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 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:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The formula to calculate worst case of sales lost projection under the scenario analysis:

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

The formula to calculate worst-case of sales gained projection under the scenario analysis:

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

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

$\begin{array}{c}\text{Unit sales for best case = }\left[\begin{array}{l}\text{Value of base case for unit sales }\\ \text{+}\left(\begin{array}{l}\text{ Percenatge of accurate estimate}\\ \times \text{ Value of base case forunit sales}\end{array}\right)\end{array}\right]\\ =\left[75,000+\left(\frac{10}{100}\times 75,000\right)\right]\\ =\left[75,000+\left(0.1\times 75,000\right)\right]\end{array}$

$\begin{array}{c}=75,000+7,500\\ =82,500\text{ units}\end{array}$

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:

$\begin{array}{c}\text{Price for best case = }\left[\begin{array}{l}\text{Value of base case for price }\\ \text{+}\left(\begin{array}{l}\text{ Percenatge of accurate estimate}\\ \times \text{ Value of base case for price}\end{array}\right)\end{array}\right]\\ =\$715+\left(\frac{10}{100}\times \$715\right)\\ =\$715+\left(0.10\times \$715\right)\end{array}$

$\begin{array}{c}=\$715+\$71.5\\ =\$787\end{array}$

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:

$\begin{array}{c}\text{Variable costs for best case = }\left[\begin{array}{l}\text{Value of base case for variable costs}\\ -\left(\begin{array}{l}\text{ Percenatge of accurate estimate}\\ \times \text{ Value of base case for variable costs}\end{array}\right)\end{array}\right]\\ =\left[\$385-\left(\frac{10}{100}\times \$385\right)\right]\\ =\left[\$385-\left(0.10\times \$385\right)\right]\end{array}$

$\begin{array}{c}=\$385-\$38.5\\ =\$347\end{array}$

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:

$\begin{array}{c}\text{Fixed costs for best case = }\left[\begin{array}{l}\text{Value of base case for fixed costs}\\ -\left(\begin{array}{l}\text{ Percenatge of accurate estimate}\\ \times \text{}\text{ Value of base case for fixed costs}\end{array}\right)\end{array}\right]\\ =\left[\$9,400,000-\left(\frac{10}{100}\times \$9,400,000\right)\right]\\ =\left[\$9,400,000-\left(0.10\times \$9,400,000\right)\right]\end{array}$

$\begin{array}{c}=\$9,400,000-\$940,000\\ =\$8,460,000\end{array}$

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:

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

$\begin{array}{c}=10,000-1,000\\ =9,000\text{ units}\end{array}$

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

Compute the best-case of sales gained projection under the scenario analysis:

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

$\begin{array}{c}=12,000+1,200\\ =13,200\text{ units}\end{array}$

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

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

$\begin{array}{c}\text{Unit sales for worst case = }\left[\begin{array}{l}\text{Value of base case unit sales }\\ -\left(\begin{array}{l}\text{ Percenatge of accurate estimate}\\ \times \text{ Value of base case unit sales}\end{array}\right)\end{array}\right]\\ =\left[75,000-\left(\frac{10}{100}\times 75,000\right)\right]\\ =\left[75,000-\left(0.10\times 75,000\right)\right]\end{array}$

$\begin{array}{c}=75,000-7,500\\ =67,500\text{ units}\end{array}$

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:

$\begin{array}{c}\text{Price for worst case = }\left[\begin{array}{l}\text{Value of base case for price }\\ \text{+}\left(\begin{array}{l}\text{ Percenatge of accurate estimate}\\ \times \text{ Value of base case for price}\end{array}\right)\end{array}\right]\\ =\$715-\left(\frac{10}{100}\times \$715\right)\\ =\$715-\left(0.10\times \$715\right)\end{array}$

$\begin{array}{c}=\$715-\$71.5\\ =\$644\end{array}$

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:

$\begin{array}{c}\text{Variable costs for worst case = }\left[\begin{array}{l}\text{Value of base case for variable costs}\\ \text{+ }\left(\begin{array}{l}\text{ Percenatge of accurate estimate}\\ \times \text{ Value of base case for variable costs}\end{array}\right)\end{array}\right]\\ =\left[\$385+\left(\frac{10}{100}\times \$385\right)\right]\\ =\left[\$385+\left(0.10\times \$385\right)\right]\end{array}$

$\begin{array}{c}=\$385+\$38.5\\ =\$424\end{array}$

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:

$\begin{array}{c}\text{Fixed costs for worst case = }\left[\begin{array}{l}\text{Value of base case for fixed costs}\\ +\left(\begin{array}{l}\text{ Percenatge of accurate estimate}\\ \times \text{}\text{ Value of base case for fixed costs}\end{array}\right)\end{array}\right]\\ =\$9,400,000+\left(\frac{10}{100}\times \$9,400,000\right)\\ =\$9,400,000+\left(0.10\times \$9,400,000\right)\end{array}$

$\begin{array}{c}=\$9,400,000+\$940,000\\ =\$10,340,000\end{array}$

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:

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

$\begin{array}{c}=10,000+1,000\\ =11,000\text{ units}\end{array}$

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

Compute the worst-case of sales gained projection under the scenario analysis:

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

$\begin{array}{c}=12,000-1,200\\ =10,800\text{ units}\end{array}$

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 calculate total 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:

$\begin{array}{c}\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}\\ =\$787\times 82,500\\ =\$64,927,500\end{array}$

Hence, the total sales of the new clubs are $64,927,500.

