use the b/c ratio method to select one of these two alternatives: alternative 1

Question

use the b/c ratio method to select one of these two alternatives:
alternative 1 has an initial cost of 100$, has annual maintenance costs of $5 per year and has potential damage costs of $950.
alternative 2 has an initial cost of $110, annual maintenance costs of $9 per year and potential damage costs of $350. the interest rate is 20% per year, we will exmaine the case on a 20-year study period and we assume that the damage costs occur in the middle of the period, which is year 10? Thank you for your help.

Explanation / Answer

B/C ratio of incremental costs is greater than 1 and hence Alternative 2 should be chosen

Year 1 2 Incremental Cost 0 -100 -110 -10 1 -5 -9 -4 2 -5 -9 -4 3 -5 -9 -4 4 -5 -9 -4 5 -5 -9 -4 6 -5 -9 -4 7 -5 -9 -4 8 -5 -9 -4 9 -5 -9 -4 10 -955 -359 600-4 11 -5 -9 -4 12 -5 -9 -4 13 -5 -9 -4 14 -5 -9 -4 15 -5 -9 -4 16 -5 -9 -4 17 -5 -9 -4 18 -5 -9 -4 19 -5 -9 -4 20 -5 -9 -4 Present value of Benefit= 600/1.2^10= 96.90 Present value of costs = 10 +4*(1-1/1.2^20)/20%= 29.48 B/C ratio= 96.90/29.48= 3.29

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