Chapter 10
Problem 5 (chapter 9) Find NPV, IRR, Payback and Profitability Index using 7 year MACRS depreciation.
Net Invest 1 2 3 4 5 6 7
rev(sav) 15000 15000 15000 15000 15000 15000 15000
less exp 0 0 0 0 0 0 0
less dep 14290 24490 17490 12490 8930 8920 8930
EBT 710 -9490 -2490 2510 6070 6080 6070
less tax 284 -3796 -996 1004 2428 2432 2428
EAT 426 -5694 -1494 1506 3642 3648 3642
plus dep 14290 24490 17490 12490 8930 8920 8930
NCF -100000 14716 18796 15996 13996 12572 12568 12572
PV(ncf) $90,181 $13,378 $15,534 $12,018 $9,559 $7,806 $7,094 $6,451
Using the calculator, find the PV of the cash flows by entering the NCF as FV, 10%=i, n=year, and then compute for PV.
Depreciation Schedule
deprec 14290 24490 17490 12490 8930 8920 8930
year 1 2 3 4 5 6 7
percent 0.1429 0.2449 0.1749 0.1249 0.0893 0.0892 0.0893
basis 100000
NPV ($9,819)
IRR 7.66%
Net Present Value
PV(c.f.) $90,181
minus Net Invest -100000
equals NPV ($9,819)
To find IRR using the trial and error method, find % that makes NPV equal to 0.
year 1 2 3 4 5 6 7
pv $98,469 $13,626 $16,115 $12,698 $10,287 $8,556 $7,920 $7,336
for example change 10% to 8% in row 37 and notice the NPV ($1531) is closer to zero..
Net Present Value
PV(c.f.) $98,469
minus Net Invest -100000
equals NPV ($1,531)
Change it to 7% and see what happens.
Profitability Index = PV(cash flows) / Net Invest = $0.90
Payback: accumulate the NCF until you get the net investment back.
year NCF cum
1 14716 14716
2 18796 33512
3 15996 49508
4 13996 63504
5 12572 76076
6 12568 88644
7 12572 101216
8 10784 112000
9 9000 121000
10 9000 130000
11 9000 139000
12 9000 148000
Payback is between 6 and 7 years. Interpolate to find the exact number of years to nearest tenth.
11356 is needed to reach 100000 after year six, this is 11356/12572 or 0.903277
therefore the payback is 6.9 years
ACRS depreciation.
8 9 10 11 12
15000 15000 15000 15000 15000
0 0 0 0 0
4460 0 0 0 0
10540 15000 15000 15000 15000
4216 6000 6000 6000 6000
6324 9000 9000 9000 9000
4460 0 0 0 0
10784 9000 9000 9000 9000
$5,031 $3,817 $3,470 $3,154 $2,868
and then compute for PV.
4460 0 0 0 0
8 9 10 11 12
0.0446 0 0 0 0
8 9 10 11 12
$5,826 $4,502 $4,169 $3,860 $3,574
years