
To determine: The best-case and worst-case
Introduction:
Net present value (NPV) refers to the current discounted value of the future cash flows. The company should accept the project, if the net present value is positive or greater than zero and vice-versa. If there are two mutually exclusive projects, then the company has to select the project that has higher net present value.

Answer to Problem 21QP
The best-case NPV is $53,849,087.272.
The NPVof worst-caseis -$19,007,791.712.
Explanation of Solution
Given information:
The new clubs sold $715 per set and number of sets sold is 75,000 set per year. The cheaper club was sold for $425 per set and number of sets sold is 12,000 set per year. The expensive clubs was sold for $1,150 in which the company has lost sales of 10,000 sets.
The variable cost of the new club is $385 per set, variable cost of the expensive cub is $620, and the variable cost of the cheaper club is $195. The fixed costs each years is $9,400,000. The accurate estimate is ±10%.
Formula:
The formula to calculate best-case of unit sales projection under the scenario analysis:
The formula to calculate best-case of price projection under the scenario analysis:
The formula to calculate best-case of variable costs projection under the scenario analysis:
The formula to calculate best-case of fixed costs projection under the scenario analysis:
The formula to calculate best-case of sales lost projection under the scenario analysis:
The formula to calculate best-case of sales gained projection under the scenario analysis:
The formula to calculate worst-case of unit sales projection under the scenario analysis:
The formula to calculate worst-case of price projection under the scenario analysis:
The formula to calculate worst-case of variable costs projection under the scenario analysis:
The formula to calculate worst-case of fixed costs projection under the scenario analysis:
The formula to calculate worst case of sales lost projection under the scenario analysis:
The formula to calculate worst-case of sales gained projection under the scenario analysis:
Compute the best-case of unit sales projection under the scenario analysis:
Hence, the best-case of unit sales projection under the scenario analysis are 82,500 units.
Compute best-case of price projection under the scenario analysis:
Hence, the best-case of price projection under the scenario analysis are $787.
Compute the best-case of variable costs projection under the scenario analysis:
Hence, the best-case of variable costs projection under the scenario analysis are $347.
Compute the best-case of fixed costs projection under the scenario analysis:
Hence, the best-case of fixed costs projection under the scenario analysis are $8,460,000.
Compute best-case of sales lost projection under the scenario analysis:
Hence, the best-case of sales lost projection under the scenario analysis are 9,000 units.
Compute the best-case of sales gained projection under the scenario analysis:
Hence, the best-case of sales gained projection under the scenario analysis are 13,200 units.
Compute the worst-case of unit sales projection under the scenario analysis:
Hence, the worst-case of unit sales projection under the scenario analysis are 67,500 units.
Compute worst-case of price projection under the scenario analysis:
Hence, the worst-case of price projection under the scenario analysis are $644.
Compute the worst-case of variable costs projection under the scenario analysis:
Hence, the worst-case of variable costs projection under the scenario analysis are $424.
Compute the worst-case of fixed costs projection under the scenario analysis:
Hence, the worst-case of fixed costs projection under the scenario analysis are $10,340,000.
Compute worst-case of sales lost projection under the scenario analysis:
Hence, the worst-case of sales lost projection under the scenario analysis are 11,000 units.
Compute the worst-case of sales gained projection under the scenario analysis:
Hence, the worst-case of sales gained projection under the scenario analysis are 10,800 units.
Note: After estimating the best-case and worst-case for the variables find out the total sales and total variable costs for the best-case scenario in each variable.
Formulae:
The formula to calculate total sales:
The formula to calculate total variable costs:
The formula to calculate total sales of the entire clubs:
The formula to calculate total variable costs of the entire clubs:
Compute the total sales of new clubs:
Hence, the total sales of the new clubs are $64,927,500.
Compute the total sales of expensive clubs:
Hence, the total sales of the expensive clubs are -$10,350,000.
Compute the total sales of cheaper clubs:
Hence, the total sales of the cheaper clubs are $5,610,000.
Compute the total sales of the entire clubs:
Hence, the total sales of the entire clubs are $60,187,500.
Table that indicating the entire sales for clubs:
Particulars | Price per sets (in $) (A) | Number of set Sold (in units) (B) | Total sales (in $) (C)=(A)×(B) |
New clubs | 787 | 82,500 | 64,927,500 |
Expensive clubs | 1,150 | (9,000) | (10,350,000) |
Cheaper clubs | 425 | 13,200 | 5,610,000 |
Total sales | 60,187,500 |
Hence, the total sales for the entire clubs are $60,187,500.
Compute total variable costs of new clubs:
Hence, the total variable costs of the new clubs are −$28,627,500.
Compute total variable costs of expensive clubs:
Hence, the total variable costs of the expensive clubs are $5,580,000.
Compute total variable costs of cheaper clubs:
Hence, the total variable costs of the cheaper clubs are −$2,574,000.
Compute the total variable costs of the entire clubs:
Hence, the total variable costs of the entire clubs are -$25,621,500.
