We are evaluating a project that costs $1,200,000, has a five-year life, and has

ID: 2765430 • Letter: W

Question

We are evaluating a project that costs $1,200,000, 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 88,500 units per year. Price per unit is $35.00, variable cost per unit is $21.25, and fixed costs are $765,000 per year. The tax rate is 35 percent, and we require a return of 10 percent on this project.

Required: Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent. Calculate the best-case and worst-case NPV figures. (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places (e.g., 32.16).)

NPV Best-case $

Worst-case $

Explanation / Answer

Calculation of Best case NPV:

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Initial Cost

$(1,200,000.00)

Tax Saving on Depreciation :

Depreciation = (Cost - Salvage Value) / life

= (1200000-0) / 5 = 240000

Tax Saving on Depreciation = 240000*35% =

$ 84,000.00

Sales Revenue net of Tax = (88500 Units*110%) *($35 *110%) * (1-35%) =

$ 2,436,183.75

Less: Variable costs net of Tax = 88500 Units *$21.25 *90% * (1-35%) =

$(1,100,165.63)

Less: Fixed costs net of Tax = $765000 *90% * (1-35%) =

$ (447,525.00)

Net Cash Flows (CF)

$(1,200,000.00)

$ 972,493.13

PVF (10%)

1.00000

0.90909

0.82645

0.75131

0.68301

0.62092

PV = CF*PVF =

$(1,200,000.00)

$ 884,084.66

$ 803,713.33

$ 730,648.48

$ 664,225.89

$ 603,841.72

NPV = Sum of PVs =

$ 2,486,514.07

Calculation of Worst case NPV:

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Initial Cost

$(1,200,000.00)

Tax Saving on Depreciation :

Depreciation = (Cost - Salvage Value) / life

= (1200000-0) / 5 = 240000

Tax Saving on Depreciation = 240000*35% =

$ 84,000.00

Sales Revenue net of Tax = (88500 Units*90%) *($35 *900%) * (1-35%) =

$ 1,630,833.75

Less: Variable costs net of Tax = 88500 Units *$21.25 *110% * (1-35%) =

$(1,344,646.88)

Less: Fixed costs net of Tax = $765000 *110% * (1-35%) =

$ (546,975.00)

Net Cash Flows (CF)

$(1,200,000.00)

$ (176,788.13)

PVF (10%)

1.00000

0.90909

0.82645

0.75131

0.68301

0.62092

PV = CF*PVF =

$(1,200,000.00)

$ (160,716.48)

$ (146,105.89)

$ (132,823.53)

$ (120,748.67)

$ (109,771.52)

NPV = Sum of PVs =

$(1,870,166.09)

Calculation of Best case NPV:

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Initial Cost

$(1,200,000.00)

Tax Saving on Depreciation :

Depreciation = (Cost - Salvage Value) / life

= (1200000-0) / 5 = 240000

Tax Saving on Depreciation = 240000*35% =

$ 84,000.00

Sales Revenue net of Tax = (88500 Units*110%) *($35 *110%) * (1-35%) =

$ 2,436,183.75

Less: Variable costs net of Tax = 88500 Units *$21.25 *90% * (1-35%) =

$(1,100,165.63)

Less: Fixed costs net of Tax = $765000 *90% * (1-35%) =

$ (447,525.00)

Net Cash Flows (CF)

$(1,200,000.00)

$ 972,493.13

PVF (10%)

1.00000

0.90909

0.82645

0.75131

0.68301

0.62092

PV = CF*PVF =

$(1,200,000.00)

$ 884,084.66

$ 803,713.33

$ 730,648.48

$ 664,225.89

$ 603,841.72

NPV = Sum of PVs =

$ 2,486,514.07

Calculation of Worst case NPV:

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Initial Cost

$(1,200,000.00)

Tax Saving on Depreciation :

Depreciation = (Cost - Salvage Value) / life

= (1200000-0) / 5 = 240000

Tax Saving on Depreciation = 240000*35% =

$ 84,000.00

Sales Revenue net of Tax = (88500 Units*90%) *($35 *900%) * (1-35%) =

$ 1,630,833.75

Less: Variable costs net of Tax = 88500 Units *$21.25 *110% * (1-35%) =

$(1,344,646.88)

Less: Fixed costs net of Tax = $765000 *110% * (1-35%) =

$ (546,975.00)

Net Cash Flows (CF)

$(1,200,000.00)

$ (176,788.13)

PVF (10%)

1.00000

0.90909

0.82645

0.75131

0.68301

0.62092

PV = CF*PVF =

$(1,200,000.00)

$ (160,716.48)

$ (146,105.89)

$ (132,823.53)

$ (120,748.67)

$ (109,771.52)

NPV = Sum of PVs =

$(1,870,166.09)

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