The owner of a small business is planning on expanding his business. The expansi
ID: 2393391 • Letter: T
Question
The owner of a small business is planning on expanding his business. The expansion will take an initial investment of S12,000 in cash from his existing business. The owner is interested in estimating the risk involved in the expansion. If there is more than a 10% risk ofhaving a negative net present value of the investment for the expansion, he might reconsider the expansion. The expansion will have revenues and expenses associated with it The following are the assumptions about the income and expenses (a) Quarter 1 Sales A normally distributed variable with a minimum of $110,000 and a maximum of S140,000 (b) Cost of Goods Sold Ratio: Rate Prob 70%-75% 75%-80% 80%-85% 30% 60% 10% (c) General and Administrative Expenses Salaries: S14,000 for Quarters 1 and 2 $15,500 for Quarters 3 and 4 The following are 96's of Gross Profit Commissions: 10% Utilities Telephone Avriable with a skewed left distribution with a minimum value of 3%, a most likely value of 6%, and a maximum value of 890Explanation / Answer
Quarter 1
Amount ($)
Amount ($)
Sales (110000 x 0.5 + 140000 x 0.5)
125000
Cost of goods sold (125000 x 76.5%)
95625
Gross profit
29375
Salaries
14000
Commission (29375 x 10%)
2937.5
Utilities (29375 x %)
1468.75
Telephone (29375 x 6%)
1762.5
Travel (29375 x 3%)
881.25
Entertainment promotion (29375 x 7.5%)
2203.125
Payroll taxes (14000 x 7%)
980
24233.13
Net profit before tax
5141.875
Less: Tax @36% (5141.875 x 36%)
1851.075
Net profit after tax
3290.8
Quarter 2
Amount ($)
Amount ($)
Gross profit
32312.5
Salaries
14000
Commission (32312.5 x 10%)
3231.25
Utilities (32312.5 x5 %)
1615.625
Telephone (32312.5 x 6%)
1938.75
Travel (32312.5 x 3%)
969.375
Entertainment promotion (32312.5 x 7.5%)
2423.438
Payroll taxes (14000 x 7%)
980
25158.44
Net profit before tax
7154.063
Less: Tax @36% (7154.063 x 36%)
2575.463
Net profit after tax
4578.6
Quarter 3
Amount ($)
Amount ($)
Gross profit
35543.75
Salaries
15500
Commission (35543.75 x 10%)
3554.375
Utilities (35543.75 x5 %)
1777.188
Telephone (35543.75 x 6%)
2132.625
Travel (35543.75 x 3%)
1066.313
Entertainment promotion (35543.75 x 7.5%)
2665.781
Payroll taxes (15500 x 7%)
1085
27781.28
Net profit before tax
7762.469
Less: Tax @36% (7762.469 x 36%)
2794.489
Net profit after tax
4967.98
Quarter 4
Amount ($)
Amount ($)
Gross profit
39098.13
Salaries
15500
Commission (39098.13 x 10%)
3909.813
Utilities (39098.13 x5 %)
1954.906
Telephone (39098.13 x 6%)
2345.888
Travel (39098.13 x 3%)
1172.944
Entertainment promotion (39098.13 x 7.5%)
2932.359
Payroll taxes (15500 x 7%)
1085
28900.91
Net profit before tax
10197.22
Less: Tax @36% (10197.22 x 36%)
3670.998
Net profit after tax
6526.218
Total net profit after tax (3290.8 + 4578.6 + 4967.98 + 6526.22)
19363.6
PV factor @8% pa.
0.925926
Present value of net profit for year (19363.60 x 0.926)
17929.26
Less: Initial investment
12000
Net present value (NPV)
5929.257
As can be seen from the above calculation that the expansion with an initial investment of $12,000 is expected to give positive return to the organization as the NPV of the expansion project is positive with $5929.26. Thus, the project should be accepted.
Note:
It is important to note that the most probable values have been taken to compute the above table of net present value of the expansion project.
Since it has been said that the quarterly revenue is expected to increase by 10% hence, assuming that the cost of goods sold would be constant at 76.50% of sales the gross profits have been adjusted with an increase of 10% for each quarter in the computation.
Workings:
Cost of goods sold for each quarter.
Rate
Middle rate
Probability
Expected rate (Middle rate x Prob.)
(70% - 75%)
72.50%
30%
21.7500%
(75% - 80%)
77.50%
60%
46.500%
(80% - 85%)
82.50%
10%
8.2500%
76.5000%
Quarter 1
Amount ($)
Amount ($)
Sales (110000 x 0.5 + 140000 x 0.5)
125000
Cost of goods sold (125000 x 76.5%)
95625
Gross profit
29375
Salaries
14000
Commission (29375 x 10%)
2937.5
Utilities (29375 x %)
1468.75
Telephone (29375 x 6%)
1762.5
Travel (29375 x 3%)
881.25
Entertainment promotion (29375 x 7.5%)
2203.125
Payroll taxes (14000 x 7%)
980
24233.13
Net profit before tax
5141.875
Less: Tax @36% (5141.875 x 36%)
1851.075
Net profit after tax
3290.8
Quarter 2
Amount ($)
Amount ($)
Gross profit
32312.5
Salaries
14000
Commission (32312.5 x 10%)
3231.25
Utilities (32312.5 x5 %)
1615.625
Telephone (32312.5 x 6%)
1938.75
Travel (32312.5 x 3%)
969.375
Entertainment promotion (32312.5 x 7.5%)
2423.438
Payroll taxes (14000 x 7%)
980
25158.44
Net profit before tax
7154.063
Less: Tax @36% (7154.063 x 36%)
2575.463
Net profit after tax
4578.6
Quarter 3
Amount ($)
Amount ($)
Gross profit
35543.75
Salaries
15500
Commission (35543.75 x 10%)
3554.375
Utilities (35543.75 x5 %)
1777.188
Telephone (35543.75 x 6%)
2132.625
Travel (35543.75 x 3%)
1066.313
Entertainment promotion (35543.75 x 7.5%)
2665.781
Payroll taxes (15500 x 7%)
1085
27781.28
Net profit before tax
7762.469
Less: Tax @36% (7762.469 x 36%)
2794.489
Net profit after tax
4967.98
Quarter 4
Amount ($)
Amount ($)
Gross profit
39098.13
Salaries
15500
Commission (39098.13 x 10%)
3909.813
Utilities (39098.13 x5 %)
1954.906
Telephone (39098.13 x 6%)
2345.888
Travel (39098.13 x 3%)
1172.944
Entertainment promotion (39098.13 x 7.5%)
2932.359
Payroll taxes (15500 x 7%)
1085
28900.91
Net profit before tax
10197.22
Less: Tax @36% (10197.22 x 36%)
3670.998
Net profit after tax
6526.218
Total net profit after tax (3290.8 + 4578.6 + 4967.98 + 6526.22)
19363.6
PV factor @8% pa.
0.925926
Present value of net profit for year (19363.60 x 0.926)
17929.26
Less: Initial investment
12000
Net present value (NPV)
5929.257
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