Description
The instructions require you to develop and run a simulation model using Excel and write up an Executive Summary for this Case Study.
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Explanation & Answer
Attached.
BRU-THRU
In this case, BRU-THRU is beverage chain supply store in New York and this store are designed
to enable customers collect beverages, snacks and party supplies apparently, without getting out
of the car. They have a service lane which runs across the mile of the store and customers drive
into the store.as such, when a customer comes to pick his products at the store after arriving he
request his products while in the car and remain on the lane to be served while he is in the car.
In this context BRU-THRU president again wants to start up another new store just in the near
shopping center and there by planning has to be done to improve from the current running store
system to a more advanced system. Notably, profit and system efficiency are key components to
start a new store. However planning has to be done to project the operation of the store and as
such this included, profitability of the store, potential number of lost sale due to waiting on
lines.in this case the fixed cost of $ 1275 in a day included salaries ,and rent.
As such, in implementing the new system we have to note the operations of the store in terms of
activities in due time of 6 minutes each and count the number of customers being served at that
particular time within that interval time.as shown in the figure below.
Number of customers arriving
Probability
0
0.32
1
0.41
2
0.18
3
0.07
4
0.02
In this case the revenue generated by each customer is normally distributed with a mean of $15
and a standard deviation of $4.
Therefore the profit per day with the number of customer being served as well as loses put into
consideration given by
NUMBER OF CUSTOMERS * PROBERBILY IN ONE DAY *30 to get the both loses and
profit in one day incurring to 30 days.
Methods used
In this case methods used to distinguish the implementation the current system with the new on
include
Sampling
This where the comparison of activities and operation in the current system
Data analysis
In this case data is being analyzed in both current and the new implemented system
Findings
It is imperative to note that implementing a system a new system BRU-THRU president has to
consider the above findings to improve the his business in terms of profit, customer services and
effective operations between his workers and clients.
As a conclusion, it’s imperative to note that BRU-THRU is beverage chain supply store in New
York and this store are designed to enable customers collect beverages, snacks and party supplies
apparently, without getting out of the car. As such, implementing a new beverage store with the
aim of providing quality service and making profit as well and this is done in consideration of
the operation and services to the clients saving time and making more profit in due time.
Recommendation
In regards to BRU-THRU beverage store it’s imperative to note that implementation of a new
system in consideration to the key components mentioned above its clearly seen that with the
above information in terms of profit and service the stores operation will be affected positive
since the system will work effectively and I there recommend the above system to be
implemented by the president.
Attached.
AAPL Beta Estimation Page 1 of 21
This page shows the reformatted Excel regression output and graph of the line of best fit. The last tab
of the spreadsheet shows how to convert price and index data into the returns used in this analysis.
Monthly data
Adj. R-squared measures the %
variation in loss and profit returns
due to its relation with the market.
SUMMARY OUTPUT
number of customers
300
0.47032
2.01%
0.45%
0.10023
60
profit
loses
Observations
BRU-THRU
Alpha is the predictable firm-specific
component of returns. Over this period
loss average monthly return was about
3.4% higher than the market index. You
can see the positive alpha (regression
intercept > 0 on the graph).
20%
15%
df
SS
0.1655
0.5827
0.7482
MS
0.1655
0.0100
Coefficients Standard Error
0.034
0.0131
1.004
0.2474
t Stat
2.5939
4.0588
1
$1,275
$1,275
Intercept
F
Significance F
16.4735
0.0001
PROFIT
10%
implimentation process
operation
daiy
Total
5%
0%
P-value Lower 95% Upper 95%Lower 95.0%
Upper 95.0%
0.0120
0.0077 0.059986 0.00773
-5% 0.059986
0.0001
0.5090 1.499489 0.508955 1.499489
-10%
Beta is the slope of the regression
line. Beta measures how sensitive
profit returns are to market-wide
information (beta = 1 implies about the
same sensitivity as the average stock).
The graph depicts a regression line
with a slope = +1.00.
