Chapter 11, Problem 21QP

Summary Introduction

To determine: The best-case and worst-case net present value (NPV)

Introduction:

Net present value (NPV) refers to the current discounted value of the future cash flows. The company must 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 $59,730,546.67 and the NPVof worst-caseis −$2,867,597.69.

Explanation of Solution

Given information:

The new clubs sold $825 per set and the number of sets sold is 55,000 set per year. The cheaper club was sold for $410 per set and the number of sets sold is 12,000 set per year. The expensive clubs was sold for $1,100 in which the company has lost sales of 10,000 sets.

The variable cost of the new club is $395 per set, the variable cost of the expensive cub is $650, and the variable cost of the cheaper club is $185. The fixed costs for every year is $9,200,000. The accurate estimate is ±10%. The net working capital is $1,400,000. The tax rate is 40% and the cost of capital is 10%. Cost of plant and machinery is $29,400,000.

Formulae:

The formula to calculate the best-case of unit sales projection under the scenario analysis:

$\text{Unit sales for the best case}=\left[\begin{array}{l}\text{Value of base case for unit sales }\\ +\left(\begin{array}{l}\text{ Percenatge of accurate estimate}\\ \times \text{ Value of base case for unit sales}\end{array}\right)\end{array}\right]$

The formula to calculatethebest-case of price projection under the scenario analysis:

$\text{Price for the best case}=\left[\begin{array}{l}\text{Value of base case for price }\\ +\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{Value of base case for price}\end{array}\right)\end{array}\right]$

The formula to calculatethebest-caseof variable costs projection under the scenario analysis:

$\text{Variable costs for the best case}=\left[\begin{array}{l}\text{Value of base case for variable costs}\\ -\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{Value of base case for variable costs}\end{array}\right)\end{array}\right]$

The formula to calculatethebest-caseof fixed costs projection under the scenario analysis:

$\text{Fixed costs for the best case}=\left[\begin{array}{l}\text{Value of base case for fixed costs}\\ -\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{}\text{Value of base case for fixed costs}\end{array}\right)\end{array}\right]$

The formula to calculate thebest-caseof sales lost projection under the scenario analysis:

$\text{Sales lost for the best case}=\left[\begin{array}{l}\text{Value of base case for sales lost}\\ -\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{Value of base case for sales lost}\end{array}\right)\end{array}\right]$

The formula to calculatethebest-caseof sales gained projection under the scenario analysis:

$\text{Sales gained for the best case}=\left[\begin{array}{l}\text{Value of base case for sales gained}\\ +\left(\begin{array}{l}\text{ Percenatge of accurate estimate}\\ \times \text{}\text{ Value of base case for sales gained}\end{array}\right)\end{array}\right]$

The formula to calculatetheworst-case of unit sales projection under the scenario analysis:

$\text{Unit sales for the worst case}=\left[\begin{array}{l}\text{Value of base case for unit sales }\\ -\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{Value of base case for unit sales}\end{array}\right)\end{array}\right]$

The formula to calculatetheworst-case of price projection under the scenario analysis:

$\text{Price for the worst case}=\left[\begin{array}{l}\text{Value of base case for price }\\ -\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{Value of base case for price}\end{array}\right)\end{array}\right]$

The formula to calculate the worst-case of variable costs projection under the scenario analysis:

$\text{Variable costs for the worst case}=\left[\begin{array}{l}\text{Value of base case for variable costs}\\ +\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{Value of base case for variable costs}\end{array}\right)\end{array}\right]$

The formula to calculatetheworst-case of fixed costs projection under the scenario analysis:

$\text{Fixed costs for the worst case}=\left[\begin{array}{l}\text{Value of base case for fixed costs}\\ +\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{}\text{Value of base case for fixed costs}\end{array}\right)\end{array}\right]$

The formula to calculatetheworst caseof sales lost projection under the scenario analysis:

$\text{Sales lost for the worst case}=\left[\begin{array}{l}\text{Value of base case for sales lost}\\ +\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{Value of base case for sales lost}\end{array}\right)\end{array}\right]$

