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 $200,000, an operating cost of $6,000 per quarter, and a salvage value of $30,000 after its 2-year life. Package L has a first cost of $280,000 with a lower operating cost of $2,200 per quarter and an estimated $30,000 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

Package K offers the lower present worth analysis.

Explanation:

This can be determined using the following 3 steps.

Step 1: Calculations of present worth of Package K

First cost = $200,000

Present value of quarterly operating cost = quarterly operating cost * ((1- (1/(1 + r))^n)/r) (1)

Where;

r = quarterly interest rate = interest rate per year / Number of quarters in a year = 20% / 4 = 5%, or 0.05

n = number of quarters = Number of years * Number of quarters in a year = 2 * 4 = 8

Substituting the values into equation (1), we have:

Present value of quarterly operating cost = $6,000 * ((1- (1/(1 + 0.05))^8)/0.05) = $38,779.28

Present value of salvage value = Salvage value / (1 + quarterly interest rate)^Number of quarters = $30,000 / (1 + 0.05)^8 = $20,305.18

Present worth of package K = First cost + Present value of quarterly operating cost - Present value of salvage value = $200,000 + $38,779.28 - $20,305.18 = $218,474.10

Step 2: Calculations of present worth of Package L

First cost = $280,000

Present value of quarterly operating cost = quarterly operating cost * ((1- (1/(1 + r))^n)/r) (1)

Where;

r = quarterly interest rate = interest rate per year / Number of quarters in a year = 20% / 4 = 5%, or 0.05

n = number of quarters = Number of years * Number of quarters in a year = 4 * 4 = 16

Substituting the values into equation (1), we have:

Present value of quarterly operating cost = $2,200 * ((1- (1/(1 + 0.05))^16)/0.05) = $23,843.09

Present value of salvage value = Salvage value / (1 + quarterly interest rate)^Number of quarters = $30,000 / (1 + 0.05)^16 = $13,743.35

Present worth of package L = First cost + Present value of quarterly operating cost - Present value of salvage value = $280,000 + $23,843.09 - $13,743.35 = $218,474.10 = $269,900.25

Step 3: Comparison of present worth

Present worth of package K = $218,474.10

Present worth of package L = $269,900.25

Therefore, Package K offers the lower present worth analysis.

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