Table that indicating the variable costs:
Particulars | Variable cost per Sets (in $) (A) | Number of set sold (in units) (B) | Total variable costs (in $) (C)=(A)×(B) |
New clubs | ($347) | 82,500 | ($28,627,500) |
Expensive clubs | ($620) | (9,000) | $5,580,000 |
Cheaper clubs | ($195) | 13,200 | ($2,574,000) |
Total variable costs | ($25,621,500) |
Hence, the variable costs for the clubs are −$25,621,500.
Note: Inorder toprepare pro forma income statement,
The formula to calculate depreciation of plant and equipment:
The formula to calculate EBIT:
The formula to calculate tax when tax rate is given:
The formula to calculate net income:
Compute depreciation expense of plant and equipment:
Hence, the depreciation expense is $4,300,000.
Compute the EBIT:
Hence, the EBIT is $21,806,000.
Compute tax when tax rate is given:
Hence, the tax is $8,722,400.
Compute the net income:
Hence, the net income is $13,083,600.
Table that indicating pro form income statement:
Pro forma income statement | |
Particulars | Amounts (in $) |
Sales | 60,187,500 |
Variable costs | 25,627,500 |
Fixed costs | 8,460,000 |
Depreciation | 4,300,000 |
Earnings before interest and taxes | 21,806,000 |
Taxes | 8,722,400 |
Net income | 13,083,600 |
Hence, the net income as per the pro forma income statement is $13,083,600.
Note: After preparing pro forma income statement, determine the operating cash flow (OCF) and NPV of best-case.
The formula to calculate OCF:
The formula to calculate NPV (after change in price):
Where,
OCF refers to the operating cash flows
Compute the operating cash flow (OCF):
Hence, the OCF is $17,383,600.
Compute the NPV:
Hence, the NPVof best-caseis $53,849,087.272.
Note: After estimating the NPV of best-case find out the total sales and total variable costs for the worst-case scenario in each variable.
Formulae:
The formula to calculate total sales:
The formula to calculate total variable costs:
The formula to calculate total sales of the entire clubs:
The formula to calculate total variable costs of the entire clubs:
Compute the total sales of new clubs:
Hence, the total sales of the new clubs are $43,470,000.
Compute the total sales of expensive clubs:
Hence, the total sales of the expensive clubs are -$12,650,000.
Compute the total sales of cheaper clubs:
Hence, the total sales of the cheaper clubs are $4,590,000.
Compute the total sales of the entire clubs:
Hence, the total sales of the entire clubs are $35,410,000.
Table that indicating the entire sales for clubs:
Particulars | Price per sets (in $) (A) | Number of set sold (in units) (B) | Total sales (in $) (C)=(A)×(B) |
New clubs | 644 | 67,500 | 43,470,000 |
Expensive clubs | 1,150 | (11,000) | (12,650,000) |
Cheaper clubs | 425 | 10,800 | 4,590,000 |
Total sales | 35,410,000 |
Hence, the total sales for the entire clubs are $35,410,000.
Compute total variable costs of new clubs:
Hence, the total variable costs of the new clubs are −$28,620,000.
Compute total variable costs of expensive clubs:
Hence, the total variable costs of the expensive clubs are $6,820,000.
Compute total variable costs of cheaper clubs:
Hence, the total variable costs of the cheaper clubs are -$2,106,000.
Compute the total variable costs of the entire clubs:
Hence, the total variable costs of the entire clubs are -$23,906,000.
Table that indicating the variable costs:
Particulars | Variable cost per sets (in $) (A) | Number of set sold (in units) (B) | Total variable costs (in $) (C)=(A)×(B) |
New clubs | ($424) | 67,500 | ($28,620,000) |
Expensive clubs | ($620) | (11,000) | $6,820,000 |
Cheaper clubs | ($195) | 10,800 | ($2,106,000) |
Total variable costs | ($23,906,000) |
Hence, the variable costs for the clubs are -$23,906,000.
Note: Inorder toprepare pro forma income statement, depreciation Earnings before interest and taxes (EBIT), and tax has to be computed to ascertain net income from this statement.
The formula to calculate EBIT:
The formula to calculate tax when tax rate is given:
The formula to calculate net income:
Compute the EBIT:
Hence, the EBIT is -$3,136,000.
Compute tax when tax rate is given:
Hence, the tax is -$1,254,400.
Compute the net income:
Hence, the net income is -$1,881,600.
Table that indicating pro form income statement:
Pro forma income statement | |
Particulars | Amounts (in $) |
Sales | 35,410,000 |
Variable costs | 23,906,000 |
Fixed costs | 10,340,000 |
Depreciation | 4,300,000 |
Earnings before interest and taxes | -3,136,000 |
Taxes | -1,254,400 |
Net income | -1,881,600 |
Hence, the net income as per the pro forma income statement is −$1,881,600.
Note: After preparing pro forma income statement, determine the operating cash flow (OCF) and NPV of worst-case.
The formula to calculate OCF:
The formula to calculate NPV (after change in price):
Where,
OCF refers to the operating cash flows
Compute the operating cash flow (OCF):
Hence, the OCF is $2,418,400.
Compute the NPV:
Hence, the NPVof worst-caseis -$19,007,791.712.
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