Question

You and your partner have become very interested in cross-country motorcycle racing and wish to purchase entry-level equipment. You have identified two alternative sets of equipment and gear. Package K has a first cost of $150,000, an operating cost of $6,500 per quarter, and a salvage value of $30,000 after its 2-year life. Package L has a first cost of $210,000 with a lower operating cost of $2,500 per quarter and an estimated $15,000 salvage value after its 4-year life. Which package offers the lower present worth analysis at an interest rate of 20% per year, compounded quarterly

Answer 1

Explanation: To determine which package offers the lower present worth analysis, we need to calculate the present worth of each package using the formulas provided. The present worth of an investment is the current value of the future cash flows generated by that investment.

Package K:

First, we need to calculate the quarterly operating cost for 2 years: $6,500/quarter x 4 quarters/year x 2 years = $52,000

Then we need to calculate the total cost of the package: $150,000 + $52,000 + $30,000 = $232,000

Now we need to calculate the present worth of Package K: $232,000 / (1+0.2)^4 = $150,441.18

Package L:

First, we need to calculate the quarterly operating cost for 4 years: $2,500/quarter x 4 quarters/year x 4 years = $40,000

Then we need to calculate the total cost of the package: $210,000 + $40,000 + $15,000 = $265,000

Now we need to calculate the present worth of Package L: $265,000 / (1+0.2)^8 = $150,441.18

As we can see, package K has the same present worth of $150,441.18 at 20% per year, compounded quarterly. So both package K and package L has the same present worth analysis.