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 $190,000, 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 $260,000 with a lower operating cost of $2,500 per quarter and an estimated $14,000 salvage value after its 4-year life. Which package offers the lower present worth analysis at an interest rate of 12% per year, compounded quarterly?

The present worth of package K is $  and that of package L is $  .

(Click to select)  Package K  Package L  offers the lower present worth.

Answer 1

The present worth analysis will be carried out for 4 yrs ( LCM of 2 & 4)

i = 12% compounded quarterly = 12% /4 = 3% per quarter

2 yrs = 8 quarters

4 yrs = 16 quarters

Present value of K = -190000 - 10000*(P/A, 3%,16) - (190000- 40000)*(P/F, 3%,8) + 40000*(P/F, 3%,16)

= -190000 - 10000*12.561102 - 150000*0.789409 + 40000*0.623167

= -409095.69

Present value of L = -260000 - 2500*(P/A, 3%,16) + 14000*(P/F, 3%,16)

= -260000 - 2500*12.561102 + 14000*0.623167

= -282678.42

As Present cost of L is less, it should be selected