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chapter4A - Additional Solutions Chapter Four Comparison...

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Additional Solutions: Chapter Four: Comparison Methods 1 4S.1 The new company has $1 500 000: 500 000 at 10% interest, 500 000 from investors who expect 15% growth, and $500 000 from you, where you also expect 15% growth. So your weighted cost of capital (WCC) is WCC = (1 0.15 + 0.5 0.1)/1.5. Your MARR should be at least as great as the WCC. (For some reason no-one got this right, so it’s not included in the total mark for the assignment.) *4S.2 Each of the windmills will produce 2 800 365 24 0.25 kWh/year = 6 132 000 kWh/year This represents an income of 6 132 000 0.049 = £300 000/ year. So the payback period for a single windmill is about five years The payback period for the project as a whole will be longer, as we see from this table: End of Year Cash Out (000) Cash In (000) Balance(000) Total (000) 1 1 500 0 - 1 500 - 1 500 2 1 500 300 - 1 200 - 2 700 3 1 500 600 - 900 - 3 600 4 1 500 900 - 600 - 4 200 5 0 1 200 1 200 - 3 000 6 0 1 200 1 200 - 1 800 7 0 1 200 1 200 - 600 8 0 1 200 1 200 600 This shows that the payback period is seven and a half years. For the nuclear power station, once the station comes on line it will generate Energy = 10 000 365 24 0.8 kWh/year = 70 000 000 kWh/year.
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This will produce an income of £3 430 000 per year, from which Victoria deducts the £300 000 spent on uranium fuel to obtain a net income of £3 130 000 per year. So after the plant comes on line at the end of the third year, it will be a further 7 000 / 3 130 = 2.24 years before the project becomes profitable. This shows that the payback period is 5.2 years. Based on payback period, the nuclear power station looks like the better investment. However, note that if Victoria were to define the first project as building a single windmill, it would then appear that this was the better investment, since the payback time would be slightly shorter than that for the power station. Then, having chosen to build a single windmill, she could next year consider building one additional windmill. This would again have a payback period of five years, so again would be preferred to the nuclear power station. This illustrates the weakness of the `payback period' method of comparing projects. Victoria now goes on to consider the `present worth' method of comparison, giving all figures in £ 000's: PW(windmill) = - 1 500( P/A ,0.2,4)( F/P ,0.2,1) + 300( P/A ,0.2,20) + 300( P/A , 0.2,20)( P/F ,0.2,1) + 300( P/A , 0.2, 20) ( P/F ,0.2,2) + 300( P/A , 0.2,20) ( P/F ,0.2,3) + 100(( P/F ,0.2,21) + ( P/F ,0.2,22) + ( P/F ,0.2,23) + (P/F ,0.2,24)) Note the factor of ( F/P ,0.2,1) in the construction costs is needed to represent the fact that this series starts at the beginning of the first year. There are several ways we could have represented the energy
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