Question

Blooper Industries must replace its magnoosium purification system. Quick & Dirty Systems sells a relatively cheap purification system for $12 million. The system will last 4 years. Do-It-Right sells a sturdier but more expensive system for $13 million; it will last for 5 years. Both systems entail $2 million in operating costs; both will be depreciated straight-line to a final value of zero over their useful lives; neither will have any salvage value at the end of its life. The firm’s tax rate is 30%, and the discount rate is 15%. Either machine will be replaced at the end of its life.

a. What is the equivalent annual cost of investing in the cheap system? (Do not round intermediate calculations. Enter your answer as a positive value. Enter your answer in millions rounded to 2 decimal places.)

b. What is the equivalent annual cost of investing in the more expensive system? (Do not round intermediate calculations. Enter your answer as a positive value. Enter your answer in millions rounded to 2 decimal places.)

c. Which system should Blooper install?

Answer 1

Answer :

Calculation of Equated Annual Cost of Cheap System

Equated Annual Cost = (Present Value of Annual Operating Cash Flow + Initial Investment) / PVAF @ 15% for 4 years

Annual Operating Cash Flow = Operating Cost * ( 1 - Tax rate) + Tax Shield on Depreciation

= -2,000,000 * (1 - 0.30) + [0.30 * (12,000,000 / 4)

= -1,400,000 + [0.30 * 3,000,000]

= -500,000

Present Value of Annual Operating Cash Flow = Annual Operating Cash Flow * PVAF @ 15% for 4 years

= -500,000 * 2.85497836268

= -1,427,489.18134

Equated Annual Cost = [-(1,427,489.18134 + 12,000,000) ] / PVAF @ 15% for 4 years

= - 13427489.18134 / 2.85497836268

= -4,703,184.21912 or 4,703,184.22

Calculation of Equated Annual Cost of Expensive System

Equated Annual Cost = (Present Value of Annual Operating Cash Flow + Initial Investment) / PVAF @ 15% for 5 years

Annual Operating Cash Flow =Operating Cost * ( 1 - Tax rate) + Tax Shield on Depreciation

= -2,000,000 * (1 - 0.30) + [0.30 * (13000000 / 6)

= -1,400,000 + 650000

= -750,000

Present Value of Annual Operating Cash Flow = Annual Operating Cash Flow * PVAF @ 15% for 5 years

= -750,000 * 3.35215509796

= -2,514,116.32347

Equated Annual Cost = [-(2514116.32347 + 13,000,000) ] / PVAF @ 15% for 5 years

= - 15,514,116.3234 / 3.35215509796

= -4,628,102.18203 or 4,628,102.18

Therefore Blooper should install expensive System.