Managing Finance and Budgets

Lecture 7

Activities & Solutions

Accounting Rate of Return – Further Example

PROJECT ONE PROJECT TWOInvestment £300,000 £ 500,000

Cashflow Dep’n Net Profit Cashflow Dep’n Net ProfitYear 1: 90,000 60,000 30,000 120,000 100,000 20,000Year 2: 160,000 60,000 100,000 140,000 100,000 40,000Year 3: 120,000 60,000 60,000 160,000 100,000 60,000Year 4: 70,000 60,000 10,000 240,000 100,000 140,000Year 5: 70,000 60,000 10,000 320,000 100,000 220,000Totals: 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

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%

PPIn 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 = 45000Average Investment = (360000 + 0) 6 = 60000

ARR = 45000/60000 = 75%

PPIn the first three years, Total Cash flow = £330000,so the PP will occur sometime in year fourProportion 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

Machine 2: ARR = 75% PP = 3 years 3 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 90,900Year 2: 90,000 0.826 74,340 110,000 0.826 90,860Year 3: 90,000 0.751 67,590 120,000 0.751 90,120Year 4: 50,000 0.683 34,150 120,000 0.683 81,960Year 5: 50,000 0.621 31,050 90,000 0.621 55,890Year 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 83,300Year 2: 90,000 0.694 62,460 110,000 0.694 76,340Year 3: 90,000 0.579 52,110 120,000 0.579 69,480Year 4: 50,000 0.482 24,100 120,000 0.482 57,840Year 5: 50,000 0.402 20,100 90,000 0.402 36,180Year 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 -£6,260NPV 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.