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Q.1 Consider 3 projects for 50 years, and interest rate 10%. Use incremental B/C analysis to select project X, Y or Z. Х I O&

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Answer #1

All figures in $'000s

Project X Y Z
Investment $8500 $10000 $12000
Operating & maintenance costs $750 $725 $700
Market value $1250 $1725 $2000
Benefits $2150 $2265 $2500

All projects have equal life of 50 years and interest rate is 10%

(i+1) - 1 i(1+i)n i,n) = (1 + i)-n i= 10% and n=50

We first find the present values of costs and benefits for each project

10%, 50) – MV 50) for project X Present value of costs, C = 1 + OM C4 = 8500 + 750 * 9.915 – 1250 * 0.00852 C = 8500 + 7436.2

10%, 50) for project Y, Present value of costs, Cy=I + OM* %, 50) – MV * Cy = 10000 + 725 * 9.915 – 1725 * 0.00852 Cy = 10000

%, 50) – MV*- 10%,50) for project 2, Present value of costs, C. = I + OM C. = 12000 + 700 * 9.915 – 2000 * 0.00852 C. = 12000

= 1.3385 Benefit - cost ratio for project X, BC, B Benefit - cost ratio for project Y, BCy B. 21317.25 15925.6 22457.475 1717

Benefit - cost ratio for project Z, BC, = C 24787.5 18923.46 = 1.3098

Since benefit-cost ratio exceeds 1,but project X has the highest ratio among the 3 projects

But for incremental benefit-cost analysis,we compare the projects incrementally

We first do incremental comparison between projects Z and Y

B- C-C- incremental Benefit-cost ratio for project Z over Y, BC.-y= 24787.5 - 22457.475 2330.025 18923.46 - 17173.678 1749.78

We now do incremental between projects Z and X

B. - B, incremental Benefit-cost ratio for project Z over X, BC.-- = BC3-1 C: - C, 24787.5 - 21317.25 3470.25 18923.46 – 1592

Based on incremental benefit-cost analysis, project Z is recommended for selection

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