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```					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

```
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