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 $220,000, an operating cost of $8,500 per quarter, and a salvage value of $50,000 after its 2-year life. Package L has a first cost of $170,000 with a lower operating cost of $3,900 per quarter and an estimated $27,000 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 $ ???

that of package L is $ ???

Which package offers the lower present worth, K or L???

Answer 1

Case 1 : Package K

We assume that package K can be repeated with same cash flows

Quarterly interest rate=8%/4=2%

PW of package K for 2 years of useful life=-220000-8500*(P/A,0.02,8)+50000*(P/F,0.02,8)

Let us calculate the interest factors

(P/F,0.02,8)=1/(1+0.02)^8=0.853490

PW of package K for 2 years of useful life=-220000-8500*7.325481+50000*0.853490 =-239592.09

PW of package K for 4 years of study period=-239592.09-239592.09*(P/F,0.02,8)

PW of package K for 4 years of study period=-239592.09-239592.09*0.853490

PW of package K for 4 years of study period=-$444,081.54

(Negative sign indicates that that its a cost)

Case 2 : Package L

PW of package L for 4 years of useful life=-170000-3900*(P/A,0.02,16)+27000*(P/F,0.02,16)

Let us calculate the interest factors

(P/F,0.02,16)=1/(1+0.02)^16=0.728446

PW of package L for 4 years of useful life=-170000-3900*13.577709+27000*0.728446

PW of package L for 4 years of useful life=-$203,285.02

(Negative sign indicates that that its a cost)

Absolute value is lower in case of package L. It should be preferred