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A video rental store will cost $640,000 to open. Assuming annual sales of $1 million, variable...

A video rental store will cost $640,000 to open. Assuming annual sales of $1 million, variable costs of 35%, fixed costs of $300,000, depreciation of $100,000, and a tax rate of 35%, calculate the NPV of the project over a 10-year horizon (no inflation or salvage value assumed) with a 12% cost of capital. Conduct a sensitivity analysis by allowing investment, sales, variable costs, and fixed costs to vary by plus/minus 10% from their original estimates. Which variable appears to affect profitability the most?
Detailed problem solving steps are required

Solutions

Expert Solution

Sales 1,000,000
Less: Variable cost 350,000
Less: Fixed cost 300,000
less: Depreciation 100,000
Profit before tax 250,000
Less: Tax @35% 87,500
Profit after tax 162,500
Add: Depreciation 100,000
Cash flows p.a. 262,500

Calculation of NPV

Year Amount PVF@12% Discounted value
Initial investment 0 640,000 1 (640,000)
Cash flows p.a. 1-10 262,500 5.650 1,483,125
NPV 843,125

Case 1: Investment varies by 10%

Year Amount PVF@12% Discounted value
Initial investment 0 704,000 1 (704,000)
Cash flows p.a. 1-10 262,500 5.650 1,483,125
NPV 779,125

Sensitivity = (779,125 - 843,125)/ 843,125

= -7.59% if Investment increases by 10%

and +7.59% if investment decreases by 10%

Case 2: If sales varies

Sales 1,100,000
Less: Variable cost 350,000
Less: Fixed cost 300,000
less: Depreciation 100,000
Profit before tax 350,000
Less: Tax @35% 122,500
Profit after tax 227,500
Add: Depreciation 100,000
Cash flows p.a. 327,500

Calculation of NPV

Year Amount PVF@12% Discounted value
Initial investment 0 640,000 1 (640,000)
Cash flows p.a. 1-10 327,500 5.650 1,850,375
NPV 1,210,375

Sensitivity = (1,210,375 - 843,125)/ 843,125

= 43.56% if sales increases by 10%, and -43.56% if sales decreases by 10%

Case 3: If Variable cost varies

Sales 1,000,000
Less: Variable cost 385,000
Less: Fixed cost 300,000
less: Depreciation 100,000
Profit before tax 215,000
Less: Tax @35% 75,250
Profit after tax 139,750
Add: Depreciation 100,000
Cash flows p.a. 239,750

Calculation of NPV

Year Amount PVF@12% Discounted value
Initial investment 0 640,000 1 (640,000)
Cash flows p.a. 1-10 239,750 5.650 1,354,588
NPV 714,588

Sensitivity = (714,588 - 843,125)/ 843,125

= -15.25% if variable cost increases by 10%, and 15.25% if variable cost decreases by 10%

Case 4: If fixed cost varies

Sales 1,000,000
Less: Variable cost 350,000
Less: Fixed cost 330,000
less: Depreciation 100,000
Profit before tax 220,000
Less: Tax @35% 77,000
Profit after tax 143,000
Add: Depreciation 100,000
Cash flows p.a. 243,000

Calculation of NPV

Year Amount PVF@12% Discounted value
Initial investment 0 640,000 1 (640,000)
Cash flows p.a. 1-10 243,000 5.650 1,372,950
NPV 732,950

Sensitivity = (732,950 - 843,125)/ 843,125

= -13.07% ifi fixed cost increases by 10%, and 13.07% if fixed cost decreases by 10%

Change in the value of Sales has affected the NPV the most

ekkarill92 answered 2 years ago
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