how we got the table

EXAMPLE 9-7 Replacement Analysis Using the Coterminated Assumption Suppose that we are faced with the same replacement problem as in Example except that the period of needed service is (a) three years or (b) four years. The is, a finite analysis period under the coterminated assumption is being used. In each case, which alternative should be selected? Solution (a) For a planning horizon of three years, we might intuitively think that either the defender should be kept for three years or it should be replaced immediately by the challenger to serve for the next three years. From Table 9-3, the EUAC for the defender for three years is $11,950; from Table 9-2, the EUAC for the challenger for three years is $12,918. Thus, following this reasoning, the defender would be kept for three years. This, however, is not quite right. Focusing on the Total (Marginal) Cost for Each Year columns, we can see that the defender has the lowest cost in the first two years, but in the third year its cost is $13,650; the EUAC of one year of service for the challenger is only $13,500. Hence, it would be more economical to replace the defender after the second year. This conclusion can be confirmed by enumerating all replacement possibilities and their respective costs and then computing the EUAC for each, as will be done for the four-year planning horizon in Part (b). TABLE 9-4 Determination of When to Replace the Defender for a Planning Horizon of Four Years (Example 9-7, Part (b)] Keep K eep Defender Challenger for for Total (Marginal) Costs for Each Year - 1 2 3 4 $13,500" $12,375' $12,8134 $14,2754 10,500 13,500 12,375 12,813 10,500 12,000 13,500 12,375 10,500 12,000 13,650 13,500 10,500 12,000 13,650 15,000 3 2 EUAC at 10% for 4 Years $13,211 12,225 12,006 12,284 12,607 Least cost alternative 4 Column 6 of Table 9-2. Column 6 of Table 9-3 EXAMPLE 9-7 Replacement Analysis Using the Coterminated Assumption Suppose that we are faced with the same replacement problem as in Example except that the period of needed service is (a) three years or (b) four years. The is, a finite analysis period under the coterminated assumption is being used. In each case, which alternative should be selected? Solution (a) For a planning horizon of three years, we might intuitively think that either the defender should be kept for three years or it should be replaced immediately by the challenger to serve for the next three years. From Table 9-3, the EUAC for the defender for three years is $11,950; from Table 9-2, the EUAC for the challenger for three years is $12,918. Thus, following this reasoning, the defender would be kept for three years. This, however, is not quite right. Focusing on the Total (Marginal) Cost for Each Year columns, we can see that the defender has the lowest cost in the first two years, but in the third year its cost is $13,650; the EUAC of one year of service for the challenger is only $13,500. Hence, it would be more economical to replace the defender after the second year. This conclusion can be confirmed by enumerating all replacement possibilities and their respective costs and then computing the EUAC for each, as will be done for the four-year planning horizon in Part (b). TABLE 9-4 Determination of When to Replace the Defender for a Planning Horizon of Four Years (Example 9-7, Part (b)] Keep K eep Defender Challenger for for Total (Marginal) Costs for Each Year - 1 2 3 4 $13,500" $12,375' $12,8134 $14,2754 10,500 13,500 12,375 12,813 10,500 12,000 13,500 12,375 10,500 12,000 13,650 13,500 10,500 12,000 13,650 15,000 3 2 EUAC at 10% for 4 Years $13,211 12,225 12,006 12,284 12,607 Least cost alternative 4 Column 6 of Table 9-2. Column 6 of Table 9-3