Question

A company is considering replacing its air conditioner. They have narrowed their selection to two alternativesthat will offer considerable savings over their current system. If the effective annual interest rate is 8%,and the lifetime of the machines will be 15 years,what is the benefit cost ratio of eachmachine, and which machine should the company choose

Answer 1

A. Alternative 1 1.88

Alternative 2 1.73

Incremental Analysis 1.34

B. Alternative 2

Step-by-step explanation:

A. Calculation to determine the benefit cost ratio of each machine,

First step is to calculate the present value of each Alternative

ALTERNATIVE 1

Calculation for alternative 1 Benefit and cost

Benefits = ($1500)(P/A, 8%, 15)

Benefits= ($1500)(8.5595)

Benefits= $12,839

Cost = $7,000 – ($500)(P/F, 8%,15)

Cost= $7,000 – ($500)(0.3152)

Cost = $6842

Now let calculate Alternative 1 Ratio of Benefit to Cost using this formula

Ratio of Benefit to Cost = Benefit/Cost

Let plug in the formula

Ratio of Benefit to Cost=$12,839/$6842

Ratio of Benefit to Cost= 1.88

Therefore the benefit cost ratio for Alternative 1 is 1.88

ALTERNATIVE 2

Calculation for alternative 2 Benefit and cost

Benefits = ($1900)(P/A, 8%,15)

Benefits= ($1900)(8.5595)

Benefits= $16,263

Cost = $9000 + ($1250)(P/F,8%,15)

Cost= $9000 + ($1250)(0.3152)

Cost=$9394

Now let calculate Alternative 1 Ratio of Benefit to Cost using this formula

Ratio of Benefit to Cost = Benefit/Cost

Let plug in the formula

Ratio of Benefit to Cost= $16,263/$9394

Ratio of Benefit to Cost = 1.73

Therefore the benefit cost ratio for Alternative 2 is 1.73

B. In order to know which machine should the company choose we have to determine the incremental analysis for each of the machine

Incremental Analysis = ($16,263- $12,839)/ ($9394 - $6842)

Incremental Analysis= 1.34

Based on the above calculation for Incremental Analysis we can see that the Incremental Analysis is greater than 1 which means that the machine that the company should choose is ALTERNATIVE 2