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(1) Hours per unit 1 2 2 1/ 2 3 Total
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(2) Units observed 100 200 400 300 1000
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(3) Expected probability 0.1 0.2 0.4 0.3 1.00
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(4) Expected hours 0.1 0.4 1.0 0.9 2.4
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(5) Expected cost at $5 $0.50 2.00 5.00 4.50 $12.00
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TABLE 11.4 Objective Probability and Expected Values
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The objective probabilities in column (3) are used to accumulate the expected direct-labor hours in column (4) [column (3) times column (1)]. The expected past figures in column (5) are found by multiplying the labor rate of $5.00 an hour by the expected hours in column (4). The totals in column (4) and (5) are expected values the average direct-labor hours per unit and direct-labor cost per unit that can be expected on the basis of past production experience.
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Subjective Probability
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Subjective probability is not based on observation of past events. It is a manager s estimate of the likelihood that certain events will occur in the future. Assume that a sales budget is being prepared. The manager estimates that chances are even (0.5) that sales will be the same as last year 1000 units. The probability of selling 1100 units is estimated to be 0.25 and the probability of selling 1200 units, 0.15. The manager estimates there is a 1-in-10 chance of selling 1300 units. The expected sales, based on these estimates of the future, are calculated in Table 11.5. The resulting figure for expected sales, 1085, can be used in the sales budget.
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(1) Sales in units 1000 1100 1200 1300 (2) Subject probability 0.5 0.25 0.15 0.10 1.00 TABLE 11.5
Expected Sales
(3) Expected sales, (2) (1) 500 275 180 130 1085
Eleven
Notice that use of probabilities enables the manager to reduce a range of values to a single value. The manager can still retain for later reference the original data used to make the estimate. The use of probability measures, together with the data a manager must accumulate, helps deal with the uncertainty that is characteristic of every business operation.
Capital Budget
Capital is invested in a fixed asset only if the asset is expected to bring in enough profit to (1) recover the cost of the equipment and (2) provide a reasonable return on the investment. The purpose of a capital budget analysis is to provide a sound basis for deciding whether the asset under consideration will in fact do this if it is purchased. The following elements must be considered in managing a capital budget decision: The cost of the fixed asset The expected net cash flow provided by use of the asset The opportunity of investing funds in capital equipment The present value
Cost of the Fixed Asset
The cost of the fixed asset is usually comprised of the purchase price, transportation, and installation cost of the asset. However, buying the asset may mean that other investments will have to be made additional inventories, for example. If so, these too should be included as part of the total investment outlay.
11.4.6 The Expected Net Cash Flow
The net cash flow may be either (1) the cash cost savings or (2) the increased sales revenue minus the increased cash costs due to using the new asset. No deduction for depreciation is made in calculating cash flow.
Opportunity Cost
Opportunity cost is the return that the business could realize by investing the money in the best alternative investment. For example, if the best alternative is to place the money in a savings account that pays 5 percent annually, the opportunity cost is 5 percent on the amount of the investment.
11.4.8 The Present Value
Scientific capital budgeting is based on the concept of present value for example, $1.00 put in a savings account at 5 percent interest will
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be worth $1.05 at the end of one year, $1.1025 at the end of the second year, and $1.1576 at the end of the third year.* Suppose an opportunity to invest some money with the expectation of receiving $1.1576 (including the amount invested and the interest or other income) at the end of the third year. Investment must not be more than $1.00, because the present value of $1.1576 to be received three years hence is $1.00 (based on the best alternative investment at 5 percent). *First year: Second year: Third: $1.00 + 0.05 ($1.00) = 1.05 $1.00 = $1.05 1.05 (1.05 $1.00) = 1.052 $1.00 = $1.1025 1.05 (1.052 $1.00) = 1.053 $1.00 = $1.1576
This present value is found by discounting the expected future value by the opportunity cost rate. This is accomplished by reversing the process for finding a future value, as follows: $1.1576 1.053 = $1.00 or, in general terms, Present value = value n years hence (1 + discount rate)n Table 11.6 shows another way of applying the present-value concept to capital expenditure decisions. Consider an investment of $6.50 in an asset that would yield the amounts shown in Table 11.6 if placed in a savings account at 5 percent. At the end of five years, the amounts received from the asset investment would total $7.00 (including the salvage value of the asset), whereas the savings account would be worth $6.50 1.053, or $7.52. Therefore, the $6.50 should not be invested in the asset. The present-value analysis in column (4) of Table 11.6 shows that the present value of the asset investment is $6.30, which is 20 cents less than the amount that would be invested. In other words, the value of the investment opportunity is minus 20 cents. If the amount
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