We are evaluating a project that costs $670,000, has a five-year life, and has n

ID: 2727593 • Letter: W

Question

We are evaluating a project that costs $670,000, has a five-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 59,000 units per year. Price per unit is $44, variable cost per unit is $24, and fixed costs are $760,000 per year. The tax rate is 35 percent, and we require a return of 18 percent on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent. I need the best case & worst case scenario for NPV.

Explanation / Answer

Calculation of best case NPV:

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Sales (59000 units *110% ) *($44*110%)

$ 3,141,160.00

Less: Variable costs (59000 units *110% ) *($24*90%)

$ (1,401,840.00)

Less: Fixed Costs (760000*90%)

$ (684,000.00)

Less: Depreciation (670000-0) / 5)

$ (134,000.00)

Profit Before tax

$ 921,320.00

Less: Tax = Profit before tax * 35%

$ (322,462.00)

Profit after tax

$ 598,858.00

Add: Depreciation

$ 134,000.00

Cash Flows after tax

$ 732,858.00

Cost of Project

$ (670,000.00)

Net cash Flows (CF)

$ (670,000.00)

$ 732,858.00

PVF (18%)

1.00000

0.84746

0.71818

0.60863

0.51579

0.43711

1/(1+18%)^0

1/(1+18%)^1

1/(1+18%)^2

1/(1+18%)^3

1/(1+18%)^4

1/(1+18%)^5

PV = CF * PVF

$ (670,000.00)

$ 621,066.10

$ 526,327.20

$ 446,040.00

$ 378,000.00

$ 320,338.99

NPV = Sum of PV =

$ 1,621,772.30

Calculation of Worst case NPV:

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Sales (59000 units *90% ) *($44*90%)

$ 2,102,760.00

Less: Variable costs (59000 units *90% ) *($24*110%)

$ (1,401,840.00)

Less: Fixed Costs (760000*110%)

$ (836,000.00)

Less: Depreciation (670000-0) / 5)

$ (134,000.00)

Profit Before tax

$ (269,080.00)

Less: Tax = Profit before tax * 35%

$ 94,178.00

Profit after tax

$ (174,902.00)

Add: Depreciation

$ 134,000.00

Cash Flows after tax

$ (40,902.00)

Cost of Project

$ (670,000.00)

Net cash Flows (CF)

$ (670,000.00)

$ (40,902.00)

PVF (18%)

1.00000

0.84746

0.71818

0.60863

0.51579

0.43711

1/(1+18%)^0

1/(1+18%)^1

1/(1+18%)^2

1/(1+18%)^3

1/(1+18%)^4

1/(1+18%)^5

PV = CF * PVF

$ (670,000.00)

$ (34,662.71)

$ (29,375.18)

$ (24,894.22)

$ (21,096.80)

$ (17,878.64)

NPV = Sum of PV =

$ (797,907.55)

Calculation of best case NPV:

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Sales (59000 units *110% ) *($44*110%)

$ 3,141,160.00

Less: Variable costs (59000 units *110% ) *($24*90%)

$ (1,401,840.00)

Less: Fixed Costs (760000*90%)

$ (684,000.00)

Less: Depreciation (670000-0) / 5)

$ (134,000.00)

Profit Before tax

$ 921,320.00

Less: Tax = Profit before tax * 35%

$ (322,462.00)

Profit after tax

$ 598,858.00

Add: Depreciation

$ 134,000.00

Cash Flows after tax

$ 732,858.00

Cost of Project

$ (670,000.00)

Net cash Flows (CF)

$ (670,000.00)

$ 732,858.00

PVF (18%)

1.00000

0.84746

0.71818

0.60863

0.51579

0.43711

1/(1+18%)^0

1/(1+18%)^1

1/(1+18%)^2

1/(1+18%)^3

1/(1+18%)^4

1/(1+18%)^5

PV = CF * PVF

$ (670,000.00)

$ 621,066.10

$ 526,327.20

$ 446,040.00

$ 378,000.00

$ 320,338.99

NPV = Sum of PV =

$ 1,621,772.30

Calculation of Worst case NPV:

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Sales (59000 units *90% ) *($44*90%)

$ 2,102,760.00

Less: Variable costs (59000 units *90% ) *($24*110%)

$ (1,401,840.00)

Less: Fixed Costs (760000*110%)

$ (836,000.00)

Less: Depreciation (670000-0) / 5)

$ (134,000.00)

Profit Before tax

$ (269,080.00)

Less: Tax = Profit before tax * 35%

$ 94,178.00

Profit after tax

$ (174,902.00)

Add: Depreciation

$ 134,000.00

Cash Flows after tax

$ (40,902.00)

Cost of Project

$ (670,000.00)

Net cash Flows (CF)

$ (670,000.00)

$ (40,902.00)

PVF (18%)

1.00000

0.84746

0.71818

0.60863

0.51579

0.43711

1/(1+18%)^0

1/(1+18%)^1

1/(1+18%)^2

1/(1+18%)^3

1/(1+18%)^4

1/(1+18%)^5

PV = CF * PVF

$ (670,000.00)

$ (34,662.71)

$ (29,375.18)

$ (24,894.22)

$ (21,096.80)

$ (17,878.64)

NPV = Sum of PV =

$ (797,907.55)

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