The formula to calculateworst-caseof sales gained projection under the scenario analysis:

$\text{Sales gained for worst case}=\left[\begin{array}{l}\text{Value of base case for sales gained}\\ -\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{Value of base case for sales gained}\end{array}\right)\end{array}\right]$

Compute thebest-case of unit sales projection under the scenario analysis:

$\begin{array}{c}\text{Unit sales for the best case}=\left[\begin{array}{l}\text{Value of base case for unit sales }\\ +\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{Value of base case forunit sales}\end{array}\right)\end{array}\right]\\ =\left[55,000+\left(\frac{10}{100}\times 55,000\right)\right]\\ =\left[55,000+\left(0.1\times 55,000\right)\right]\\ =55,000+5,500\\ =60,500\text{ units}\end{array}$

Hence, the best-case of unit sales projection under the scenario analysis are 60,500 units.

Compute the best-case of price projection under the scenario analysis:

$\begin{array}{c}\text{Price for the best case}=\left[\begin{array}{l}\text{Value of base case for price }\\ +\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{Value of base case for price}\end{array}\right)\end{array}\right]\\ =\$825+\left(\frac{10}{100}\times \$825\right)\\ =\$825+\left(0.10\times \$825\right)\\ =\$825+\$82.5\\ =\$907.5\end{array}$

Hence, the best-case of price projection under the scenario analysis are $907.5.

Computethebest-case of variable costs projection under the scenario analysis:

$\begin{array}{c}\text{Variable costs for the best case}=\left[\begin{array}{l}\text{Value of base case for variable costs}\\ -\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{Value of base case for variable costs}\end{array}\right)\end{array}\right]\\ =\left[\$395-\left(\frac{10}{100}\times \$395\right)\right]\\ =\left[\$395-\left(0.10\times \$395\right)\right]\\ =\$395-\$39.5\\ =\$355.5\end{array}$

Hence, the best-case of variable costs projection under the scenario analysis are $355.5.

Computethebest-case of fixed costs projection under the scenario analysis:

$\begin{array}{c}\text{Fixed costs for the best case}=\left[\begin{array}{l}\text{Value of base case for fixed costs}\\ -\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{}\text{Value of base case for fixed costs}\end{array}\right)\end{array}\right]\\ =\left[\$9,200,000-\left(\frac{10}{100}\times \$9,200,000\right)\right]\\ =\left[\$9,200,000-\left(0.10\times \$9,200,000\right)\right]\\ =\$9,200,000-\$920,000\\ =\$8,280,000\end{array}$

Hence, the best-case of fixed costs projection under the scenario analysis are $8,280,000.

Computethebest-caseof sales lost projection under the scenario analysis:

$\begin{array}{c}\text{Sales lost for the best case}=\left[\begin{array}{l}\text{Value of base case for sales lost}\\ -\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{}\text{Value of base case for sales lost}\end{array}\right)\end{array}\right]\\ =10,000-\left(\frac{10}{100}\times 10,000\right)\\ =10,000-\left(0.10\times 10,000\right)\\ =10,000-1,000\\ =9,000\text{ units}\end{array}$

Hence, the best-case of sales lost projection under the scenario analysis are 9,000 units.

Computethebest-caseof sales gained projection under the scenario analysis:

$\begin{array}{c}\text{Sales gained for the best case}=\left[\begin{array}{l}\text{Value of base case for sales gained}\\ +\left(\begin{array}{l}\text{ Percenatge of accurate estimate}\\ \times \text{}\text{Value of base case for sales gained}\end{array}\right)\end{array}\right]\\ =12,000+\left(\frac{10}{100}\times 12,000\right)\\ =12,000+\left(0.10\times 12,000\right)\\ =12,000+1,200\\ =13,200\text{ units}\end{array}$

Hence, the best-case of sales gained projection under the scenario analysis are 13,200 units.

