Question

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Consider a project with a 6-year life. The initial cost to set up the project is...

Consider a project with a 6-year life. The initial cost to set up the project is $450,000. This amount is to be linearly depreciated to zero over the life of the project. The firm expects to be able to sell the equipment for $90,000 after 6 years.

The price per unit is $380, variable costs are $304 per unit and fixed costs are $45,000 per year. The project has a required return of 12% and a tax rate of 28%.

How many units must be sold per year for the project to achieve financial break-even?

Solutions

Expert Solution

Annual depreciation = Initial cost/Number of useful years

                             = $ 450,000/6 = $ 75,000

To achieve financial breakeven, NPV of the project should be zero.

Contribution per unit = Sales – Variable cost = $ 380 - $ 304 = $ 76

Suppose annual breakeven sales unit is X.

Contribution for X units = $ 76 X

NPV of the project

= Annual cash inflows x PVIFA (r, n) + after tax scrap value x PVIF (r, n) – Initial investment

Hence,

[(76 X – $ 45,000) - $ 75,000] x (1-0.28) + $ 75,000 x PVIFA (12 %, 6) + {$ 90,000 x (1-0.28)} x PVIF (12 %, 6) - $ 450,000 = 0

[(76 X – $ 45,000) - $ 75,000] x 0.72 + $ 75,000 x PVIFA (12 %, 6) + ($ 90,000 x 0.72) x PVIF (12 %, 6) - $ 450,000 = 0

[(76 X – $ 45,000) - $ 75,000] x 0.72 + $ 75,000 x PVIFA (12 %, 6) + ($ 90,000 x 0.72) x PVIF (12 %, 6) = $ 450,000

[{(76 X – $ 45,000) - $ 75,000} x 0.72 + $ 75,000] x 4.1114 + ($ 90,000 x 0.72 x 0.50663) = $ 450,000

[{(76 X – $ 45,000) - $ 75,000} x 0.72 + $ 75,000] x 4.11141 + $ 32,829.624 = $ 450,000

[{(76 X – $ 45,000) - $ 75,000} x 0.72 + $ 75,000] x 4.11141 = $ 450,000 - $ 32,829.624

[{(76 X – $ 45,000) - $ 75,000} x 0.72 + $ 75,000] x 4.11141 = $ 417,170.376

[{(76 X – $ 45,000) - $ 75,000} x 0.72 + $ 75,000] = $ 417,170.376/4.11141

{(76 X – $ 45,000) - $ 75,000} x 0.72 + $ 75,000 = $ 101,466.498354579

{(76 X – $ 45,000) - $ 75,000} x 0.72 = $ 101,466.498354579 - $ 75,000

{(76 X – $ 45,000) - $ 75,000} x 0.72 = $ 26,466.498354579

(76 X – $ 45,000) - $ 75,000 = $ 26,466.498354579/0.72

(76 X – $ 45,000) - $ 75,000 = $ 36,759.0254924709

76 X – $ 45,000 = $ 36,759.0254924709 + $ 75,000

76 X – $ 45,000 = $ 111,759.025492471

76 X = $ 111,759.025492471 + $ 45,000

76 X = $ 156,759.025492471

X = $ 156,759.025492471/76

X = 2062.618756 or 2,063 units

2,063 units must be sold per year for the project to achieve financial breakeven.

jeff jeffy answered 1 year ago
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