ESD.71 - Engineering System Analysis for DesignSolutions to Problem Set 2a) Since concrete and asphalt road beds have different life spans, they cannot becompared over one life span each. They can be considered over multiple lifespans, repeating the projects until a common multiple of years is reached.Practically, this can be done by finding close multiples around 30 or more years,since the present values of sums further in the future are insignificant. Thecalculations may be quickly performed by considering the difference between thetwo cash flows. Choosing 3 life spans for asphalt and 2 for concrete (51 and 54years respectively) gives sufficiently close projects lives.Figure 1 gives the cash flow of the costs and savings of initially choosing concrete overasphalt, in terms of dollars per square yard. The initial extra cost of the concrete is $21 -$17.8 = $3.2. Note that by focusing on the incremental difference of one alternative over theother, rather than on each separately, there are fewer and simpler calculations.$17.8/yd2$17.8/yd2 $17.8/yd2027 _ 5417 34 51 Years -$3.2/yd2 -$17.8/yd2 -$17.8/yd2Figure 125451342717/37.0$1.18.171.18.171.18.171.18.171.18.172.3)__(ydasphaltoverconcreteNPVFor concrete to be as inexpensive as asphalt, the cost of concrete must be reduced by $0.37 per square yard. At $20.63 per square yard, NPV=0, and both materials have equivalent costs over time.b) The costs are equal at r = 9.2%c) If the national government pays one half of the initial cost of the road:NPV = -0.37 + 3.2/2 = $1.23/yd2So choose concrete.If the discount rate is 6%, NPV = $2.03/ yd2 So choose concrete.An important observation at the outset is that the four alternatives available to your friendbear similar risk. Even lending to another entrepreneur is stated to be guaranteed to return$30,000 in 5 years. On this premise, the returns from the 4 alternatives are comparable. Ifthe four alternatives did not bear the same risk, a direct comparison would not have been possible since investments of higher risk generally have higher returns. This is implied in ASA p. 229: “the discount rate should be the lowest acceptable rate of return to any investor.”All r1, r2, r3, r4 here are net of inflation, if we think with inflation, just add 4% to all these rates.1. To assess the investment on building insulation requires that your friend picks an appropriate time horizon as well. Say this is infinite. Then the return of this investment is found by equalizing $40,000 with a perpetuity of (5600)gal/yr ($1)/gal = $5,600 $/year:115,60040, 000 0 0.14 14%- = � = =rrAs calculated above, the return on the first alternative does not include inflation. 2. The second alternative has a return of 12% with inflation, so %82r.3.%12%4120000$3200$3r4. As for 4r, it can be determined from454130,000 (2)(30,000) 0 14.9%(1 )- + = � =+rrSince the 60,000 received in 5 years from now are inflated, the ex-inflation 4' 14.9% 4% 10.9% 11%= - = �rTherefore, if your friend’s budget is only $20,000 the discount rate at which investment opportunities of this risk should be valued is 14%, since he/she can use additional money to insulate the building. If the budget is $60,000, then we can assume your friend will use the first $40,000 for thebuilding and the next $20,000 (<$80,000) for pay for the annuity. So the discount rate
View Full Document
Unlocking...