Computetheworst-case of unit sales projection under the scenario analysis:

$\begin{array}{c}\text{Unit sales for the worst case}=\left[\begin{array}{l}\text{Value of base case unit sales }\\ -\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{Value of base case unit sales}\end{array}\right)\end{array}\right]\\ =\left[55,000-\left(\frac{10}{100}\times 55,000\right)\right]\\ =\left[55,000-\left(0.10\times 55,000\right)\right]\\ =55,000-5,500\\ =49,500\text{ units}\end{array}$

Hence, the worst-case of unit sales projection under the scenario analysis are 49,500 units.

Computetheworst-case of price projection under the scenario analysis:

$\begin{array}{c}\text{Price for the worst case}=\left[\begin{array}{l}\text{Value of base case for price }\\ +\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{Value of base case for price}\end{array}\right)\end{array}\right]\\ =\$825-\left(\frac{10}{100}\times \$825\right)\\ =\$825-\left(0.10\times \$825\right)\\ =\$825-\$82.5\\ =\$742.5\end{array}$

Hence, the worst-case of price projection under the scenario analysis are $742.5.

Computetheworst-case of variable costs projection under the scenario analysis:

$\begin{array}{c}\text{Variable costs for the worst case}=\left[\begin{array}{l}\text{Value of base case for variable costs}\\ +\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{Value of base case for variable costs}\end{array}\right)\end{array}\right]\\ =\left[\$395+\left(\frac{10}{100}\times \$395\right)\right]\\ =\left[\$395+\left(0.10\times \$395\right)\right]\\ =\$395+\$39.5\\ =\$434.5\end{array}$

Hence, the worst-case of variable costs projection under the scenario analysis are $434.5.

Computetheworst-case of fixed costs projection under the scenario analysis:

$\begin{array}{c}\text{Fixed costs for the worst case}=\left[\begin{array}{l}\text{Value of base case for fixed costs}\\ +\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{Value of base case for fixed costs}\end{array}\right)\end{array}\right]\\ =\$9,200,000+\left(\frac{10}{100}\times \$9,200,000\right)\\ =\$9,200,000+\left(0.10\times \$9,200,000\right)\\ =\$9,200,000+\$920,000\\ =\$10,120,000\end{array}$

Hence, the worst-case of fixed costs projection under the scenario analysis are $10,120,000.

Computetheworst-caseof sales lost projection under the scenario analysis:

$\begin{array}{c}\text{Sales lost for the worst case}=\left[\begin{array}{l}\text{Value of base case for sales lost}\\ +\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{}\text{Value of base case for sales lost}\end{array}\right)\end{array}\right]\\ =10,000+\left(\frac{10}{100}\times 10,000\right)\\ =10,000+\left(0.10\times 10,000\right)\\ =10,000+1,000\\ =11,000\text{ units}\end{array}$

Hence, the worst-case of sales lost projection under the scenario analysis are 11,000 units.

Computetheworst-caseof sales gained projection under the scenario analysis:

$\begin{array}{c}\text{Sales gained for the worst case}=\left[\begin{array}{l}\text{Value of base case for sales gained}\\ -\left(\begin{array}{l}\text{Percenatge of accurate estimate}\\ \times \text{}\text{Value of base case for sales gained}\end{array}\right)\end{array}\right]\\ =12,000-\left(\frac{10}{100}\times 12,000\right)\\ =12,000-\left(0.10\times 12,000\right)\\ =12,000-1,200\\ =10,800\text{ units}\end{array}$

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:

$\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}$

The formula to calculate total variable costs:

$\text{Total Variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}$

The formula to calculate total sales of the entire clubs:

$\text{Total sales of all clubs}=\left(\begin{array}{l}\text{Total sales of new clubs}\\ +\text{Total sales of expensive clubs}\\ +\text{Total sales of cheaper clubs}\end{array}\right)$

The formula to calculatetotal variable costs of the entire clubs:

$\text{Total variable costs of all clubs}=\left(\begin{array}{l}\text{Total variable costs of new clubs}\\ +\text{Total variable costs of expensive clubs}\\ +\text{Total variable costs of cheaper clubs}\end{array}\right)$

Compute the total sales of new clubs:

$\begin{array}{c}\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}\\ =\$907.5\times 60,500\\ =\$54,903,750\end{array}$

Hence, the total sales of the new clubs are $54,903,750.

