Question 6 3.00000 points Save Answer A firm is trying to decide which of two ma

Question

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 wi nte estat 7% which machines d 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

Explanation / Answer

Correct Answer:

B

Working note:

R = 7%

Time n = 5 years

Annual worth of the investment = 1000/((1-1/1.07^5)/.07) = $243.89

Annual benefit by machine A = $300

So, B/C ratio for machine A = 300/243.89 = 1.23

Present value of the benefits for machine B = 400/1.07 + 350/1.07^2 + 300/1.07^3 + 250/1.07^4 + 200/1.07^5

Present value of the benefits for machine B = $1257.75

Hence,

Uniform annual benefits by machine B = 1257.75/((1-1/1.07^5)/.07) = $306.75

B/C ratio for the machine B = 306.75/243.89 = 1.26

Due to higher B/C ratio of 1.26, machine B will be selected.

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