Question

Problem #3: Sam is considering buying a new lawnmower. He has a choice between a Yard Machine mower and a Lawn Guy mower. Sam has a MARR of 10%. The salvage value of each mower at the end of its service life is zero.

	Yard Machine mower	Lawn Guy mower
First Cost	$450	$350
Life	10 Years	10 Years
Annual Gas Cost	$80	$100
Annual Maintenance Cost	$30	$40

1. Using the information above, determine which alternative is preferable. Use the Present Worth comparison.
2. Instead of using the present worth comparison in part (a), use the Annual Worth comparison method to justify your selection.

Answer 1

a) Ans: The Alternative - Yard Machine Mower is preferable.

Explanation:

Yard Machine Mower;

Initial cost ( P ) = $450

Annual cost ( A ) = $80 + $30 = $110

Interest rate ( i ) = 10%

Number of interest period ( n) = 10

PW = P + A ( P/A , i , n )

= $450 + $110 ( P/A , 10% , 10 )

= $450 + $110 (6.1446 ) =$450 + $675.91

=$1125.91

Lawn Guy Mower;

Initial cost ( P ) = $350

Annual cost ( A ) = $100 + $40 = $140

Interest rate ( i ) = 10%

Number of interest period ( n) = 10

PW = P + A ( P/A , i , n )

= $350 + $140 ( P/A , 10% , 10 )

= $350 + $140 (6.1446 ) =$350 + $860.24

=$1210.24

Here , The present worth cost of Yard Machine Mower is less than the Lawn Guy Mower . Therefore , Yard Machine Mower is preferable.

b) Ans: The Alternative - Yard Machine Mower is preferable.

Explanation:

Yard Machine Mower;

Initial cost ( P ) = $450

Annual cost ( A ) = $80 + $30 = $110

Interest rate ( i ) = 10%

Number of interest period ( n) = 10

AW = P ( A/P , i , n ) + A

= $450( A/P , 10% , 10 ) + $110

= $450 (0.1627 ) + $110 = $73.22 + $110

= $183.22

Lawn Guy Mower;

Initial cost ( P ) = $350

Annual cost ( A ) = $100 + $40 = $140

Interest rate ( i ) = 10%

Number of interest period ( n) = 10

AW = P ( A/P , i , n ) + A

= $350( A/P , 10% , 10 ) + $140

= $350 (0.1627 ) + $140 = $56.95 + $140

= $196.95

Here , The annual  worth cost of the Yard Machine Mower is less than the Lawn Guy Mower . Therefore , Yard Machine Mower is preferable.