-15%
-20%
-20%
ˆ
number of customers arriving
Observation
0
1
2
3
4
Proberbility
0.32
0.41
0.18
0.07
0.02
-15%
CAPM
-10%
-5%
0%
LOSS
5%
10%
ˆ CAPM
Ri
rf 1 RMKT rf
15%
20%
AAPL 4-Factor Alpha & Betas Page 2 of 21
In recent years, estimating alpha over and above multiple sources of systematic risk has become the industry practice. In the Fama-French 4-factor model, there are systematic risk factors for the market
(Mkt-RF), the size premium (SMB stands for small minus big, the amount by which small-cap stock returns are expected to exceed large-cap stock returns), the value premium (HML stands for high minus
low, the amount by which the returns of high book-to-market (value) stocks are expected to exceed the returns of low book-to-market (growth) stocks, and momentum (UMD represents a momentum
factor that takes into account the extra returns expected to be earned when professional investors chase momentum trends, or the amount by which the returns of stocks with good price momentum -AAPL's alpha and market beta are substantially different when measured against the 4-factor model because the market factor used in the Fama-French model is less volatile than the NASDAQ index used
on the previous spreadsheet tab. AAPL registers a market beta of 1.56, higher than their single-factor market beta of 1.00, when measured against a less volatile market index. Because their market beta
is higher, their alpha is lower -- 2.4% per month compared with the 3.4% obtained from the single-factor model. Even though AAPL only has significant exposure to the market beta (the t-statistics on the
remaining systematic factors are insignificant), the higher market component of risk in AAPL's returns when measured according to the 4-factor model lowers the amount by which their returns appear to
beat the market (alpha), after adjusting for risk. It could be argued, however, that the higher F-stat of the first regression model indicates that it does a better job of modeling AAPL's returns than the 2nd
model, which includes insignificant factors (the higher the F-stat, the more vigorously we reject the hypothesis "the entire model is garbage"). One last technical note: the regression depicted on this page
uses the more statistically correct method of regressing AAPL's excess returns (over and above the risk-free rate) on the excess market factor returns (the factors Mkt-RF, SMB, HML and UMD are
constructed as excess returns and require no additional adjustment).
The data below have already been converted to monthly percentage changes.
Date
AAPL
AAPL-RF Mkt-RF
SMB
HML
UMD
RF
9.12
8.99
4.34
4.35
1.09
-1.70
0.13
2.53
2.38
-5.11
5.78
4.23
7.92
0.15
-4.04
-4.18
-1.19
-3.69
2.37
3.05
0.14
-23.95
-24.08
-7.15
3.50
1.55
6.17
0.13
-13.88
-14.03
-8.26
-5.11
-3.70
3.41
0.15
-3.28
-3.42
0.66
-2.17
2.15
1.68
0.14
-1.76
-1.90
-10.14
2.73
1.13
9.09
0.14
10.76
10.62
7.36
-2.99
-6.57
-5.17
0.14
-3.49
-3.61
6.01
3.16
-1.52
16.26
0.12
-7.61
-7.72
-5.44
-0.54
3.85
9.63
0.11
0.28
0.18
-2.44
1.37
-0.84
1.53
0.10
4.60
4.51
-1.63
-0.35
-1.54
1.29
0.09
-5.86
-5.96
0.93
0.88
-1.71
1.50
0.10
0.57
0.47
8.18
1.21
-0.08
-9.48
0.10
26.30
26.21
6.26
4.71
0.27
10.79
0.09
6.12
6.02
1.53
1.47
0.64
-1.06
0.10
10.60
10.53
2.24
5.64
-2.11
-0.35
0.07
7.31
7.24
2.42
2.64
1.78
-0.55
0.07
-8.40
-8.48
-0.99
0.56
0.99
-0.07
0.08
10.42
10.35
5.96
2.91
1.75
3.70
0.07
-8.65
-8.72
