Question 6 300000 points Save Answer A firm is trying to dec

Question 6 3.00000 points Save Answer A firm is trying to decide which of two machines to install to reduce excessive costs of repairs due less reliable old machines. The new machines cost $1000 and have useful lives of five years, and no salvage value. Machine A can be expected to result in $300 savings annually. Machine B will provide cost savings of $400 the first year, but will decline $50 annually, making the second-year savings $350, the third year savings $300, and so forth. With interest at 7%, which machine should be purchased based on benefit-cost ratio? a. Machine A with a benefit-cost ratio of 2.19 b. Machine B with a benefit-cost ratio of 1.26 c. Machine A with a benefit-cost ratio of 1.23 d. Both machines have equal cost-benefit ratio of 1.39

Solution

Machine A

Initial Cost = $1,000

Annual savings = $300

Time period = 5 years

Interest rate = 7%

Present worth of benefit = $300(P/A, 7%, 5) = $300 * 4.1002 = $1,230.06 or 1,230

Calculate benefit-cost ratio of Machine A -

Benefit-cost ratio = PW of benefit/Initial cost = 1,230/1,000 = 1.23

The benefit-cost ratio of Machine A is 1.23

Machine B

Initial Cost = $1,000

Annual saving in first year = $400

This decreases by $50 annually.

Present worth of benefit = $400(P/F, 7%, 1) + $350(P/F, 7%, 2) + $300(P/F, 7%, 3) + $250(P/F, 7%, 4) + $200(P/F, 7%, 5)

Present worth of benefit = ($400 * 0.9346) + ($350 * 0.8734) + ($300 * 0.8163) + ($250 * 0.7629) + ($200 * 0.7130)

Present worth of benefit = 373.84 + 305.69 + 244.89 + 190.72 + 142.6 = 1,257.74 or 1,260

Calculate benefit-cost ratio of Machine B -

Benefit-cost ratio = PW of benefit/Initial cost = 1,260/1,000 = 1.26

The Benefit-cost ratio of Machine B is 1.26

The benefit-cost ratio of machine B is greater. So, machine B should be purchased.

So,

Machine B with benefit-cost ratio of 1.26 should be purchased.

Hence, the correct answer is the option (b).