i.
Expected savings per year, expected life and rate of return for expected values.
Answer to Problem 38P
Expected savings per year is $1980, expected life is 6 years and rate of return for the expected values is 12.18%.
Explanation of Solution
Given:
Cost of robot = $81000
Probability for optimistic annual savings of $22000 is 0.1
Probability for pessimistic annual savings of $18000 is 0.2
Probability for most likely annual savings of $20000 is 0.7
Probability for optimistic useful life of 4 year is 1/6
Probability for pessimistic useful life of 12 years is 2/3
Probability for most likely useful life of 5 year is 1/6.
Calculation:
Expected Savings (EAS):
=
Expected Saving - $19800
Expected Useful Life:
=
Hence, expected useful life is 6 years
Rate of return (RR) for optimistic:
Present value can be calculated as follows:
Interest rate = 12%
As calculated value is equal to actual Value, thus rate of return is 12.18%.
Conclusion:
Expected savings per year is $1980, expected life is 6 years and rate of return for the expected values is 12.18%.
ii.
Expected rate of return for combination of savings per year and life.
Answer to Problem 38P
Expected rate of return for combination of savings per year and life is 10.48%.
Explanation of Solution
Given:
Cost of robot = $81000
Probability for optimistic annual savings of $22000 is 0.1
Probability for pessimistic annual savings of $18000 is 0.2
Probability for most likely annual savings of $20000 is 0.7
Probability for optimistic useful life of 4 year is 1/6
Probability for pessimistic useful life of 12 years is 2/3
Probability for most likely useful life of 5 year is 1/6.
Calculation:
Expected rate of return for combination of savings per year and life:
Interest rate = 11%
When interest rate is substituted as 11%, then calculated value is less than the actual value. Thus decrease interest rate further. If 10.84% is substituted, then actual value is equivalent to calculated value.
Conclusion:
Thus, 10.84% is rate of return for combination of savings per year.
iii.
Answers for part a and b match or not.
Answer to Problem 38P
Answers donot match.
Explanation of Solution
Given:
Cost of robot = $81000
Probability for optimistic annual savings of $22000 is 0.1
Probability for pessimistic annual savings of $18000 is 0.2
Probability for most likely annual savings of $20000 is 0.7
Probability for optimistic useful life of 4 year is 1/6
Probability for pessimistic useful life of 12 years is 2/3
Probability for most likely useful life of 5 year is 1/6.
Concept used:
Since time period varies in part a and part b, rate of return for part a and part b are different.
Conclusion:
Answers donot match.
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