Compute the total sales of expensive clubs:

$\begin{array}{c}\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}\\ =\$1,100\times -9,000\\ =-\$9,900,000\end{array}$

Hence, the total sales of the expensive clubs are −$9,900,000.

Compute the total sales of cheaper clubs:

$\begin{array}{c}\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}\\ =\$410\times 13,200\\ =\$5,412,000\end{array}$

Hence, the total sales of the cheaper clubs are $5,412,000.

Compute the total sales of the entire clubs:

$\begin{array}{c}\text{Total sales of all clubs}=\left(\begin{array}{l}\text{Total sales of new clubs}\\ +\text{Total sales of expensive clubs}\\ +\text{Total sales of cheaper clubs}\end{array}\right)\\ =\$54,903,750+\left(-\$9,900,000\right)+\$5,412,000\\ =\$54,903,750-\$9,900,000+\$5,412,000\\ =\$50,415,750\end{array}$

Hence, the total sales of the entire clubs are $50,415,750.

Table that indicatesthe entire sales for clubs is as follows:

Particulars	Price per sets (in $) (A)	Number of set sold (in units) (B)	Total sales (in $) (C)=(A)×(B)
New clubs	$907.5	60,500	$54,903,750
Expensive clubs	$1,100	(9,000)	$(9,900,000)
Cheaper clubs	$410	13,200	$5,412,000
Total sales			$50,415,750

Hence, the total sales for the entire clubs are $50,415,750.

Compute total variable costs of new clubs:

$\begin{array}{c}\text{Total variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}\\ =-\$355.5\times 49,500\\ =-\$17,597,250\end{array}$

Hence, the total variable costs of the new clubs are −$17,597,250.

Compute total variable costs of expensive clubs:

$\begin{array}{c}\text{Total variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}\\ =\left(-\$650\right)\times \left(-9,000\right)\\ =\$5,850,000\end{array}$

Hence, the total variable costs of the expensive clubs are $5,850,000.

Compute total variable costs of cheaper clubs:

$\begin{array}{c}\text{Total variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}\\ =\left(-\$185\right)\times 13,200\\ =-\$2,442,000\end{array}$

Hence, the total variable costs of the cheaper clubs are −$2,442,000.

Compute the total variable costs of the entire clubs:

$\begin{array}{c}\text{Total variable costs of all clubs}=\left(\begin{array}{l}\text{Total variable costs of new clubs}\\ +\text{Total variable costs of expensive clubs}\\ +\text{Total variable costs of cheaper clubs}\end{array}\right)\\ =\left(-\$17,597,250\right)+\$5,850,000+\left(-\$2,442,000\right)\\ =-\$14,189,250\end{array}$

Hence, the total variable costs of the entire clubs are −$14,189,250.

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	($355.5)	49,500	($17,597,250)
Expensive clubs	($650)	(9,000)	$5,850,000
Cheaper clubs	($185)	13,200	($2,442,000)
Total variable costs			($14,189,250)

Hence, the variable costs for the clubs are −$14,189,250.

Note: Inorder topreparethe pro forma income statement, depreciation of plant and equipment, earningsbefore interest and taxes (EBIT), and tax has to be computed to ascertain the net income from this statement.

