Question

Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $3,132,000 and will last for six years. Variable costs are 35 percent of sales, and fixed costs are $270,000 per year. Machine B costs $5,355,000 and will last for nine years. Variable costs for this machine are 30 percent of sales and fixed costs are $205,000 per year. The sales for each machine will be $11.6 million per year. The required return is 10 percent, and the tax rate is 35 percent. Both machines will be depreciated on a straight-line basis. The company plans to replace the machine when it wears out on a perpetual basis. Calculate the EAC for each machine.

Answer 1

All financials below are in $.

Machine A:

Initial investment, C₀ = 3,132,000

Annual sales, S = 11,600,000

Variable cost, VC = 35% of S = 35% x  11,600,000 =  4,060,000

Fixed cost = FC = 270,000

N = Life of the project = 6 years

Annual Depreciation, D = C₀ / N =  522,000

Tax rate, T = 35%

Annual depreciation tax shield = DTS = D x T = 522,000 x 35% =  182,700

Annual cash flows, C = DTS - (VC + FC) x (1 - T) = 182,700 - (4,060,000 + 270,000) x (1 - 35%) = - 2,631,800

Discount rate, R = 10%

Hence, NPV = - C₀ + C / R x [1 - (1 + R)^-N] = -3,132,000 - 2,631,800 / 10% x [1 - (1 + 10%)^-6] =  - 14,594,175.11

Hence, EAC = NPV x R / [1 - (1 + R)^-N] =  -14,594,175.11 x 10% / [1 - (1 + 10%)^-6] =  - 3,350,930.32

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Machine B:

Initial investment, C₀ = 5,355,000

Annual sales, S = 11,600,000

Variable cost, VC = 30% of S = 30% x  11,600,000 =   3,480,000

Fixed cost = FC = 205,000

N = Life of the project = 9 years

Annual Depreciation, D = C₀ / N =  595,000

Tax rate, T = 35%

Annual depreciation tax shield = DTS = D x T = 595,000 x 35% = 208,250

Annual cash flows, C = DTS - (VC + FC) x (1 - T) = 208,250 - ( 3,480,000 + 205,000) x (1 - 35%) = - 2,187,000

Discount rate, R = 10%

Hence, NPV = - C₀ + C / R x [1 - (1 + R)^-N] = -5,355,000 - 2,187,000 / 10% x [1 - (1 + 10%)^-9] =  - 15,726,985.09

Hence, EAC = NPV x R / [1 - (1 + R)^-N] =  - 5,726,985.09 x 10% / [1 - (1 + 10%)^-9] =  - 3,611,031.85