Question

Problem 12-12 (algorithmic) Question Help The tree diagram in figure below describes the uncertain cash flows for an engineering project. The analysis period is two years, and MARR = 12% per year. Based on this information, a. What are the E(PW), V(PW), and SD(PW) of the project? b. What is the probability that PW20? WClick the icon to view the tree diagram. Click the icon to view the interest and annuity table for discrete compounding when the MARR is 12% per year. Time Period 1 2 $17,200 0.2 $5,500 0.1 $19,700 0.7 $24,200 0.1 $21,100 0.1 - $32,000 $12,000 0.7 0.7 $24,900 0.2 $29,700 0.2 $22,000 0.2 $19,500 0.3 $26,300 0.5 $31,800 Discrete Compounding; i 12% Single Payment Uniform Series Compound Amount Compound Amount Sinking Capital Recovery Present Present Fund Worth Factor Worth Factor Factor Factor Factor Factor To Find A To Find F To Find P To Find F To Find P To Find A Given A Given P Given F Given A Given F Given P P/F N F/P F/A PIA A/F A/P 0.8929 0.8929 1.1200 1.0000 1.0000 1.1200 1 2 1.2544 0.7972 2.1200 1.6901 0.4717 0.5917 3.3744 3 1.4049 0.7118 2.4018 0.2963 0.4163 4 0.6355 4.7793 3.0373 1.5735 0.2092 0.3292 5 3.6048 1.7623 0.5674 6.3528 0.1574 0.2774 -N

Answer 1

In this given problem we have 9 possible Present worth

Lets calculate each individually

1) NPW=-32000+5500/1.12+17200/1.12^2=-13377.55 with Probability (0.1*0.2=0.02)
2) NPW=-32000+5500/1.12+19700/1.12^2=-11284.55 with Probability (0.1*0.1=0.01)
3) NPW=-32000+5500/1.12+24200/1.12^2=-7797.19 with Probability (0.1*0.7=0.07)
4) NPW=-32000+12000/1.12+21100/1.12^2=-4464.92 with Probability (0.7*0.1=0.07)
5) NPW=-32000+12000/1.12+24900/1.12^2=-1435.59 with Probability (0.7*0.7=0.49)
6) NPW=-32000+12000/1.12+29700/1.12^2=2390.94 with Probability (0.7*0.2=0.14)
7) NPW=-32000+19500/1.12+22000/1.12^2=2948.98 with Probability (0.2*0.2=0.04)
8) NPW=-32000+19500/1.12+26300/1.12^2=6376.91 with Probability (0.2*0.3=0.06)
9) NPW=-32000+19500/1.12+31800/1.12^2=10761.48 with Probability (0.5*0.2=0.1)

E(PW)= Sum product of Each outcome*probability
=0.02*(-13377.55)+0.01*(-11284.55)+0.07*(-7797.19)+0.07*(-4464.92)+0.49*(-1435.59)+0.14*(2390.94)+0.04*(2948.98)+0.06*(6376.91)+0.01*(10761.48)=-999.263

E(PW)=-999.26

V(PW)=0.02*(-13377.55^2)+0.01*(-11284.55^2)+0.07*(-7797.19^2)+0.07*(-4464.92^2)+0.49*(-1435.59^2)+0.14*(2390.94^2)+0.04*(2948.98^2)+0.06*(6376.91^2)+0.01*(10761.48^2)

V(PW)=16259831.36

SD(PW)=4032.35

Ans B)

Probability (PW>=0)=0.14+0.04+0.06+0.1=34%