Final answer:
To determine the highest cost for the aluminum tank to be the preferred option at a MARR of 6%, we compare the equivalent annual costs (EAC) of all tank options. The steel and fiberglass tanks have EACs of $25,064 and $24,990, respectively. Therefore, the aluminum tank should cost no more than $209,000 to be the preferred option.
Step-by-step explanation:
To determine the highest cost for the aluminum tank so that it is the preferred option, we have to compare the equivalent annual costs (EAC) of each tank. EAC is the cost per year of owning and operating an asset over its entire lifespan. We calculate EAC using the formula:
EAC = Initial Cost × (MARR ÷ (1+MARR)n) ÷ ((1+MARR)n - 1)
Where MARR is the minimum acceptable rate of return and n is the number of years the tank is expected to last. For the steel tank, the EAC is:
EACsteel = $226,000 × (0.06 ÷ (1 + 0.06)15) ÷ ((1 + 0.06)15 - 1) = $226,000 × 0.1109 = $25,064
For the fiberglass tank, the EAC is:
EACfiberglass = $314,000 × (0.06 ÷ (1 + 0.06)30) ÷ ((1 + 0.06)30 - 1) = $314,000 × 0.0796 = $24,990
To make the aluminum tank the preferred option, its EAC must be less than those for both steel and fiberglass tanks. Let Costaluminum be the initial cost of the aluminum tank:
EACaluminum < EACsteel and EACaluminum < EACfiberglass
Maximum Costaluminum = EACfiberglass ÷ ((1+MARR)25 - 1) ÷ (0.06 ÷ (1 + 0.06)25)
Maximum Costaluminum = $24,990 ÷ (4.2918) ÷ 0.071591 = $209,000 (to the nearest $1,000)
Hence, the aluminum tank should cost no more than $209,000 if it is to be the preferred option.