Computing The Benefit Ratio Of The Difference Between The Alternatives

Two alternatives are being considered for a certain proiect: If money is worth $12%$ annually, compute the benefit ratio of the difference between the alternatives.

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### Step-by-step

- Explanationfor step 1

where r is the discount rate (in this case, 12%), t is the time period, and Cash Flows represent the cash inflows and outflows associated with the alternative. Once we calculate the NPV for each alternative, we can subtract the NPV of the first alternative from the NPV of the second alternative to find the difference. We can then divide the difference by the initial investment of the first alternative to find the benefit ratio

- Explanation for step 2

The NPV for Alternative A can be calculated as follows: NPV(A) = -$10,000 + ($3,000 / (1 + 0.12)^1) + ($4,000 / (1 + 0.12)^2) + ($5,000 / (1 + 0.12)^3) = -$10,000 + $2,678.57 + $3,312.99 + $3,681.05 = $1,672.61 The NPV for Alternative B can be calculated as follows: NPV(B) = -$12,000 + ($6,000 / (1 + 0.12)^1) + ($7,000 / (1 + 0.12)^2) + ($8,000 / (1 + 0.12)^3) = -$12,000 + $5,357.14 + $5,615.08 + $5,675.31 = $4,647.53

**Final answer**

The difference in NPV between the two alternatives is: NPV(B) – NPV(A) = $4,647.53 – $1,672.61 = $2,974.92 The benefit ratio of the difference between the alternatives is: Benefit Ratio = (NPV(B) – NPV(A)) / Initial Investment of Alternative A = $2,974.92 / $10,000 = 0.2975 So the benefit ratio of the difference between the two alternatives is 0.2975, which means that Alternative B generates 29.75% more benefits than Alternative A for the same initial investment. Computing The Benefit Ratio Of The Difference Between The Alternatives