Midwest Power and Light operates 14 coal-fi red power plants in several states a
ID: 1208183 • Letter: M
Question
Midwest Power and Light operates 14 coal-fi red power plants in several states around the United States. The company recently settled a lawsuit by agreeing to pay $60 million in mitigation costs related to acid rain. The settlement included $21 million to reduce emissions from barges and trucks in the Ohio River Valley, $24 million for projects to conserve energy and produce alternative energy, $3 million for Chesapeake Bay, $2 million for Shenandoah National Park, and $10 million to acquire ecologically sensitive lands in Appalachia. The question of how to distribute the money over time has been posed. Plan A involves spending $5 million now and the remaining $55 million equally over a 10-year period (that is, $5.5 million in each of years 1 through 10). Plan B requires expenditures of $5 million now, $25 million 2 years from now, and $30 million 7 years from now. Determine which plan is more economical on the basis of a present worth analysis over a 10-year period at an interest rate of 10% per year.Explanation / Answer
FOR PLAN A WE WILL FIND OUT THE PRESENT VALUE OF MONEY TO SPENT. WE WILL MAKE USE OF THE PRESENT VALUE TABLE TO FIND OUT THE PV FACTOR FOR EACH YEAR @10%.
PLAN A $ 5000000 IMMEDIATELY. NOW WE WILL CALCULATE THE VALUE OF 5.5 MILLION FOR NEXT 10 YEARS WITH HELP OF PV FACTORS AND MULTIPLYING THEM.
YEAR AMOUNT PV FACTOR * PRESENT VALUE
1 5500000 0.9091 5000050
2 5500000 0.8264 4545200
3 5500000 0.7513 4132150
4 5500000 0.6830 3756500
5 5500000 0.6209 3414950
6 5500000 0.5645 3104750
7 5500000 0.5132 2822600
8 5500000 0.4665 2565750
9 5500000 0.4241 2332550
10 5500000 0.3855 2120250
TOTAL PRESENT VALUE WILL BE 5000000 + 5000050 + 4545200 + 4132150 + 3756500 + 3414950 + 3104750 + 2822600 + 2565750 + 2332550 + 2120250 = 38794750
PLAN B
5 MILLION NOW THEN AFTER 2 YEARS 25000000 @10%, THE PV FACTOR WILL BE 0.8264, AND 30000000 MILLION AFTER 7 YEARS @10% THE PV FACTOR WILL BE 0.5132.
25000000 * 0.8264 = 20660000
30000000 * 0.5132 = 15396000
= 5000000 + 20660000 + 15396000 = 41056000
SO WE SEE THAT THE PRESENT WORTH OF PLAN A IS 38794750 AND THE PRESENT WORTH OF PLAN B IS 41056000. HENCE PLAN A IS BETTER BECAUSE IT IS MORE ECONOMICAL AS COMPARED TO PLAN B.