newnansm17 - Chapter 17: Rationing Capital Among Competing...

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Chapter 17: Rationing Capital Among Competing Projects 17-1 (a) With no budget constraint, do all projects except Project #4. Cost = $115,000 (b) Ranking the 9 projects by NPW/Cost Project Cost Uniform Benefit NPW at 12% NPW/Cost 1 $5 $1.03 $0.82 0.16 2 $15 $3.22 $3.19 0.21 3 $10 $1.77 $0 0 5 $5 $1.19 $1.72 0.34 6 $20 $3.83 $1.64 0.08 7 $5 $1.00 $0.65 0.13 8 $20 $3.69 $0.85 0.04 9 $5 $1.15 $1.50 0.30 10 $10 $2.23 $2.60 0.26 Projects ranked in order of desirability Project Cost NPW at 12% NPW/Cost Cumulative Cost 5 $5 $1.72 0.34 $5 9 $5 $1.50 0.30 $10 10 $10 $2.60 0.26 $20 2 $15 $3.19 0.21 $35 1 $5 $0.82 0.16 $40 7 $5 $0.65 0.13 $45 6 $20 $1.64 0.08 $65 8 $20 $0.85 0.04 $85 3 $10 $0 0 $95 (c) At $55,000 we have more money than needed for the first six projects ($45,000), but not enough for the first seven projects ($65,000). This is the “lumpiness” problem. There may be a better solution than simply taking the first six projects, with total NPW equal to 10.48. There is in this problem. By trial and error we see that if we forego Projects 1 and 7, we have ample money to fund Project 6. For this set of projects, Σ NPW = 10.65. To maximize NPW the proper set of projects for $55,000 capital budget is: Projects 5, 9, 10, 2, and 6
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17-2 (a) Select projects, given MARR = 10%. Incremental analysis is required. Project ∆ Cost ∆ Uniform Annual Benefit ∆ Rate of Return Conclusion 1 Alt 1A- Alt. 1C $15 $2.22 7.8% Reject 1A Alt. 1B- Alt. 1C $40 $7.59 13.7% Reject 1C Select 1B 2 Alt. 2B- Alt. 2A $15 $2.57 11.2% Reject 2A Select 2B 3 Alt. 3A- Alt. 3B $15 $3.41 18.6% Reject 3B Select 3A 4 $10 $1.70 11% Select 4 Conclusion: Select Projects 1B, 2B, 3A, and 4. (b) Rank separable increments of investment by rate of return Alternative Cost or ∆ Cost ∆ Rate of Return For Budget of $100,000 1C $10 20% 1C $10* 3A $25 18% 3A $25 2A $20 16% 2A $20 1B- 1C $40 13.7% 1B $50 2B- 2A $15 11.2% - 4 $10 11% - Σ = $95 * The original choice of 1C is overruled by the acceptable increment of choosing 1B instead of 1C. Conclusion: Select Projects 3A, 2A, and 1B. (c) The cutoff rate of return equals the cost of the best project foregone. Project 1B, with a Rate of Return of 13.7% is accepted and Project 2B with a Rate of Return of 11.2% is rejected. Therefore the cutoff rate of return is actually 11.2%, but could be considered as midway between 13.7% and 11.2% (12%). (d) Compute NPW/Cost at i = 12% for the various alternatives Project Cost Uniform Benefit NPW NPW/Cost 1A $25 $4.61 $1.05 0.04 1B $50 $9.96 $6.28 0.13 1C $10 $2.39 $3.50 0.35 2A $20 $4.14 $3.39 0.17 2B $35 $6.71 $2.91 0.08 3A $25 $5.56 $6.42 0.26 3B $10 $2.15 $2.15 0.21 4 $10 $1.70 -$0.39 -0.03
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Project Ranking Project Cost NPW/Cost 1C $10 0.35 3A $25 0.26 3B $10 0.21 2A $20 0.17 1B $50 0.13 2B $35 0.08 1A $25 0.04 4 $10 -0.03 (e) For a budget of $100 x 10 3 , select: 3A($25) + 2A ($20) + 1B ($50) thus Σ = $95 17-3 (a) Cost to maximize total ohs - no budget limitation Select the most appropriate gift for each of the seven people
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newnansm17 - Chapter 17: Rationing Capital Among Competing...

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