You and your partner have become very interested in crosscou

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 $160,000, an operating cost of $10,000 per quarter, and a salvage value of $40,000 after its 2-year life. Package L has a first cost of $240,000 with a lower operating cost of $3,700 per quarter and an estimated $26,000 salvage value after its 4-year life. Which package offers the lower present worth analysis at an interest rate of 8% per year, compounded quarterly? The present worth of package K is $ package L is $ Package L ? | offers the lower present worth.

Solution

Present worth for Package L

=-240000-3700/(1.02)-3700/(1.02)^2-3700/(1.02)^3-3700/(1.02)^4-3700/(1.02)^5-3700/(1.02)^6-3700/(1.02)^7-3700/(1.02)^8-3700/(1.02)^9-3700/(1.02)^10-3700/(1.02)^11-3700/(1.02)^12-3700/(1.02)^13-3700/(1.02)^14-3700/(1.02)^15-3700/(1.02)^16+26000/(1.08)^4

=-$271,126

Present worth for Package L

=-160000-3700/(1.02)-10000/(1.02)^2-10000/(1.02)^3-10000/(1.02)^4-10000/(1.02)^5-10000/(1.02)^6-10000/(1.02)^7-10000/(1.02)^8+40000/(1.08)^2

=-$192,784

Package L has Lower Present Worth