Question

A contractor is considering the following three alternatives:

Purchase a new computer system for $15,000. The system is expected to last six years with a salvage value of $1,000.

Lease a computer system for 6 years for $3,000 per year payable at the beginning of each year.

Purchase a used computer system for $8,200. The system is expected to last 3 years with zero salvage value.

Draw cash flow diagrams for each alternative for this problem. For part c., assume that the purchase price of a used computer system will remain the same over the next six years. Which is the best choice using an annual return value of 7%? Which is the best choice for an annual return value of 10%?

Answer 1

To determine the best alternative, we must calculate net present value of each option. Since these are costs, the alternative with the lowest NPV should be selected.

Best alternative at 7% return rate:

Alternative 1: Purchase a new computer system for $15,000

NPV = [(Cash flow₁)/(1+r)¹] + [(Cash flow₂)/(1+r)²] + [(Cash flow₃)/(1+r)³]…..+ [(Cash flow_n)/(1+r)ⁿ] – [Salvage Value / (1+r)ⁿ]

NPV = -$15,000 + {$1,000/(1+0.07)⁶} = -$14,333.66

Alternative 2: Lease a computer system for 6 years for $3,000 per year payable at the beginning of each year

NPV = -$3,000 + {-$3,000/(1.07)} + {-$3,000/(1.07)²} + {-$3,000/(1.07)³} + {-$3,000/(1.07)⁴} + {-$3,000/(1.07)⁵} = -$15,300.60

Alternative 3: Purchase a used computer system for $8,200. The system is expected to last 3 years with zero salvage value

NPV = -$8,200 + {-$8,200/(1.07)³} = -$14,893.64

At 7% rate of return, alternative 1 has the lowest cost in terms of NPV, so it should be selected.

Best alternative at 10% return rate:

Alternative 1: Purchase a new computer system for $15,000

NPV = -$15,000 + {$1,000/(1+0.10)⁶} = -$14,435.50

Alternative 2: Lease a computer system for 6 years for $3,000 per year payable at the beginning of each year

NPV = -$3,000 + {-$3,000/(1.10)} + {-$3,000/(1.10)²} + {-$3,000/(1.10)³} + {-$3,000/(1.10)⁴} + {-$3,000/(1.10)⁵} = -$ 14,372.37

Alternative 3: Purchase a used computer system for $8,200. The system is expected to last 3 years with zero salvage value

NPV = -$8,200 + {-$8,200/(1.10)³} = -$14,360.80

At 10% rate of return, alternative 3 has the lowest cost in terms of NPV, so it should be selected.