Please help me understand this problem. I have tried working through it but I am
ID: 2518895 • Letter: P
Question
Please help me understand this problem. I have tried working through it but I am not sure my answer is correct. Please show all work and explain if possible. Thanks
Consider the following projects: Project A Poject B Initial investment: $120,000 Annual savings: S39,000 Lifetime: 4 Initial investment: $150,000 Annual savings: S35,000 Lifetime: 6 Assuming that your MAAR is 10%, which project would you recommend and why? 1 | 1.10000000 | 0.90909091 I 1.00000000 | 1.00000000 | 0.90909091 | 1.10000000 21.21000000 0.82644628 2.10000000 0.47619048 .73553719 0.57619048 31.33100000 0.75131480 3.310000000.30211480 2.48685199 0.40211480 41.46410000 0.68301346 4.64100000 0.21547030 3.16986545 0.31547080 51.61051000 0.62092132 6.10510000 0.16379748 3.79078677 0.26379748 6 1.77156100 0.56447393 7.71561000 0.129607384.35526070 0.22960738 71.948717100.51315812 9.48717100 0.10540550 4.86841882 0.20540550 8 2.143588810.46650738 11.43588810 0.08744402 5.33492620 0.18744402 92.357947690.42409762 13.5794769 0.07364054 5.75902382 0.17364054 10 2.59374246 0.38554329 15.93742460 0.062745396.1445671 0.16274539 11| 2.85311671 | 0.35049390 | 18.53116706| 0.05396314 | ?.49506101 | 0.15396314 12| 3.13842838 | 0.31863082 | 21.38428377| 0.04676332 | ?.81369182 | 0.14676332 13 3.45227121 0.28966438 24.52271214 0.04077852 7.10335620 0.14077852 14 3.797498340.26333125 27.97498336 0.03574622 7.36668746 0.13574622 15 4.17724817 0.23939205 31.77248169 0.03147378 7.60607951 0.13147378 16 4.594972990.21762914 35.94972986 0.02781662 7.823708640.12781662 175.05447028 0.19784467 40.54470285 0.02466413 8.02155331 0.12466413 18 5.5599173 0.1798587945.59917313 0.02193022 8.20141210 0.12193022 19 6.115909040.16350799 51.5909045 0.01954687 8.364920090.1195468 20 6.727499950.14864363 57.27499949 0.01745962 8.51356372 0.11745962 O A. Project A because NPV- $3,625 B. Project B because AEW-$1,201 O C. Project B because NPV S3,823 O D. Project A because AEW $1,143Explanation / Answer
A:
Present value of inflows=$39000*Present value of annuity factor(10%,4)
=$39000*3.16986545
=$123624.75
NPV=Present value of inflows-Present value of inflows outflows
=$123624.75-$120000
=$3625(Approx).
Equivalent annual annuity=[(rate*NPV)]/[1-(1+rate)^-time period]
=(0.1*3625)/[1-(1.1)^-4]
=(362.5/0.316986544)
=$1143(Approx).
B:
Present value of inflows=$35000*Present value of annuity factor(10%,6)
=$35000*4.35526070
=$152434.12
NPV=Present value of inflows-Present value of inflows outflows
=$152434.12-$150000
=$2434(Approx).
Equivalent annual annuity=[(2434*0.1)]/(1-(1.1)^-6]
=(243.4/0.435526069)
=$558.86(Approx)
Hence A must be preferred having higher equivalent annuity (since projects are of unequal lives;equivalent annual worth needs to be computed).
Hence the correct option is D.