Compute the total sales of expensive clubs:

$\begin{array}{c}\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}\\ =\$1,150\times -9,000\\ =-\$10,350,000\end{array}$

Hence, the total sales of the expensive clubs are -$10,350,000.

Compute the total sales of cheaper clubs:

$\begin{array}{c}\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}\\ =\$425\times 13,200\\ =\$5,610,000\end{array}$

Hence, the total sales of the cheaper clubs are $5,610,000.

Compute the total sales of the entire clubs:

$\begin{array}{c}\text{Total sales of all clubs}=\left(\begin{array}{l}\text{Total sales of new clubs}\\ \text{+ Total sales of expensive clubs}\\ +\text{Total sales of cheaper clubs}\end{array}\right)\\ =\$64,927,500+\left(-\$10,350,000\right)+\$5,100,000\\ =\$64,927,500-\$10,350,000+\$5,610,000\\ =\$60,187,500\end{array}$

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:

$\begin{array}{c}\text{Total Variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}\\ =-\$347\times 82,500\\ =-\$28,627,500\end{array}$

Hence, the total variable costs of the new clubs are −$28,627,500.

Compute total variable costs of expensive clubs:

$\begin{array}{c}\text{Total Variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}\\ =\left(-\$620\right)\times \left(-9,000\right)\\ =\$5,580,000\end{array}$

Hence, the total variable costs of the expensive clubs are $5,580,000.

Compute total variable costs of cheaper clubs:

$\begin{array}{c}\text{Total Variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}\\ =\left(-\$195\right)\times 13,200\\ =-\$2,574,000\end{array}$

Hence, the total variable costs of the cheaper clubs are −$2,574,000.

Compute the total variable costs of the entire clubs:

$\begin{array}{c}\text{Total variable costs of all clubs}=\left(\begin{array}{l}\text{Total variable costs of new clubs}\\ \text{+ Total variable costs of expensive clubs}\\ +\text{Total variable costs of cheaper clubs}\end{array}\right)\\ =\left(-\$28,627,500\right)+\$5,580,000+\left(-\$2,574,000\right)\\ =-\$25,621,500\end{array}$

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, depreciation of plant and equipment, Earnings before interest and taxes (EBIT), and tax has to be computed to ascertain 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:

$\begin{array}{c}\text{Depreciation expense}=\frac{\text{Cost of the assets}}{\text{Useful life}}\\ =\frac{\$30,100,000}{7}\\ =\$4,300,000\end{array}$

Hence, the depreciation expense is $4,300,000.

Compute the EBIT:

$\begin{array}{c}\text{EBIT}=\text{Sales}-\left(\text{Variable costs}+\text{Fixed costs}+\text{Depreciation}\right)\\ =\$60,187,500-\left(\$25,621,500+\$8,460,000+\$4,300,000\right)\\ =\$60,187,500-\$38,381,500\\ =\$21,806,000\end{array}$

Hence, the EBIT is $21,806,000.

Compute tax when tax rate is given:

$\begin{array}{c}\text{Tax}=\text{EBIT}\times \text{Tax rate}\\ =\$21,806,000\times \left(\frac{40}{100}\right)\\ =\$21,806,000\times 0.40\\ =\$8,722,400\end{array}$

Hence, the tax is $8,722,400.

Compute the net income:

$\begin{array}{c}\text{Net income}=\text{EBIT}-\text{Tax}\\ =\$21,806,000-\$8,722,400\\ =\$13,083,600\end{array}$

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:

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

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):

$\begin{array}{c}\text{OCF}=\text{Net income + Depreciation}\\ =\$13,083,600+\$4,300,000\\ =\$17,383,600\end{array}$

Hence, the OCF is $17,383,600.

Compute the NPV:

$\begin{array}{c}\text{NPV}=\left[\begin{array}{l}-\text{ Initial investment}-\text{New working capital}\\ +\text{ OCF}\times \left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of \$1 period for R\% of N period}\end{array}\right)+\frac{\text{New working capital}}{{\left(1+\text{Cost of capital}\right)}^{\text{t}}}\end{array}\right]\\ =\left[\begin{array}{c}-\$30,100,000-\$1,400,000+\$17,383,600\\ \times \left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of }\$1\text{ period for }10\%\text{ of }7\text{ period}\end{array}\right)+\frac{\$1,400,000}{{\left(1+\frac{10}{100}\right)}^7}\end{array}\right]\\ =-\$31,500,000+\$17,383,600\times \left(4.86842\right)+\left(\frac{\$1,400,000}{{\left(1+0.10\right)}^7}\right)\\ =-\$31,500,000+\$\text{84,630,665}\text{.912}+\left(\frac{\$1,400,000}{1.9487171}\right)\end{array}$

$\begin{array}{c}=\$53,130,665.912+\$718,421.36\\ =\$53,849,087.272\end{array}$

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:

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

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 calculate total 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:

$\begin{array}{c}\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}\\ =\$644\times 67,500\\ =\$43,470,000\end{array}$

Hence, the total sales of the new clubs are $43,470,000.