1.59
2.23
1.39
1.63
0.07
2.30
2.22
4.47
-2.87
2.76
-5.67
0.08
5.52
5.45
2.24
2.60
1.66
2.58
0.07
6.03
5.97
1.49
-1.20
0.37
-1.14
0.06
13.04
12.95
-1.16
1.85
-0.01
0.20
0.09
-4.66
-4.74
-2.50
-2.53
-1.69
-5.33
0.08
8.84
8.78
1.35
-0.12
-0.31
1.64
0.06
15.97
15.89
2.08
2.25
1.72
2.08
0.08
-0.61
-0.71
-3.87
-3.82
4.42
-2.32
0.10
6.68
6.57
0.16
-1.56
1.13
-1.54
0.11
12.35
12.24
1.95
2.82
0.40
5.28
0.11
35.19
35.08
1.67
0.49
-0.95
-1.54
0.11
27.98
27.83
4.67
4.11
1.96
3.24
0.15
-3.97
-4.13
3.36
0.18
-0.35
-2.82
0.16
19.41
19.25
-2.82
-1.67
2.52
3.12
0.16
16.67
16.51
2.11
-0.76
2.85
3.19
0.16
-7.11
-7.32
-1.90
-1.37
1.71
0.93
0.21
-13.46
-13.67
-2.73
-3.95
-0.49
-0.84
0.21
10.26
10.02
3.55
3.01
-1.16
0.46
0.24
-7.42
-7.65
0.92
2.58
2.84
2.10
0.23
15.87
15.63
4.09
2.77
-0.47
0.05
0.24
9.94
9.64
-0.89
-0.88
1.44
2.24
0.30
14.33
14.04
0.77
-0.64
1.22
3.50
0.29
7.42
7.15
-2.35
-1.05
-0.74
-1.37
0.27
17.76
17.45
3.73
0.98
-1.75
0.39
0.31
6.00
5.68
0.03
-0.47
0.51
0.77
0.32
5.04
4.69
3.66
5.32
1.18
2.77
0.35
-9.30
-9.64
-0.50
-0.31
-0.76
-1.80
0.34
-8.42
-8.79
1.54
3.51
0.04
1.22
0.37
12.23
11.87
0.94
-1.22
3.07
0.65
0.36
-15.09
-15.52
-3.53
-3.00
2.75
-3.66
0.43
-4.18
-4.58
-0.44
-0.47
1.51
1.52
0.40
18.67
18.27
-0.59
-3.90
3.25
-2.24
0.40
-0.16
-0.58
2.09
0.80
-1.66
-3.48
0.42
13.46
13.05
1.54
-1.21
-0.49
-0.98
0.41
5.33
4.92
3.30
1.68
0.49
-0.18
0.41
13.05
12.63
1.95
0.70
0.39
-1.00
0.42
-7.44
-7.84
0.68
-0.93
2.56
0.81
0.40
1.05
0.61
1.50
0.02
0.00
0.22
0.44
-1.31
-1.69
-1.78
1.38
0.32
-1.32
0.38
196801
196802
196803
196804
196805
196806
196807
196808
196809
196810
196811
196812
196901
196902
196903
196904
196905
196906
196907
196908
196909
196910
196911
196912
197001
197002
197003
197004
197005
197006
197007
197008
197009
197010
197011
197012
197101
197102
197103
197104
197105
197106
197107
197108
197109
197110
197111
197112
197201
197202
197203
197204
197205
197206
197207
197208
197209
197210
197211
197212
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.49
R Square
23.8%
Adjusted R Square
18.3%
Standard Error
10.19
Observations
60
ANOVA
df
Regression
Residual
Total
Intercept
Mkt-RF
SMB
HML
UMD
4
55
59
SS
1785.74
5707.17
7492.91
Coefficients Standard Error
0.024
1.46
1.565
0.43
0.098
0.62
0.345
0.71
0.237
0.39
MS
446.44
103.77
F
4.30
Significance F
0.00
t Stat
P-value
1.68
0.10
3.65
0.00
0.16
0.88
0.48
0.63
0.62
0.54
Lower 95%
-0.48
0.70
-1.15
-1.08
-0.53
R i rf 1 RMKT rf 2 RSMB 3 RHML 4 RUMD
ˆ
FF 4
FF 4
FF 4
FF 4
FF 4
R i rf ˆ 1
RMKT rf ˆ2
RSMB ˆ3
RHML ˆ4
R UMD
SIF Alpha and Beta Estimation Page 3 of 21
SIF Dates
SIF Port (Notice that this example uses weekly data -- the AAPL example used monthly data).
196801 100,179
196802 100,902
SIF Returns SIF x 100 SIF-RF
0.722%
0.722
0.622
Mkt-RF
1.250
SMB
HML
RF
-0.940
-0.560
0.100
S&P 500 NASDAQ
1.441
0.015
Single-factor regression
SIF x 100 vs. S&P 500
196803
99,101
-1.785%
-1.785
-1.885
-1.250
-0.540
-0.950
0.100
-1.185
-0.007
196804
196805
93,535
92,673
-5.617%
-0.922%
-5.617
-0.922
-5.717
-1.027
-5.310
-1.810
-1.310
-1.000
-0.870
-1.170
0.100
0.105
-4.899
-1.775
-0.047
-0.020
196806
196807
196808
93,660
93,020
95,756
1.066%
-0.684%
2.942%
1.066
-0.684
2.942
0.961
-0.789
2.837
1.120
-1.070
2.670
2.080
-0.200
-0.860
-0.940
0.980
-0.230
0.105
0.105
0.105
1.436
-0.530
2.312
0.013
-0.016
0.029
Regression Statistics
Multiple R
0.776
R Square
60.2%
Adjusted R Square
