Question

1. After graduating UK with a major in finance, you have developed a brilliant new widget. You sell your widgets for $6. You need to buy a machine to produce your widgets. You are considering two machines: [25 points]

Machine A:

• Cost $2,000,000
• Annual fixed cost per machine: $250,000; Variable cost per unit $1.40
• Annual production capacity: 300,00 widgets (i.e., you cannot produce more than 300,000 widgets)
• Market life = 5 years; terminal (market) value =0

Machine B:

• Cost $6,000,000
• Annual fixed cost per machine: $25,000; Variable cost per unit $0.40
• Annual production capacity: 600,00 widgets (i.e., you cannot produce more than 600,000 widgets)
• Market life = 5 years; terminal (market) value = $200,000

Additional Details:

• You have already had an inspector evaluate Machine A for $2,000 and Machine B for $6,000.
• Both machines can be depreciated using straight-line depreciation over a 5-year period. Book value should =0 at the end of 5 years.
• The tax rate is 30%
  • If Net Income is negative, assume a tax of 0 (i.e. the government will not pay you if you lose money, and there are no tax-loss carry forwards)
• The discount rate is 6%
• You expect to be able to sell up to 400,000 widgets
  • Assume you can only buy one machine

1. Compare the differential NPV of Machine B and Machine A as the number of widgets produced varies from 200,000 to 700,000 in increments of 100,000. [5 points]
2. Intuitively explain why the differential is so sensitive to level of widget production. Your explanation should include two factors. [4 points]

Answer 1

Calculation of NPV

Statement showing the evaluation of two Machines

                                                                                                           Machine A                          Machine B

Purchase Cost                                                                                         2000,000                                6000,000

Annual Fixed Cost                                                                                  250,000                                     25,000

Variable Cost                                                                                           420,00                                     24000 (300,00*1.40)   (600,00*.40)   

Depreciation                                                                                           400,000                            1,200,000

                                                                                                           2,000,000/5                            6,000,000/5

Tax saving on Depreciation                                                             (120,000)                                  (360,000)                                                        

Total Out flow                                                                                    572,000                              889,000

Total Inflow                                                                                        2,400,000                           2,400,000

Net present Value (400,000*6)                                                 1,828,000                            6,49,000

Conclusion Machine A is better because Net present Value is positive

Ans B Sensitive Analysis

1 NPV on Sales 1,828,000/2,400,000 649,000/2,400,000   

76.17% 27%