Problem 4 Hanover, Inc. purchases a machine for $44,000 that has an estimated sa
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Question
Problem 4 Hanover, Inc. purchases a machine for $44,000 that has an estimated salvage value of $6,000, and an estimated life of 4 years. The company's required rate of return is 6.5% and its cost of capital is 4.2%. The machine is expected to generate the following cash flows and income over the next 4 years: Year1Year 2 Year 3 Year4 Operating cash flows Operating income $15,800 $17,200 $16,500 $15,100 6,300 7,000 5,600 Express anwers using 3 decimal places. A. Determine the machine's payback period. B. Determine the IRR of the machine. C. Determine the ARR D. Should the machine be purchased? Why or why not?Explanation / Answer
The quation required to claculate the Payback period using discounting method. The required rate of return and cost of capital is given as 6.50% and 4.20%. The decision to chose the discounting rate is depend upon the risk apetite of firm. Firm may select the cost of capital as a discounting rate if there is no avenue for investment at higher rate is not available. Here in this case, the discounting rate is assumed to be 6.50% and the following assumption is considered.
a) Firm is having an option in the market of investment the cash flow @ 6.50%.
The below table represent cash outflow and cash inflow in the four years of machine life.
As summation of discounted cash inflow up to three years is USD 43660 and discounted cash flow in 4 years would be USD 16402 so thorugh interpolation method we can calculate the month in which remaining USD 340 (44000-43660) would be recovered. The remaining days would be calcluated as 340*12/16402. The USD amount 16402 is the total discounted cash flow generated in 4 years. Therefore the discounted payback period would be 3 years and 24 days.
The IRR is the rate at which total cash inflow would equal to total cash outflow. The IRR in this case is 14.68%.
ARR is the accounting rate of return and is claculated as average return/ Average investment= USD 6650/22000=30.22%. Since numerator is shown in average terms therefore the denominator would also required to be shown in average terms.
USD 6650= Average of all oprating income mentioned in question.
As NPV of machine is positive i.e USD 16061 therefore machinery would be purchased.
* Note 1) while calculating the PV of cash flow, the salvage value of machine i.e USD 6000 is to recieved at the end of 4th year and is not factored in 4th year of cash flow.
2) while calcluating the ARR, the operating income is considered because they are arrived by follwing the accounting policies. The salvage value is not considered in operating income.
Year cash flow discounted cash flow 0 -44000 -44000 1 15800 14836 2 17200 15165 3 16500 13660 4 15100 11738 4 6000 4664 Total discounted cash infow 60061 NPV 16061Related Questions
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