59.8%
Standard Error
2.868
Observations
114
196809
196810
95,328
94,077
-0.447%
-1.312%
-0.447
-1.312
-0.552
-1.392
-0.310
-1.180
-0.030
-0.570
-1.060
-0.150
0.105
0.080
-0.364
-1.387
0.008
-0.012
ANOVA
196811
196812
96,170
98,667
2.225%
2.597%
2.225
2.597
2.145
2.517
196901
98,602
-0.066%
-0.066
-0.146
196902 101,516
2.956%
2.956
2.876
1.880
2.810
-1.230
0.280
-0.640
-0.130
0.080
0.080
0.240
-0.880
-1.110
0.080
2.290
1.820
0.070
0.080
2.112
2.796
0.066
2.020
0.014
0.027
0.011
0.029
196903 101,483
-0.033%
-0.033
-0.113
0.410
-0.960
-0.460
0.080
0.270
0.009
97,131
-4.289%
-4.289
-4.369
-3.750
-0.890
-0.700
0.080
-3.917
-0.029
196904
196905
99,230
2.161%
2.161
2.081
2.240
0.360
-0.440
0.080
2.309
0.029
196906
97,476
-1.767%
-1.767
-1.852
-1.340
-0.910
-1.170
0.085
-1.669
0.002
196907
94,168
-3.394%
-3.394
-3.479
-3.710
0.540
1.590
0.085
-3.706
df
Regression
Residual
Total
Intercept
S&P 500
1
112
113
Coefficients
0.0498
0.8676
-0.065
196908
94,493
0.345%
0.345
0.260
-0.290
-0.740
-0.550
0.085
0.347
0.004
196909
92,459
-2.153%
-2.153
-2.238
-1.490
-0.220
-0.270
0.085
-1.237
-0.015
3-Factor regression
(SIF x 100)-RF vs. 3 FF Factors
2.597
2.512
196911
94,891
0.033%
0.033
-0.034
1.650
0.180
0.250
0.067
1.588
0.017
196912
98,052
3.332%
3.332
3.265
-2.700
-1.150
-0.200
0.067
-2.440
-0.026
197001
197002
197003
93,210
96,195
94,302
-4.939%
3.202%
-1.967%
-4.939
3.202
-1.967
-5.006
3.135
-2.019
1.250
-0.170
-4.500
2.280
-1.200
-1.290
-0.510
0.180
0.220
0.067
0.067
0.052
1.125
-0.402
-4.522
0.021
-0.007
-0.063
Regression Statistics
Multiple R
0.793
R Square
62.8%
Adjusted R Square
61.7%
Standard Error
2.830
Observations
103
197004
197005
197006
197007
90,635
90,481
85,777
87,393
-3.888%
-0.170%
-5.199%
1.885%
-3.888
-0.170
-5.199
1.885
-3.940
-0.222
-5.251
1.853
-1.320
-5.420
0.920
4.980
-1.350
1.430
0.880
0.490
-0.350
-0.060
1.690
2.140
0.052
0.052
0.052
0.032
-0.752
-5.412
0.409
4.871
-0.026
-0.041
-0.006
0.037
ANOVA
197008
197009
197010
89,717
87,248
87,697
2.659%
-2.753%
0.516%
2.659
-2.753
0.516
2.627
-2.785
0.484
-4.220
1.220
0.390
0.660
-1.450
-0.740
0.510
0.280
-0.090
0.032
0.032
0.032
-4.596
1.405
0.231
-0.045
0.007
-0.008
197011
89,361
1.896%
1.896
1.864
-1.220
0.480
-0.760
0.032
-1.661
-0.014
196910
94,860
2.597%
2.690
-1.500
-0.890
0.085
2.807
0.025
197012
86,879
-2.777%
-2.777
-2.819
-2.940
-0.550
0.170
0.042
-2.800
-0.026
197101
197102
83,392
85,991
-4.013%
3.117%
-4.013
3.117
-4.055
3.075
-0.360
1.840
0.780
-0.670
-0.310
0.250
0.042
0.042
-0.404
3.212
0.000
0.021
197103
197104
197105
85,712
89,208
89,906
-0.325%
4.079%
0.782%
-0.325
4.079
0.782
-0.367
4.037
0.740
-0.220
4.250
-2.480
1.260
-0.460
-0.620
-0.330
0.090
0.370
0.042
0.042
0.042
-1.075
4.195
-2.742
0.001
0.049
-0.034
197106
197107
87,676
91,509
-2.480%
4.372%
-2.480
4.372
-2.522
4.330
4.220
0.280
-0.190
-0.560
0.260
-0.720
0.042
0.042
4.314
0.540
0.049
0.008
197108
197109
197110
197111
197112
92,914
92,798
92,684
90,461
92,493
1.535%
-0.125%
-0.122%
-2.399%
2.247%
1.535
-0.125
-0.122
-2.399
2.247
1.493
-0.167
-0.164
-2.441
2.205
1.040
-1.070
2.820
-3.040
1.810
-0.640
0.910
0.070
1.270
0.790
0.850
0.170
-0.260
0.090
-0.410
0.042
0.042
0.042
0.042
0.042
1.149
-1.812
2.670
-3.467
1.777
0.022
-0.013
0.034
-0.033
0.032
197201
197202
197203
197204
197205
197206
197207
197208
197209
197210
197211
197212
90,376
90,292
90,965
88,461
85,776
82,710...