QUESTION 4 REGRESSION ANALYSIS
a.
High-low method:
Particulars Amoun
t (in $)
Highest activity cost 48000
Lowest activity cost 46000
Highest machine hours 3,800
Lowest machine hours 1800
Highest cost - lowest cost 2000
Highest unit - lowest units 2000
(Highest - lowest cost) / (Highest - lowest
units) 1
Variable cost = 1 per unit
Fixed cost: $48000 – (3800 * 1)
= $48000 - $3800
= $44200
Thus, cost equation is
Y = $44200 + X
Hence, in the case of 3000 machine hours overhead cost will be
= $44200 + (1 * 3000)
= $44200 + $3000
= $47200
b.
Null hypothesis (H0): There is no significant statistically significant difference in the mean
value of overhead cost and machine hours.

Alternative hypothesis (H1): There is a statistically significant difference in the mean value of
overhead cost and machine hours.
On the basis of MH
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.104236
344
R Square
0.010865
215
Adjusted R
Square
-
0.112776
63
Standard
Error
15447.61
363
Observations 10
ANOVA
df SS MS F
Significa
nce F
Regression 1
2096986
5.8
2096986
5.8
0.087
88 0.77444
Residual 8
1909030
134
2386287
67
Total 9
1930000
000
Coefficie
nts
Standar
d Error t Stat
P-
value
Lower
95%
Uppe
r
95%
Lowe
r
95.0
%
Uppe
r
95.0
%
Intercept
59198.78
45
21473.78
29
2.75679
347
0.024
8 9680.15
1087
17
9680.
15
1087
17
MH
-
2.304380
86
7.773521
99
-
0.29643
97
0.774
44 -20.23
15.62
14
-
20.23
15.62
14
The above depicted table shows that p value is greater than 0.05. Referring this, it can be
presented that null hypothesis is true and other one false. Hence, machine hours have not high
level of impact on overhead cost or expenses.

On the basis of Batches
Null hypothesis (H0): There is no significant statistically significant difference in the mean
value of overhead cost and batches.
Alternative hypothesis (H1): There is a statistically significant difference in the mean value of
overhead cost and batches.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.911766
618
R Square
0.831318
365
Adjusted R
Square
0.810233
161
Standard
Error
6379.219
736
Observations 10
ANOVA
df SS MS F
Significan
ce F
Regression 1
1604444
444
1604444
444
39.42
66 0.00024
Residual 8
3255555
56
4069444
4.4
Total 9
1930000
000
Coefficie
nts
Standar
d Error t Stat
P-
value
Lower
95%
Uppe
r
95%
Lowe
r
95.0
%
Uppe
r
95.0
%
Intercept
6555.555
556
7666.86
795
0.85505
001
0.417
39 -11124
2423
5.4
-
1112
4
2423
5.4
Batches
234.5679
012
37.3571
557
6.27906
212
0.000
24 148.422
320.7
14
148.4
22
320.7
14

Outcome derived through regression analysis clearly exhibits that p value accounts for
0.00024 significantly. It entails that batches place significant impact on overhead expenses from
statistical perspective.
On the basis of Batches and MH
Null hypothesis (H0): There is no significant statistically significant difference in the mean
value of overhead cost and batches as well as MH.
Alternative hypothesis (H1): There is a statistically significant difference in the mean value of
overhead cost and batches as well as MH.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.912733
424
R Square
0.833082
304
Adjusted R
Square
0.785391
534
Standard
Error
6783.921
68
Observations 10
ANOVA
df SS MS F
Significa
nce F
Regression 2
1607848
846
8039244
23
17.46
84 0.0019
Residual 7
3221511
54
4602159
3.4
Total 9
1930000
000
Coefficie
nts
Standar
d Error t Stat
P-
value
Lower
95%
Uppe
r
95%
Lowe
r
95.0
%
Uppe
r
95.0
%
Intercept 9205.657
918
12704.91
84
0.72457
434
0.492
22
-20837 3924
8
-
2083
3924
8

7
MH
-
0.930666
77
3.421799
93
-
0.27198
16
0.793
48 -9.0219
7.160
6
-
9.021
9
7.160
6
Batches
233.8274
53
39.82029
02
5.87206
803
0.000
62 139.667
327.9
87
139.6
67
327.9
87
By applying regression analysis tool on data set it has found that p value falls within the
standard limit such as 0.05. However, in comparison to MH, batches can be considered as the
considered as the most suitable predictor which in turn helps in making estimation about
overhead expenditure.
c.
By doing assessment, it has identified that multiple regression analysis technique
is highly effectual over simple. Moreover, such technique helps in assessing specific factor
which in turn has greater impact on dependent variables over others and thereby aid in decision
making. The use of multiple regression method will be helpful in analyzing the accurate
outcomes instead of implicating the simple regression for each variable. Therefore, this brings
totally different outcomes so Multiple regression method will be helpful I addressing the results
of such variables at ones.
d.
Linear regression
OH
Cost MH Batches
1 $80,00
0 2,200 300
2 40,000 2,400 120
3 63,000 2,100 250
4 45,000 2,700 160
5 44,000 2,300 200
6 48,000 3,800 170
7 65,000 3,600 260
8 46,000 1,800 160
9 33,000 3,200 150
10 66,000 2,800 210
11 72599. 2,000 150

9
1 2 3 4 5 6 7 8 9 10
$0
$10,000
$20,000
$30,000
$40,000
$50,000
$60,000
$70,000
$80,000
$90,000
f(x) = − 1187.87878787879 x + 59533.3333333333
OH Cost
QUESTION 5: CVP ANALYSIS
a.
The Unit Contribution margin of each product
Product
A
Product
B
Particulars Figures Figures
Sales 12 15
Less-: Variable Cost 8 10
Contribution 4 5
b.
Computation of Break Even Point
Product
B
Particulars Figures
Fixed Costs 5000
Sales 15
Less Variable Costs 10
5
BEP=Fixed costs/sales-variable cost 1000

c.
Product
B
Particulars Figures
Fixed Costs 5000
Sales 12
Less Variable Costs 8
BEP (in units) =Fixed costs/sales-
variable cost 4
BEP (in dollars) = BEP in units * SP
per unit
1250 * 12
= $15000
d.
Break Even Point if both product
manufacture in 3:1
Product A B
Fixed Costs in ratio 3:1 3750 1250
Sales 12 15
Less Variable Costs 8 10
Contribution 4 5
BEP (in units) = Fixed costs/sales-
variable cost 938 250
D (i)
Computation of units need to be manufactured
Particulars
Formula Product
A
Product
B
Fixed Costs 3750 1250
Desired profit (3:1 of 3500) 2625 875
Contribution per unit 4 5
Desired Sales in units
Fixed Costs
+Target
Profits/Contribut
ion per unit 1594 425

D (ii)
Product A B
Desired Sales in units 3188 850.00
Contribution per unit 4 5
Contribution 12750.00 4250.00
Less Fixed Costs 3750 1250
EBIT 9000.00 3000.00
Less Tax 30cents per dollar 2700.00 900.00
EAT in ratio 3:1(8400) 6300 2100