The formula to calculate depreciation of plant and equipment:

$\text{Depreciation expense}=\frac{\text{Cost of the assets}}{\text{Useful life}}$

The formula to calculate EBIT:

$\text{EBIT}=\text{Sales}-\left(\text{Variable costs}+\text{Fixed costs}+\text{Depreciation}\right)$

The formula to calculate tax when tax rate is given:

$\text{Tax}=\text{EBIT}\times \text{Tax rate}$

The formula to calculate net income:

$\text{Net income}=\text{EBIT}-\text{Tax}$

Compute depreciation expense of plant and equipment:

$\begin{array}{c}\text{Depreciation expense}=\frac{\text{Cost of the assets}}{\text{Useful life}}\\ =\frac{\$29,400,000}{7}\\ =\$4,200,000\end{array}$

Hence, the depreciation expense is $4,200,000.

Compute theEBIT:

$\begin{array}{c}\text{EBIT}=\text{Sales}-\left(\text{Variable costs}+\text{Fixed costs}+\text{Depreciation}\right)\\ =\$50,415,750-\left(\$14,189,250+\$8,280,000+\$4,200,000\right)\\ =\$50,415,750-\$26,669,250\\ =\$23,746,500\end{array}$

Hence, the EBIT is $23,746,500.

Compute tax when tax rate is given:

$\begin{array}{c}\text{Tax}=\text{EBIT}\times \text{Tax rate}\\ =\$23,746,500\times \left(\frac{40}{100}\right)\\ =\$23,746,500\times 0.40\\ =\$9,498,600\end{array}$

Hence, the tax is $9,498,600.

Compute the net income:

$\begin{array}{c}\text{Net income}=\text{EBIT}-\text{Tax}\\ =\$23,746,500-\$9,498,600\\ =\$14,247,900\end{array}$

Hence, the net income is $14,247,900.

Table that indicating pro form income statement:

Pro forma income statement
Particulars	Amounts
	(in $)
Sales	$50,415,750
Variable costs	$14,189,250
Fixed costs	$8,280,000
Depreciation	$4,200,000
Earnings before interest and taxes	$23,746,500
Taxes	$9,498,600
Net income	$14,247,900

Hence, the net income as per the pro forma income statement is $14,247,900.

Note: After preparing the pro forma income statement, determine the operating cash flow (OCF) and NPV of the best-case.

The formula to calculate OCF:

$\text{OCF}=\text{Net income}+\text{Depreciation}$

The formula to calculate NPV (after change in price):

$\text{NPV}=\left[\begin{array}{l}-\text{ Initial investment}-\text{New working capital}\\ +\text{ OCF}\times \left(\begin{array}{l}\text{Present value of an <x-custom-btb-me data-me-id="2167" class="microExplainerHighlight">annuity</x-custom-btb-me>}\\ \text{ of \$1 period for R\% of N period}\end{array}\right)+\frac{\text{New working capital}}{\left(1+\text{Cost of capital}\right)}\end{array}\right]$

Where,

OCF refers to the operating cash flows

Compute the operating cash flow (OCF):

$\begin{array}{c}\text{OCF}=\text{Net income}+\text{Depreciation}\\ =\$14,247,900+\$4,200,000\\ =\$18,447,900\end{array}$

Hence, the OCF is $18,447,900.

Compute the NPV:

$\begin{array}{c}\text{NPV}=\left[\begin{array}{l}-\text{ Initial investment}-\text{New working capital}\\ +\text{ OCF}\times \left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of \$1 period for R\% of N period}\end{array}\right)+\frac{\text{New working capital}}{{\left(1+\text{Cost of capital}\right)}^{\text{t}}}\end{array}\right]\\ =\left[\begin{array}{c}-\$29,400,000-\$1,400,000+\$18,447,900\\ \times \left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of }\$1\text{ period for }10\%\text{ of }7\text{ period}\end{array}\right)+\frac{\$1,400,000}{{\left(1+\frac{10}{100}\right)}^7}\end{array}\right]\\ =-\$30,800,000+\$18,447,900\times \left(4.86842\right)+\left(\frac{\$1,400,000}{{\left(1+0.10\right)}^7}\right)\\ =-\$30,800,000+\$89,812,125.318+\left(\frac{\$1,400,000}{1.9487171}\right)\end{array}$

$\begin{array}{c}=\$59,012,125.31+\$718,421.36\\ =\$59,730,546.67\end{array}$

Hence, the NPVof the best-caseis $59,730,546.67.

