The owner of a small business is planning on expanding his b

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 890

Solution

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