Compute the total sales of expensive clubs:

$\begin{array}{c}\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}\\ =\$1,150\times -11,000\\ =-\$12,650,000\end{array}$

Hence, the total sales of the expensive clubs are -$12,650,000.

Compute the total sales of cheaper clubs:

$\begin{array}{c}\text{Total sales}=\text{Sales per units}\times \text{Number of units sold}\\ =\$425\times 10,800\\ =\$4,590,000\end{array}$

Hence, the total sales of the cheaper clubs are $4,590,000.

Compute the total sales of the entire clubs:

$\begin{array}{c}\text{Total sales of all clubs}=\left(\begin{array}{l}\text{Total sales of new clubs}\\ \text{+ Total sales of expensive clubs}\\ +\text{Total sales of cheaper clubs}\end{array}\right)\\ =\$43,470,000+\left(-\$12,650,000\right)+\$4,590,000\\ =\$43,470,000-\$12,650,000+\$4,590,000\\ =\$35,410,000\end{array}$

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:

$\begin{array}{c}\text{Total Variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}\\ =-\$424\times 67,500\\ =-\$28,620,000\end{array}$

Hence, the total variable costs of the new clubs are −$28,620,000.

Compute total variable costs of expensive clubs:

$\begin{array}{c}\text{Total Variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}\\ =\left(-\$620\right)\times \left(-11,000\right)\\ =\$6,820,000\end{array}$

Hence, the total variable costs of the expensive clubs are $6,820,000.

Compute total variable costs of cheaper clubs:

$\begin{array}{c}\text{Total Variable costs}=\text{Variable costs per units}\times \text{Number of units of sold}\\ =\left(-\$195\right)\times 10,800\\ =-\$2,106,000\end{array}$

Hence, the total variable costs of the cheaper clubs are -$2,106,000.

Compute the total variable costs of the entire clubs:

$\begin{array}{c}\text{Total variable costs of all clubs}=\left(\begin{array}{l}\text{Total variable costs of new clubs}\\ \text{+ Total variable costs of expensive clubs}\\ +\text{Total variable costs of cheaper clubs}\end{array}\right)\\ =\left(-\$28,620,000\right)+\$6,820,000+\left(-\$2,106,000\right)\\ =-\$23,906,000\end{array}$

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:

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

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 the EBIT:

$\begin{array}{c}\text{EBIT}=\text{Sales}-\left(\text{Variable costs}+\text{Fixed costs}+\text{Depreciation}\right)\\ =\$35,410,000-\left(\$23,906,000+\$10,340,000+4,300,000\right)\\ =\$35,410,000-\$38,546,000\\ =-\$3,136,000\end{array}$

Hence, the EBIT is -$3,136,000.

Compute tax when tax rate is given:

$\begin{array}{c}\text{Tax}=\text{EBIT}\times \text{Tax rate}\\ =-\$3,136,000\times \left(\frac{40}{100}\right)\\ =-\$3,136,000\times 0.40\\ =-\$1,254,400\end{array}$

Hence, the tax is -$1,254,400.

Compute the net income:

$\begin{array}{c}\text{Net income}=\text{EBIT}-\text{Tax}\\ =\left(-\$3,136,000\right)-\left(-\$1,254,400\right)\\ =-\$1,881,600\end{array}$

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:

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

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):

$\begin{array}{c}\text{OCF}=\text{Net income + Depreciation}\\ =-\$1,881,600+\$4,300,000\\ =\$2,418,400\end{array}$

Hence, the OCF is $2,418,400.

Compute the NPV:

$\begin{array}{c}\text{NPV}=\left[\begin{array}{l}-\text{ Initial investment}-\text{New working capital}\\ +\text{ OCF}\times \left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of \$1 period for R\% of N period}\end{array}\right)+\frac{\text{New working capital}}{{\left(1+\text{Cost of capital}\right)}^{\text{t}}}\end{array}\right]\\ =\left[\begin{array}{c}-\$30,100,000-\$1,400,000+\$2,418,400\\ \times \left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of }\$1\text{ period for }10\%\text{ of }7\text{ period}\end{array}\right)+\frac{\$1,400,000}{{\left(1+\frac{10}{100}\right)}^7}\end{array}\right]\\ =-\$31,500,000+\$2,418,400\times \left(4.86842\right)+\left(\frac{\$1,400,000}{{\left(1+0.10\right)}^7}\right)\\ =-\$31,500,000+\$\text{11,773,786}\text{.928}+\left(\frac{\$1,400,000}{1.9487171}\right)\end{array}$

$\begin{array}{c}=-\$19,726,213.072+\$718,421.36\\ =-\$19,007,791.712\end{array}$

Hence, the NPVof worst-caseis -$19,007,791.712.