Note: After estimating the NPV of the 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:

$\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}$

The formula to calculate total variable costs:

$\text{Total Variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}$

The formula to calculate total sales of the entire clubs:

$\text{Total sales of all clubs}=\left(\begin{array}{l}\text{Total sales of new clubs}\\ +\text{Total sales of expensive clubs}\\ +\text{Total sales of cheaper clubs}\end{array}\right)$

The formula to calculatetotal variable costs of the entire clubs:

$\text{Total variable costs of all clubs}=\left(\begin{array}{l}\text{Total variable costs of new clubs}\\ +\text{Total variable costs of expensive clubs}\\ +\text{Total variable costs of cheaper clubs}\end{array}\right)$

Compute the total sales of new clubs:

$\begin{array}{c}\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}\\ =\$742.5\times 49,500\\ =\$36,753,750\end{array}$

Hence, the total sales of the new clubs are $36,753,750.

Compute the total sales of expensive clubs:

$\begin{array}{c}\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}\\ =\$1,100\times -11,000\\ =-\$12,100,000\end{array}$

Hence, the total sales of the expensive clubs are −$12,100,000.

Compute the total sales of cheaper clubs:

$\begin{array}{c}\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}\\ =\$410\times 10,800\\ =\$4,428,000\end{array}$

Hence, the total sales of the cheaper clubs are $4,428,000.

Compute the total sales of the entire clubs:

$\begin{array}{c}\text{Total sales of all clubs}=\left(\begin{array}{l}\text{Total sales of new clubs}\\ +\text{Total sales of expensive clubs}\\ +\text{Total sales of cheaper clubs}\end{array}\right)\\ =\$36,753,750+\left(-\$12,100,000\right)+\$4,428,000\\ =\$36,753,750-\$12,100,000+\$4,428,000\\ =\$29,081,750\end{array}$

Hence, the total sales of the entire clubs are $29,081,750.

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	$742.5	49,500	$36,753,750
Expensive clubs	$1,100	(11,000)	$(12,100,000)
Cheaper clubs	$410	10,800	$4,428,000
Total sales			$29,081,750

Hence, the total sales for the entire clubs are $29,081,750.

Compute total variable costs of new clubs:

$\begin{array}{c}\text{Total variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}\\ =-\$355.5\times 49,500\\ =-\$17,597,250\end{array}$

Hence, the total variable costs of the new clubs are −$17,597,250.

Compute total variable costs of expensive clubs:

$\begin{array}{c}\text{Total variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}\\ =\left(-\$650\right)\times \left(-11,000\right)\\ =\$7,150,000\end{array}$

Hence, the total variable costs of the expensive clubs are $7,150,000.

Compute total variable costs of cheaper clubs:

$\begin{array}{c}\text{Total variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}\\ =\left(-\$185\right)\times 10,800\\ =-\$1,998,000\end{array}$

Hence, the total variable costs of the cheaper clubs are −$1,998,000.

Compute the total variable costs of the entire clubs:

$\begin{array}{c}\text{Total variable costs of all clubs}=\left(\begin{array}{l}\text{Total variable costs of new clubs}\\ +\text{Total variable costs of expensive clubs}\\ +\text{Total variable costs of cheaper clubs}\end{array}\right)\\ =\left(-\$17,597,250\right)+\$7,150,000+\left(-\$1,998,000\right)\\ =-10,447,250-\$1,998,000\\ =-12,445,250\end{array}$

Hence, the total variable costs of the entire clubs are −$12,445,250.

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	($355.5)	49,500	($17,597,250)
Expensive clubs	($650)	(11,000)	$7,150,000
Cheaper clubs	($185)	10,800	($1,998,000)
Total variable costs			($12,445,250)

Hence, the variable costs for the clubs are −$12,445,250.

