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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 1 year ago

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