## Fv

(1 + r)n where r is the discount rate and n is the number of years. Company A

Total cost = \$70,000 H----20 H----40 H----5 H--:-t. H-----1--:--

(1 + 0.03) (1 + 0.03) (1 + 0.03)5 (1 + 0.03) (1 + 0.03)55

= \$70,000 + \$16,610 + \$9,197 + \$4,313 + \$3,720 H-----H \$1,141 + \$984 = \$121,022

Company B

\$20,000

(1 + 0.03)40 (1 + 0.03)50 = \$100,000 + \$8,240 + \$3,720 + \$2,768 + \$2,060 + \$1,533 + \$1,141 = \$119,462

The two options are quite similar, but it now looks like Company B bid would provide the lower life cycle cost and would be the better choice. The result is highly sensitive to the discount rate. If the discount rate had been 4% instead of 3%, Company A would have been a better choice with a life cycle cost of \$110,350 versus a cost to Company B of \$115,113. Note that (a) the total present value costs decrease as the discount rate rises and (b) the present value costs of expenses late in the life of the structure can become negligible. For this problem the crossover discount rate is about 3.2%, where for any discount rate above that value, Company A will be the preferred alternative. Company B is the best choice for any rate below 3.2% as shown in Figure 36.1a. However, if the service life is reduced to 40 years, Company A is the better choice for any value of the discount rate different from 0% (i.e., at 0% Companies A and B have the same lifetime cost of \$135,000, as shown in Figure 36.1b).

80,000

3456789 10 Discount rate, %

80,000

o 180,000

I 160,000

140,000

g 120,000

100,000

3456789 10 Discount rate, %

80,000

140,000

0 0