Question

Consider the after-tax cash flows shown in the table below. Click the icon to view the cash flows for the projects. Click the icon to view the interest factors for discrete compounding when i = 8% per year. (a) Compute the project balances for Projects A and D, as a function of project year, at i = 8%. Fill in the table below. (Round to the nearest dollar.) Project Balances А D n 0 $ $ 1 $ 2 $ $ 3 $ $ 4 $ $ 5 $ SI 6 $ SI 7 $ S 8 (b) Compute the future worth values for Projects A and D at i = 8% at the end of service life. The future worth value for Project A is $ (Round to the nearest dollar.) The future worth value for Project D is $ (Round to the nearest dollar.)

Answer 1

a) Here, i+1 = 1+0.08 = 1.08

n	Project Balance of A	Project Balance of D
0	-3000	-6,000
1	-3000(1.08)1+750 = -2490	-6000(1.08)1-600 = -7080
2	-2490(1.08)1 + 750 = -1939	-7080(1.08)1-600 = -8246
3	-1939(1.08)1+750 = -1344	-8246(1.08)1+5000 = -3906
4	-1344(1.08)1+700 = -752	-3906(1.08)1+4000 = 218
5	-702(1.08)1+700 = -58	218(1.08)1+4000 = 4235
6	-58(1.08)1+700 = 637	4235(1.08)1+3000 = 7574
7	637(1.08)1+350 = 1038	7574(1.08)1+4000 = 12,180
8	1038(1.08)1+350 = 1471

b) Future worth of project A:

FW = -3000(F/P,8%,8) +750(P/A,8%,3)(F/P,8%,8) + 700(P/A,8%,3)(F/P,8%,8) + 350(F/A,8%,2)

= -3000 * 1.851 +750 * 2.577 * 1.851 + 700 * 2.577 * 1.851 +350 * 2.080

= -5553 + 3577.5 + 3339 + 728

FW of A = 2091.5 = $2092

Future worth of Project D:

FW = -6,000(F/P,8%,7) -600(P/A,8%,2)(F/P,8%,7) +5000(P/A,8%,1)(F/P,8%,7)+4000(P/A,8%,2)(F/P,8%,7) +3000(P/A,8%,1)(F/P,8%,7) +4000(P/A,8%,1)(F/P,8%,7)

= -6000*1.714 -600*1.783*1.714 + 5000*0.926*1.714 + 4000 *1.783*1.714 + 3000*0.926*1.714 +4000*0.926*1.714

= -10,284 - 1833.6 + 7935.8 + 12224.2 + 4761.4 + 6348.6

FW of D = 19,152.4 = $19,152

c) PW of project B:

-7,300 -3000(P/A,8%,1)-2500(P/A,8%,1)-2000(P/A,8%,4)-2800(P/A,8%,2)

= -7,300 - 3000*0.926 - 2500 *0.926 - 2000 * 3.312 - 2800 *1.783

= -7300 - 2778 - 2315 - 6624 - 4992.4 = - $24,009.

PW of project C:

= -6000 - 2500(P/A,8%,7) -2800(P/A,8%,1)

= -6000 - 2500 * 5.206 -2800*0.926

= -6000 - 13015 - 2592.8

= -21,607.8 = -$21,608

So, as both the PW are negative, it implies that both are costs. So, the lower cost is preferred. So, project C will be the better choice as $21,608 < $24,009.