Question

8-14 A The following four mutually exclusive alternatives have no salvage value after 10 years. A B C D First cost $7500 $5000 $5000 $8500 Uniform annual benefit 1600 1200 1000 1700 Computed rate of return 16.8% 20.2% 15.1% 15.1% (a) Construct a choice table for interest rates from 0% to 100%. (b) Using 8% for the MARR, which alternative should be selected?

Answer 1

8-14.

b.

Alternative A

Particulars	Year	CF	Discount @ 8%	Discounted CF
Initial Cost	0	-$7500	1	-$7500
Annual Benefit	1-10	$1600	6.709	$10734.4
Net Present Value				$3234.4

Alternative B

Particulars	Year	CF	Discount @ 8%	Discounted CF
Initial Cost	0	-$5000	1	-$5000
Annual Benefit	1 - 10	$1200	6.709	$8050.8
Net Present Value				$3050.8

Alternative C

Particulars	Year	CF	Discount @ 8%	Discounted CF
Initial Cost	0	-$5000	1	-$5000
Annual Benefit	1 - 10	$1000	6.709	$6709
Net Present Value				$1709

Alternative D

Particulars	Year	CF	Discount @ 8%	Discounted CF
Initial Cost	0	-$8500	1	-$8500
Annual Benefit	1 - 10	$1700	6.709	$11405.3
Net Present Value				$2905.3

As we can see from above tables, Net Present Value of Alternative A is the highest. Therefore, alternative A should be selected.

9-59.

Alternative A

Year	CF	Discount @ 14%	Discounted CF	Cumulative CF
0	-$15000	1	-$15000
1	$5000	0.877	$4385	$4385
2	$5000	0.769	$3845	$8230
3	$5000	0.675	$3375	$11605
4	$5000	0.592	$2960	$14565
5	$5000	0.519	$2595	$17160

As we can see from the above table, Initial cost doesn't get recovered till the 5th year. Payback period lies between year 4th and 5th.

Alternative B

Year	CF	Discount @ 14%	Discounted CF	Cumulative CF
0	-$18000	1	-$18000
1	$6500	0.877	$5700.5	$5700.5
2	$6500	0.769	$4998.5	$10699
3	$6500	0.675	$4387.5	$15086.5
4	$6500	0.592	$3848	$18934.5
5	$6500	0.519	$3373.5	$22308

As we can see from the above table, Initial cost gets recovered by the 4th year. Payback period lies between 3rd and 4th year.

Therefore, alternative B should be selected because the payback period is less than alternative A.