Consider the following two mutually exclusive alternatives for reclaiming a dete
ID: 1105060 • Letter: C
Question
Consider the following two mutually exclusive alternatives for reclaiming a deteriorating inner-city neighborhood one of them must b a. If MARR is 15% 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? chosen . Notice that the IRR for both alternatives is 27.17%. Click the icon to view the alternatives description. Click the icon to view the interest and annuity table for discrete compounding when ,-15% per year. i Data Table Discrete Compounding: 15% Uniform Series Alternative und Sinking Capital Recovery Factor To Find A Given P Compound Amount Amount - $105,000$105,000 Factor Worth Factor Factor Worth Factor Factor To Find P Given F To Find A Given F To Find P To FindF Given P To Find F Given A $215,945 27.17% 0.8696 1.6257 2.2832 2.8550 0.7561 0.6575 1.3225 3.4725 4.9934 6.7424 8.7537 0.2880 0.2003 0.1483 PrintDone 2.3131 3.7845 0.2642 0.4323 0.3269 0.2472 13.7268 16.7858 20.3037 24.3493 0.0729 0.0596 0.0493 0.1993 5.2337 5.4206 0.2149 5.3503 34.3519 40.5047 47.5804 5.7245 5.8474 0.0247 0.1747 0.1710 7.0757 one Enter your answer in the answer box and then click CExplanation / Answer
ANSWER:
A) IN ORDER TO FIND WHICH ALTERNATIVE IS BETTER AT 15% WE WILL FIND THE PW OF WACH ALTERNATIVE.
PW OF ALTERNATIVE X = -105,000 + 50,000(P/F,15%,1) + 49,000(P/F,15%,2) + 72,771(P/F,15%,3) = -105,000 + 50,000 * 0.8696 + 49,000 * 0.7561 + 72,771 * 0.6575 = -105,000 + 43,480 + 37,048.9 + 47,846.9325 = 23,375.832
PW OF ALTERNATIVE Y = -105,000 + 215,945(P/F,15%,3) = -105,000 + 215,945 * 0.6575 = -105,000 + 69,037.5 = -35,962.5
SINCE THE PW OF ALTERNATIVE X IS MORE THEN THE PW OF ALTERNATIVE Y THEREFORE AT A MARR OF 15% WE CHOOSE ALTERNATIVE X.
B) FOR FINDING THE IRR WE WILL HAVE TO PUT PW EQUAL TO ZERO.
PW (Y -X ) = ( -105,000 - ( -105,000) + ( 0 - 50,000) + ( 0 - 49,000) + (215,945 - 72,771) = 0 - 50,000(P/F,I%,1) - 49,000(P/F,I%,2) + 143,174(P/F,I%,3) = 0
143,174(P/F,I%,3) = 50,000(P/F,I%,1) + 49,000(P/F,I%,2)
SOLVING FOR VARIOUS VALUES OF I WE GET
I = 27.17%
SINCE THE IRR IS SAME FOR BOTH THE ALTERNATIVES THEREFORE THE INCREMENTAL IRR WILL BE SAME AND I HAVE ALSO SOLVED VIA SOLVING FOR VARIOUS VALUES.
C) AT MARR OF 27.5%
SINCE THE VALUES OF 27.5% AREN'T AVAILABLE I HAVE SOLVED IN EXCEL.
THE FORMULA FOR FINDING PW IN EXCEL IS =NPV(27.5%,ALL THE CASH FLOWS FROM YEAR 1 TO 3) + CASH FLOW OF YEAR 0.
SINCE THE PW OF ALTERNATIVE X IS MORE THEREFORE WE CHOOSE ALTERNATIVE X.
-532 > -813
D) BALANCE AND PAYBACK PERIOD HAVE BEEN CALCULATED IN THE EXCEL AS THE CALCULATIONS ARE LENGTHY.
WE FIND THE BALANCE OF THE YEAR BY ADDING THE CASH FLOWS OF THE YEAR TO THE BALANCE OF PREVIOUS YEAR AND WITH YEAR 0 BALANCE AS THE SAME AS YEAR 0 CASH FLOWS.
WE FIND THE PAYBACK PERIOD AS THE PREVIOUS YEAR AFTER WHICH THE CASH FLOW TURNED POSITIVE + ( BALANCE OF PREVIOUS YEAR / DIVIDED BY THE CASH FLOW OF THE YEAR IN WHICH THE BALANCE TURNED POSITIVE).
SO THE PAYBACK PERIOD FOR ALTERNATIVE X IS 2.082 YEARS WHILE FOR ALTERNATIVE Y IT IS 2.486 YEARS.
E) IF WE LOOK AT THE SIMPLE PAYBACK PERIOD THEN WE WILL CHOOSE ALTERNATIVE X AS THE PAYBACK PERIOD OF X IS LESS THEN THE PAYBACK PERIOD OF Y THAT IS WE RECOVER OUR INVESTMENT EARLIER IN ALTERNATIVE X.
ALTERNATIVE X YEAR 0 1 2 3 CASH FLOWS -105,000 50000 49,000 72771 PW -532.3065789176 ALTERNATIVE Y YEAR 0 1 2 3 CASH FLOWS -105,000 0 0 215945 PW -813.2241747141