Consider the following two mutually exclusive alternatives for reclaiming a dete
ID: 1106408 • 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 27.17% a. If MARR is 12% per year, which alternative is better? b. What is the IRR on the incremental cash flow [ie., (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 a. The PW of the alternative X is $. (Round to the nearest hundreds.)Explanation / Answer
A.
R = 12%
Net present value of alternative X = 45000/1.12 + 51000/1.12^2 + 78313/1.12^3 – 105000
Net present value of alternative X = $31577.11
Net present value of alternative Y = 215945/1.12^3 – 105000
Net present value of alternative Y = $48705.39
Since, NPV is relatively higher with alternative Y, hence alternative Y should be accepted.
B.
Incremental initial investment = 105000 – 105000 = $0
Incremental Cash inflow in year 1 = - $45000
Incremental Cash inflow in year 2 = - $51000
Incremental Cash inflow in year 3 = 215945-78313 = $137632
Let, IRR = R
Then,
0 = -45000/(1+R) -51000/(1+R)^2 + 137632/(1+R)^3
At R = 27%
PV of incremental cash inflows = $137.43
At R = 28%
PV of incremental cash inflows = -$656.13
As per the method of interpolation,
R = 27% + ((137.43-0)/( 137.43-(-656.13)))*(28%-27%)
R = 27.17%
Hence, the IRR of the incremental cash flows is also 27.17%.
C.
If R = 27.5%
Net present value of alternative X = 45000/1.275 + 51000/1.275^2 + 78313/1.275^3 – 105000
Net present value of alternative X = -$549.74
Net present value of alternative Y = 215945/1.275^3 – 105000
Net present value of alternative Y = -$813.22
Since both the alternatives give negative NPV, hence no alternatives should be selected.
D.
For alternative X
Simple payback period = 45000 in year 1 + 51000 in year 2 + 9000 in year 3
Simple payback period = 2 years + 9000/78313
Simple payback period = 2.115 years
For Alternative Y
Simple payback period = year 1+ year 2 + 105000/215945 years
Simple payback period = 2+ .486 = 2.486 years
E.
Since payback period of alternative X is less, hence alternative X should be selected.