Question 10.7: Incremental B−C Analysis of Mutually Exclusive Projects Thre...
Incremental B−C Analysis of Mutually Exclusive Projects
Three mutually exclusive alternative public-works projects are currently under consideration. Their respective costs and benefits are included in the table that follows. Each of the projects has a useful life of 50 years, and MARR is 10% per year. Which, if any, of these projects should be selected? Solve by hand and by spreadsheet.
| A | B | C | |
| Capital investment | $8,500,000 | $10,000,000 | $12,000,000 |
| Annual operating and maintenance costs | 750,000 | 725,000 | 700,000 |
| Market value | 1,250,000 | 1,750,000 | 2,000,000 |
| Annual benefit | 2,150,000 | 2,265,000 | 2,500,000 |
PW(Costs, A) = $8,500,000 + $750,000(P/A, 10%, 50)
−$1,250,000(P/F, 10%, 50) = $15,925,463,
PW(Costs, B) = $10,000,000 + $725,000(P/A, 10%, 50)
−$1,750,000(P/F, 10%, 50) = $17,173,333,
PW(Costs, C) = $12,000,000 + $700,000(P/A, 10%, 50)
−$2,000,000(P/F, 10%, 50) = $18,923,333,
PW(Benefit, A) = $2,150,000(P/A, 10%, 50) = $21,316,851,
PW(Benefit, B) = $2,265,000(P/A, 10%, 50) = $22,457,055,
PW(Benefit, C) = $2,500,000(P/A, 10%, 50) = $24,787,036.
B–C(A) = $21,316,851/$15,925,463
= 1.3385 > 1.0.
Therefore, Project A is acceptable.
\Delta B/\Delta C of (B − A) = ($22,457,055 − $21,316,851)/($17,173,333 − $15,925,463)
= 0.9137 < 1.0.
Therefore, increment required for Project B is not acceptable.
\Delta B/\Delta C of (C − A) = ($24,787,036 − $21,316,851 )/ ( $18,923,333 − $15,925,463)
= 1.1576 > 1.0.
Therefore, increment required for Project C is acceptable.
Decision: Recommend Project C .
Spreadsheet Solution
A spreadsheet analysis for this example is shown in Figure 10-4. For each mutually exclusive project, the PW of total benefits (cells B11:B13) and the PW of total costs (cells C11:C13) are calculated. Note that annual operating and maintenance costs are included in the total cost calculation in accordance with the conventional B–C ratio formulation. Since the projects are mutually exclusive, they must be ranked from smallest to largest according to the equivalent worth of costs (do nothing → A → B →
C). The B–C ratio for Project A is calculated to be 1.34 (row 17), and Project A replaces do-nothing as the baseline alternative. Project B is now compared with Project A (row 18). The ratio of incremental benefits to incremental costs is less than 1.0, so Project A remains the baseline alternative. Finally, in row 19, the incremental benefits and incremental costs associated with selecting Project C instead of Project A are used to calculate an incremental B–C ratio of 1.16. Since this ratio is greater than one, the increment required for Project C is acceptable, and thus Project C becomes the recommended project.
