Consider the following two mutually exclusive alternatives for reclaiming a dete
ID: 2564780 • Letter: C
Question
Consider the following two mutually exclusive alternatives for reclaiming a deteriorating inner city neighborhood one of them must be chosen . Notice that the IRR for both alternatives is 27.15%. a. If MARR is 12% per year, which alternative is better? b. What is the IRR on the incremental cash flow (i.e., (Y-X))? c. If the MARR is 27.5% per year, which alternative is better? d. What is the simple payback period for each alternative? e. Which alternative would you recommend? Click the icon to view the alternatives description. Click the icon to view the interest and annuity table for discrete compounding when i-12% per year More Info Discrete Compounding: 12% Alternative Single Payment Uniform Series EOY Compound Amount Factor To FindF GiveN A Sinking Fund Factor To Find A Given F Capital Recovery Factor To Find A Given F Compound Amount Present Present Worth Factor To FindP Given A - $105,000 -$105,000 Factor Worth Factor $45,000 $53,000 $75,702 To FindF To Find P Given F P/F 0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523 0.4039 50 $215,843 Given IRR 1.1200 1.2544 1.4049 1.5735 1.7623 1.9738 2.2107 2.4760 2.7731 3.1058 3.4785 3.8960 4.3635 4.8871 5.4736 1.1200 0.5917 0.8929 2.1200 3.3744 4.7793 6.3528 8.1152 10.0890 12.2997 14.7757 17.5487 20.6546 24.1331 28.0291 32.3926 37.2797 0.4717 0.2963 0.2092 1574 0.1232 0.0991 0.0813 0.0677 0.0570 Done 4 3.0373 4.1114 4.5638 4.9676 5.3282 5.6502 5.9377 6.1944 6.4235 6.6282 6.8109 0.3292 0.2774 0.2432 0.2191 0.2013 0.1877 0.1770 0.1684 1614 0.1557 0.1509 0.1468 6 0.3220 0.2875 0.2567 0.2292 0.2046 0.1827 0.0414 0.0357 0.0309 0.0268 12 ri ne Enter vour answer in the answer box and then clickExplanation / Answer
a) Step 1 : For finding which alternative is better, we should compare the net present values of both the alternatives.
Calculation of Present Value of net cash inflows (Amount in $)
PVF@12%
(i)
Cash Inflows (X)
(ii)
Cash Inflows (Y)
(iii)
PV of Cash inflows (X)
(iv) = (i)*(ii)
PV of Cash inflows (Y)
(v) = (i)*(iii)
From the above analysis, it can be concluded that Alternative Y is better than alternative X as NPV of Alternative Y is greater than Alternative X.
b) IRR is the discount rate at which NPV is Zero. For calculating IRR on Incremental cash flow, we have to calculate incremental cash flows, then we have to assume two discount rates, one higher and one lower rate. (Amount in $)
IRR = Lower Rate + [(NPV at lower rate)*(Higher rate - Lower rate)/(NPV at lower rate - NPV at Higher rate)]
10% + (20,579)*(20%-10%)/(20,579 - 6,798) = 12.99% (i.e.13% approx.)
c) If MARR is 27.5% per year, then NPV of both alternatives will be negative as the MARR(27.5%) exceeds the IRR of 27.15%. Therefore no alternative is recommended due to negative net present value.
d) Simple payback period for each alternative are calculated as follows :- (Amount in $)
Payback Period (X) = 2years + 7,000/75,702 = 2.09 years
Payback Period (Y) = 3 years
e) Based on Payback period of both alternatives, Alternative X is better as its payback period is less than payback period of Alternative Y.
YearPVF@12%
(i)
Cash Inflows (X)
(ii)
Cash Inflows (Y)
(iii)
PV of Cash inflows (X)
(iv) = (i)*(ii)
PV of Cash inflows (Y)
(v) = (i)*(iii)
1 0.8929 45,000 0 40,181 0 2 07972 53,000 0 42,252 0 3 0.7118 75,702 215,843 53,885 153,637 Total 136,318 153,637 Cash Outflow (105,000) (105,000) Net Present Value 31,318 48,637