Question

You are a water filter manufacturer trying to decide if you should invest in an automatic or manually operated machinery. Both alternatives’ present costs are pegged at $5000, however, they lead to different revenue patterns thereafter. The automatic machine allows for higher production levels and thus more revenues immediately, however more energy costs over time than the manual machine means that net revenues diminish over time. The manual machine does not produce as many filters initially but has no energy cost, so its net revenues increase over time. The expected net revenues of the automatic machine are: $3200, $1500, $690, and $310 by the ends of years one to four, respectively. The expected net revenues for the manual machine are $280, $710, $1900, and $3000 by the ends of years one to four, respectively. 1. Calculate the Internal Rate of Return of each alternative and compare them. Which is more feasible? 2. Knowing the MARR is 8%, use NPW analysis to compare these alternatives and find out which one is better. 3. Calculate the benefit cost ratio of the both alternatives.

Answer 1

1.INTERNAL RATE OF RETURN(IRR)

formula for IRR = lower rate + (NPV at lower rate / (NPV at lower rate - NPV at higher rate ))*(higher rate-lower rate)

here , lets assume that the lower rate is 8% and higher rate is 12%

from the given calculations in excel , we can understand that automatic machine have higher internal rate of return which is 8.3% than manual machine which is 4.7%.this indicates that automatic machine will give higher returns than manual machine .automatic machine will be more feasible as manual machine have negative net present value that indicates loss , while auotomatic machine have positive net present value that indicates profit .(refer to the formula cell , in case doubts on applying formula )

2.from the given calculations in excel , automatic machine have higher net present worth of 24.41 than manual machine which is (418.65) . clearly , chosing manual machine will result in loss .it is better to choose automatic machine as this have positive net present worth/value eventhough future revenue diminishes over time .chosing automatic machine will not relsult in overall loss eventhough revenue decreases over time but chosing manual machine will result in overall loss eventhough revenue increases over time . as we have the estimates for only 4 years further benefits/loss for both the alteratives cannot be measured.

3. from the given calculations in excel , automatic machine have higher benefit-cost ratio which is 1 than manual machine which is 0.92 . formula for benefit cost ratio = present value of future benefits / present value of future costs.

present value of future benefits is the total present value of cash inflows (revenue)

present value of the future costs is 5000 which is the initial investment , no additional future costs are given in the question.

(you can refer to the formula cell , in case of any doubts in applying the formula )