Question

9. (10 marks) A firm is considering the purchase of a new machine to increase the productivity of existing production process. All the alternatives have a life of 10 years and they have negligible market value after 10 years. Use the IRR method (incrementally) to make your recommendation. The firm's MARR is 10% per year. Alternative Capital Investment Annual Operating Cost $100,000 $20,000 $110,000 $18,500 $125,000 $17,000 $130,000 $15,500 $150,000 $10,000

Answer 1

Comparing Alternatives 1 and 2

Incremental investment = $110,000 - $100,000 = $10,000

Incremental savings in operating cost per year = $20000- $18500 = $1500

Now Present value of savings of $1500 per year for 10 years @10% = 1500/0.10 * (1- (1/1.1)¹⁰) =9216.85

So, Incremental NPV = -10000 +9216.85 =-783.15

As the incremental NPV is negative , so Alternative 2 is not preferred over Alternative 1

Comparing Alternatives 1 and 3

Incremental investment = $125,000 - $100,000 = $25,000

Incremental savings in operating cost per year = $20000- $17000 = $3000

Now Present value of savings of $3000 per year for 10 years @10% = 3000/0.10 * (1- (1/1.1)¹⁰) =18433.70

So, Incremental NPV = -25000 +18433.70 =-6566.30

As the incremental NPV is negative ,so Alternative 3 is not preferred over Alternative 1

Comparing Alternatives 1 and 4

Incremental investment = $130,000 - $100,000 = $30,000

Incremental savings in operating cost per year = $20000- $15500 = $4500

Now Present value of savings of $4500 per year for 10 years @10% = 4500/0.10 * (1- (1/1.1)¹⁰) =27650.55

So, Incremental NPV = -30000 +27650.55 =-2349.45

As the incremental NPV is negative , so Alternative 4 is not preferred over Alternative 1

Comparing Alternatives 1 and 5

Incremental investment = $150,000 - $100,000 = $50,000

Incremental savings in operating cost per year = $20000- $10000 = $10000

Now Present value of savings of $10000 per year for 10 years @10% = 10000/0.10 * (1- (1/1.1)¹⁰) =61445.67

So, Incremental NPV = -50000 +61445.67 =11445.7

As the incremental NPV is positive , so Alternative 5 is preferred over Alternative 1

So,out of all Alternatives, Alternative 5 is the best