Managing Finance and Budgets Lecture 7 Activities & Solutions

Accounting Rate of Return – Further Example PROJECT ONE PROJECT TWO Investment £300,000 £ 500,000 Cashflow Dep’n Net Profit Cashflow Dep’n Net Profit Year 1: 90,000 60,000 30,000 120,000 100,000 20,000 Year 2: 160,000 60,000 100,000 140,000 100,000 40,000 Year 3: 120,000 60,000 60,000 160,000 100,000 60,000 Year 4: 70,000 60,000 10,000 240,000 100,000 140,000 Year 5: 70,000 60,000 10,000 320,000 100,000 220,000 Totals: 510,000 300,000 210,000 980,000 500,000 480,000 ARR = Average profit/Average investment = (210,000/5)/ (300,000/2) = 28% (480,000/5)/(500,000)/2 = 38.4% In this case, the depreciation has been included as part of the Net Profit calculation

Activity One A company is considering investing in either of two new machines which will help to increase its production. The first machine will cost £240,000, and the company estimates that it will have a working life of 5 years. The second machine will cost £360,000 and have a working life of 6 years. The net positive cash-flows as a result of cost savings from the new machine are shown below. Calculate the payback period and Accounting Rate of returns for each of the machines. Machine 1: Net Cash-flows: £ 90,000/yr for first 3 years £ 50,000/yr for remaining 2 years Machine 2: Net Cash-flows: £100,000 Year 1 £110,000 Years 2 £120,000 Years 3 and 4 £ 90,000 Years 5 and 6

Activity One –Solution Part 1 Machine 1: Cost £240K Life 5 years Net Cash-flows: £ 90K /yr for first 3 years £ 50K /yr for remaining 2 years ARR Average Profit = [ (3 x 90000) + (2 x 50000) - 240000 ]  5 = 26000 Average Investment = (240000 + 0)  5 = 48000 ARR = 26000/48000 = 54.2% PP In the first two years, Total Cash flow = £180000, so the PP will occur sometime in year three Proportion of year three = (240000-180000)/90000 = 8 months PP = 2 years and 8 months

Activity One –Solution Part 2 Machine 2: Cost £360K Life 6 years Net Cash-flows: £100K, £110K, £120K, £120K, £90K, £90K ARR Average Profit = [ (100000+110000+ 120000x2 +90000x2) - 360000 ]  6 = 45000 Average Investment = (360000 + 0)  6 = 60000 ARR = 45000/60000 = 75% PP In the first three years, Total Cash flow = £330000, so the PP will occur sometime in year four Proportion of year four = (360000-330000)/120000 = 3 months PP = 3 years and 3 months

Activity One -Summary Machine 1: ARR = 45.8% PP = 2 years 8 months Analysis: If we opt for the Machine 1, it will cost less, and we will recoup our initial expenditure 7 months sooner. However the second machine promises greater return on our investment in the long run. Decision: If the company can secure the finances (e.g. long term loan over 4 years ), then Machine 2 represents a much better investment. If finances are a problem, then we may have to settle for Machine 1.

Activity Two For the scenario described in Activity One, calculate a Net Present Value for each of the two machines, using a Discount Rate of 10% and a Discount Rate of 20%. The Discount Factors at the two rates are shown below: 10% 20% Year 1 0.909 0.833 Year 2 0.826 0.694 Year 3 0.751 0.579 Year 4 0.683 0.482 Year 5 0.621 0.402 Year 6 0.565 0.335

Activity Two – Solution (1) MACHINE ONE MACHINE TWO Discount Discount Cashflow Factor DCF Cashflow Factor DCF Inv’mnt -240,000 1 -240,000 360,000- 1 360,000- Year 1: 90,000 0.909 81,810 100,000 0.909 90,900 Year 2: 90,000 0.826 74,340 110,000 0.826 90,860 Year 3: 90,000 0.751 67,590 120,000 0.751 90,120 Year 4: 50,000 0.683 34,150 120,000 0.683 81,960 Year 5: 50,000 0.621 31,050 90,000 0.621 55,890 Year 6: 90,000 0.565 50,850 Totals: 48,940 100,580 The above figures use a Discount Rate of 10%

Activity Two – Solution (2) MACHINE ONE MACHINE TWO Discount Discount Cashflow Factor DCF Cashflow Factor DCF Inv’mnt -240,000 1 -240,000 360,000- 1 360,000- Year 1: 90,000 0.833 74,970 100,000 0.833 83,300 Year 2: 90,000 0.694 62,460 110,000 0.694 76,340 Year 3: 90,000 0.579 52,110 120,000 0.579 69,480 Year 4: 50,000 0.482 24,100 120,000 0.482 57,840 Year 5: 50,000 0.402 20,100 90,000 0.402 36,180 Year 6: 90,000 0.335 30,150 Totals: -6,260 -6,710 The above figures use a Discount Rate of 20%

Activity Two – Solution Summary DF = 10% DF = 20% NPV of Machine 1 £48,940 -£6,260 NPV of Machine 2 £100,580 -£6,710 Analysis: If the value of money is decreasing at 10% per annum (low risk, low inflation, low interest), then Machine 2 is a much better proposition, earning over £50K more. However, if the value of money is decreasing at 20% per annum (high risk, high inflation, high interest) then Machine 1 is a slightly better proposition, as its loss is somewhat less. However, the value of purchasing any machine under these circumstances is questionable.