CE167_ Fall_2011_HW4_solutions

# CE167_ Fall_2011_HW4_solutions - CE 167 Engineering and...

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CE 167: Engineering and Project Management Professor William Ibbs Fall 2011 Homework 3: Break Even, Sensitivity, Bonds, Decision Trees 25 Points Due: Sept. 6, 2011 REMEMBER: ALWAYS DRAW YOUR CASH FLOW DIAGRAM 1. [5 Points] Your construction firm is considering investing in a ready-mix concrete plant in order to provide alternative revenue streams, and you wish to know if the plant will be profitable. A plant costs \$4,710,400 in capital investment, and the variable O&M costs are \$40.52 per cubic yard of concrete produced. The current market price for RMC is \$65.00 per cubic yard. If before-tax MARR is 20%, how many yards of concrete must be sold to break-even if the plant will last 20 years and can be scrapped for \$492,600, and graph the results showing the change in cash flows as you sell more or less concrete? What is the undiscounted payback period at the breakeven point? First, find the equivalent annual fixed cost of the investment: A = -4,710,400(A/P, 20%, 20) + 492,600(A/F, 20%, 20) =-4,710,400(0.20536) + 492,600(0.00536) = -\$969,968 Solve Algebraically to find the breakeven point: \$969,968 + \$40.52B = \$65B B = 39,623 yd 3 Net Revenue (annual) = (\$65-\$40.52) * 39,623 = \$969,968 Undiscounted Payback?

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By interpolation ~ 4.85 Years. This is approximately the same as by rule of thumb: Undiscounted Payback ~ 100%/IRR ~ 5 years. If you bring the future salvage value to the present (discounted at 20%), the answer is approximately the same. When considering the undiscounted (simple) payback period, however, this is false, as the metric is supposed to tell you when you recoup funds out of pocket. Since the Salvage value is only received at the end of the project lifespan, you shouldn’t discount it to the beginning of the cash flow when calculating the undiscounted payback period. 2. [5 points] Caltrans is studying the construction of a new freeway lane to decrease congestion highway 880 in the Oakland to Hayward corridor. The anticipated capital costs of construction are \$475 million including any necessary land acquisitions, and continuing O&M activities are expected to cost \$2.5 million each year after the 5 year construction
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## This note was uploaded on 01/06/2012 for the course CIVIL AND 167 taught by Professor Ibbs during the Fall '11 term at Berkeley.

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CE167_ Fall_2011_HW4_solutions - CE 167 Engineering and...

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