Note: Inorder topreparethe pro forma income statement, depreciation earningsbefore interest and taxes (EBIT), and tax has to be computed to ascertain the net income from this statement.

The formula to calculate EBIT:

$\text{EBIT}=\text{Sales}-\left(\text{Variable costs}+\text{Fixed costs}+\text{Depreciation}\right)$

The formula to calculate tax when tax rate is given:

$\text{Tax}=\text{EBIT}\times \text{Tax rate}$

The formula to calculate net income:

$\text{Net income}=\text{EBIT}-\text{Tax}$

Compute theEBIT:

$\begin{array}{c}\text{EBIT}=\text{Sales}-\left(\text{Variable costs}+\text{Fixed costs}+\text{Depreciation}\right)\\ =\$29,081,750-\left(\$12,445,250+\$10,120,000+4,200,000\right)\\ =\$29,081,750-\$26,765,250\\ =\$2,316,500\end{array}$

Hence, the EBIT is $2,316,500.

Compute tax when tax rate is given:

$\begin{array}{c}\text{Tax}=\text{EBIT}\times \text{Tax rate}\\ =\$2,316,500\times \left(\frac{40}{100}\right)\\ =\$2,316,500\times 0.40\\ =\$926,600\end{array}$

Hence, the tax is $926,600.

Compute the net income:

$\begin{array}{c}\text{Net income}=\text{EBIT}-\text{Tax}\\ =\$2,316,500-\$926,600\\ =\$1,389,900\end{array}$

Hence, the net income is $1,389,900.

Table that indicating pro form income statement:

Pro forma income statement
Particulars	Amounts
	(in $)
Sales	$29,081,750
Variable costs	$12,445,250
Fixed costs	$10,120,000
Depreciation	$4,200,000
Earnings before interest and taxes	$2,316,500
Taxes	$926,600
Net income	$1,389,900

Hence, the net income as per the pro forma income statement is $1,389,900.

Note: After preparing pro forma income statement, determine the operating cash flow (OCF) and NPV of the worst-case.

The formula to calculate OCF:

$\text{OCF}=\text{Net income}+\text{Depreciation}$

The formula to calculate NPV (after change in price):

$\text{NPV}=\left[\begin{array}{l}-\text{ Initial investment}-\text{New working capital}\\ +\text{OCF}\times \left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of \$1 period for R\% of N period}\end{array}\right)+\frac{\text{New working capital}}{\left(1+\text{Cost of capital}\right)}\end{array}\right]$

Where,

OCF refers to the operating cash flows

Compute the operating cash flow (OCF):

$\begin{array}{c}\text{OCF}=\text{Net income + Depreciation}\\ =\$1,389,900+\$4,200,000\\ =\$5,589,900\end{array}$

Hence, the OCF is $5,589,900.

Compute the NPV:

$\begin{array}{c}\text{NPV}=\left[\begin{array}{l}-\text{ Initial investment}-\text{New working capital}\\ +\text{ OCF}\times \left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of \$1 period for R\% of N period}\end{array}\right)+\frac{\text{New working capital}}{{\left(1+\text{Cost of capital}\right)}^{\text{t}}}\end{array}\right]\\ =\left[\begin{array}{c}-\$29,400,000-\$1,400,000+\$5,589,900\\ \times \left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of }\$1\text{ period for }10\%\text{ of }7\text{ period}\end{array}\right)+\frac{\$1,400,000}{{\left(1+\frac{10}{100}\right)}^7}\end{array}\right]\\ =-\$30,800,000+\$5,589,900\times \left(4.86842\right)+\left(\frac{\$1,400,000}{{\left(1+0.10\right)}^7}\right)\\ =-\$30,800,000+\$27,213,980.95+\left(\frac{\$1,400,000}{1.9487171}\right)\end{array}$

$\begin{array}{c}=-\$3,586,019.05+\$718,421.36\\ =-\$2,867,597.69\end{array}$

Hence, the NPV of the worst-case is −$2,867,597.69.