Sheet1Projects Ltd intends to acquire a new machine costing 50,000 which is expected to have a life of five years, with a scrap value of 10,000 at the end of that time. Cash flows arising from operation of the machine are expected to occur on the last day of each year as follows. End of year 1 10,000 2 15,000 3 20,000 4 25,000 5 25,000 Required: Calculate & show working out i) the Accounting Rate of Return (ARR), ii) the Payback Period (PP), iii) the Net Present Value (NPV; assume a discount rate of 10% per annum), and iv) the Internal Rate of Return (IRR)Part (I) Accounting Rate of ReturnYearCash FlowDepreciationNet Profit (Cash Flow-Depreciation)1100008000200021500080007000320000800012000425000800017000525000800017000Total Profit55000Average Profit(Per Year)= Total Profit/No. Of Periods= 55000/5= 11000Average Investment = (beginning Investment + Ending Investment)/2 = (50000+10000)/2 = 30000Accounting Rate of Return = (Average Profit/Average Investment)*100Accounting Rate of Return = (11000/30000)*100=36.67%Note: Its assumed the its a straight line Depreciation Hence Depreciation per year would be = (Investment Value-Salvage Value)/Number of year. Hence Depreciation= (50000-10000)/5 = 8000Part (ii) Payback PeriodYearCash FlowCumulative Cash Flow0-50000-50000110000-40000215000-25000320000-50004250002000052500045000Payback period is the length of the period in which initial investment is recovered. So payback period is between year 3 & 4.

Payback period = 3+ 5000/25000 = 3.2 yearsPart (iii) NPV(NPV is the same of the present value of all future cashflows)YearCash FlowPV factor @ 10%Present Value (Cash flow * PV factor)0-500001-500001100000.90919090.9090912150000.826412396.694213200000.751315026.296024250000.683017075.336385250000.620915523.03308NPV (in Pounds)19112.26878Part (iv) IRRIRR is the rate at which the present value of cash inflow would be equal to present value of cash outflow (i.e. NPV would be zero)YearCash Flow0-50000110000215000320000425000525000IRR (Using Excel Formula)21.86%(Incase we need to calculate Accounting rate of return per year. Solution given belowYearBeg InvestmentEnding InvestmentAverage InvestmentNet ProfitAccounting Rate of Return150000420004600020004.35%2420003400038000700018.42%33400026000300001200040.00%42600018000220001700077.27%518000100001400017000121.43%IRR (Using Trial Method)IRR is the rate at which the present value of cash inflow would be equal to present value of cash outflow (i.e. NPV would be zero)As calculated in in part 3 NPV is positive @10% so we would use a discount rate greater than 10% to find out a rate at which NPV is zero. Let use 20% rateYearCash FlowPV factor @ 10%Present Value (Cash flow * PV factor)0-500001-500001100000.83338333.3333332150000.694410416.666673200000.578711574.074074250000.482312056.327165250000.401910046.9393NPV (in Pounds)2427.340535NPV is still Positive we would now use rate of 22%YearCash FlowPV factor @ 22%Present Value (Cash flow * PV factor)0-500001-500001100000.81978196.7213112150000.671910077.936043200000.550711014.137754250000.451411284.97725250000.37009249.981311NPV (in Pounds)-176.2463911Now NPV is negative. Since at 20% NPV is positive and at 22% its negative we would use some rate between these two rate. Let use 21.86%YearCash FlowPV factor @ 21.86%Present Value (Cash flow * PV factor)0-500001-500001100000.82068206.1381912150000.673410101.10563200000.552611052.142464250000.453511336.926045250000.37219303.238178NPV (in Pounds)-0.45Since NPV is approximately zero at 21.86%. so IRR is 21.86%

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