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Sunk Costs, Cost/Benefit and Payback October 1, 2010

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Sunk Costs Problem 1: Quarmby Electronics makes mobile phones. 100 000 batteries will be needed in the coming year. They can be produced in-house by two workers. The salaries of these two workers will be $50 000 each, and the cost of raw materials is $1.00 per battery. Alternatively, the batteries can be purchased from an external supplier at a unit cost of $1.90 per battery. Which option should they choose?

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Sunk Costs Problem 2: Quarmby Electronics makes mobile phones. They have just invested $500 000 in a battery-making machine. This machine requires two workers to operate, and can produce 100 000 batteries per year. The salaries of these two workers will be $50 000 each. Raw materials for the batteries cost $1.00 per battery. The machine has no salvage value. Alternatively, the batteries can be purchased from an external supplier at a unit cost of $1.90 per battery. Which option should they choose?

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Cost/Benefit Analysis This is one more method of deciding between projects, commonly used by government bodies. Calculate the ratio Present worth of Benefits Present worth of Costs If this is greater than one, do the project. Otherwise don’t.

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As in the case of Rate of Return methods, there is a potential trap:

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The government builds a bridge to Vancouver Island at a cost of $150 000 000. Each year it will cost $10 000 000 to maintain. The bridge will be a toll bridge, and is expected to bring in $20 000 000 per year in tolls. Also, the increase in tourism is estimated to be worth $5 000 000 a year in increased tax revenues. Considering a study period of 20 years and an MARR of 5%, should the project go ahead?

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Benefits ($000 000): Net revenue of 15 every year Cost ($000 000): -150 initial cost So B/C ratio = 15(P/A,0.05,20)/150 = 187/150 = 1.25

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The government builds a bridge to Vancouver Island at a cost of $150 000 000. Each year it will cost $10 000 000 to maintain. The bridge will be a toll bridge, and is expected to bring in $20 000 000 per year in tolls. Also, the increase in tourism is estimated to be worth $5 000 000 a year in increased tax revenues. Considering a study period of 20 years and an MARR of 5%, should the project go ahead? Benefits ($000 000): Revenue of 25 every year Cost ($000 000): -150 initial cost and -10 per year So B/C ratio = 25(P/A,0.05,20)/(150 + 10(P/A,0.05,20)) = 25(12.462)/(150 + 10(12.462)) = 1.13

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Fortunately, this never affects whether the B/C ratio is greater than unity. But we can’t use the size of the BC ratio to compare different projects. So once again we fall back on incremental analysis.

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Seven mutually exclusive plans for waste-disposal in a city have been put forward. Their costs and benefits are as follows: Option BenefitCosts P4,000,000500,000 Q4,000,0002,000,000 R7,000,0002,000,000 S6,000,0005,000,000 T9,000,0006,000,000 U2,000,0004,000,000 V7,000,0008,000,000 All the figures in the table are equivalent present worths, using a 25-year planning horizon and an 8% interest rate. Which alternative has the largest B/C ratio? Which is the most expensive alternative with B/C > 1? Which is the cheapest alternative with B/C > 1? Which alternative should be chosen? Example:

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Unlike all the comparison methods discussed so far, this does not necessarily give the same result as a present worth comparison. Payback Period We calculate how long the annual revenues from an initial investment take to pay off the cost of that investment. We compare this with a pre-set limit – usually between two and four years – or with the available alternatives.

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We replace five assembly-line workers with an industrial robot. The robot costs $300 000, and the workers earned $30 000 a year each. Example: So payback time = 300 000/150 000 = 2 years. WeaknessesStrengths Ignores longer-term cashflowsAvoids long-term prediction Ignores time value of moneyEasy to understand No long-tem projectsEasy to calculate

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We replace five assembly-line workers with an industrial robot. The robot costs $300 000, and the workers earned $30 000 a year each. Our MARR is 20%. Discounted Payback Period: 150 000(P/A,0.2,2) = 150 000(1.523) = 228 450 150 000(P/A,0.2,3) = 150 000(2.106) = 315 900 So payback period = 3 - (315 900 – 300 000)/(315 900 – 228 450) = 2.82 years.

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