Question

to identify which of the following two mutually exclusive investments is more economical, the b - c ratio method is used at a marr of 8% per year.
alternative a b b versus a
initial cost $370,000 $600,000 $230,000
net annual revenues $89,552 $129,656 $40,104
service life (years) 10 10 10
b - c ratio 1.62 1.45 1.17
which investment is more economical and how is it determined from the information given above
a. alternative a because it has a higher b - c ratio
b. alternative b because the incremental b - c ratio is greater than one
c. alternative b because it has higher initial cost and annual revenues
d. alternative a because the incremental b - c ratio is greater than one

Explanation:

Step1: Understand B - C ratio for mutually exclusive projects

For mutually exclusive projects, when comparing two alternatives, if the incremental B - C ratio (B - C ratio of \(B\) versus \(A\)) is greater than \(1\), the more expensive alternative (in terms of initial cost) is preferred. If it is less than \(1\), the less expensive alternative is preferred.

Step2: Analyze each option

• Option A: Just having a higher B - C ratio for a single alternative does not account for the incremental analysis which is required for mutually exclusive projects.
• Option B: The incremental B - C ratio (\(B\) versus \(A\)) is \(1.17> 1\). According to the B - C ratio method for mutually exclusive projects, when the incremental B - C ratio of the more expensive alternative (alternative \(B\) has a higher initial cost than \(A\)) is greater than \(1\), the more expensive alternative (\(B\)) is selected.
• Option C: Higher initial cost and annual revenues do not directly determine the economic preference. The B - C ratio (especially incremental) is the key factor.
• Option D: The incremental B - C ratio (\(B\) versus \(A\)) is \(1.17>1\) which would favor \(B\) not \(A\)

Answer:

B. Alternative B because the incremental B - C ratio is greater than one