20k at time zero and 15 of sales the after year nwc

(20k at time zero and 15% of sales the after)
Year NWC Change NWC Change capital Spending
0. 20K 20k 800k
1. 54K 34k
2. 90K 36k
3. 108K 18k
4. 107.25K -.75k
5. 99K -8.25k
6. 82.5K -16.5k
7. 66K -16.5k
8. 49.5k -16.5k -49.5
release of working capital
6

Salvage: .2*$800k=$160k(1-T)=$160k(1-.34)=105.6k. Note we pay tax on the whole amount
because we have depreciated the asset to zero, so to the IRS the $160k is a pure profit.
Cash flows from project:
Years OCF - Change NWC -Change Cap Spend =
0. 0 20k 800k -820,000
1. 141,169 34k 107,169
2. 248,113 36k 212,113
3. 268,673 18k 250,673
4. 231,973 -.75k 232,723
5. 205,790 -8.25k 214,040
6. 172,790 -16.5k 189,290
7. 139,790 -16.5k 156,290
8. 94,604 -16.5+-49.5k -105,600 266,204
[email protected]%= 65,488.8 =>Accept; IRR=17.236%, again Accept.
OCF can obviously increase for two reasons:
1. Sales increase from new project. OCF = (S-C)(1-T) + Dep.*T
2. Cost decreases.
Cost Reduction Example :
$100,000 machine with 12-year depreciable life, use straight line. The discount rate is 11%. The
machine will reduce cost by $11,000/year and increases current expenditures by $1000/yr. The
tax rate is 25%. Also there is one other machine that has depreciation of $20,000/yr, no salvage
value.
DEP= 100,000/12=8,333.33
OCF= (Rev.-Cost)(1-T) + DEP(T)
= (11,000-1000)(1-.25)+ 8,333.33(.25)
= 7500+2083.33= 9583.33
CF0 -$100k, CF1-12: $9583.33 Required return= 11%, NPV= -$37,781.61, IRR= 2.219 or
2.22%, so REJECT.
CF
Let’s change this problem:
Assume that you have the same cash flows described above, but now unexpectedly the project
ends you must sell the machine in the 6 th year for $70,000. How does this change the problem
and what is the salvage value?
7

sell the machine in year 6, you now will no longer receive cash flows from year 7-12, but you do
get the salvage value in the 6 th year.
So in year 6 we have accumulated depreciation of 6*8,333.33= 49,999.98 or $50k, so this means
that we have told the IRS that the machine is worth $100k-$50k= $50k. So salvage is 70k-(70k-
50k)(.25)= 65k because we have to pay taxes in the 20k profit. This means our cash flows are:
CF0: -$100k, CF1-CF5: $9583.33+$65,000. Find NPV now: -$24,705.71.
Let’s Change this again:
$100,000 machine with 6-year life and 5 year MACRS depreciable life, use MACRS. The
discount rate is 6%. The machine will reduce cost by $11,000/year and increases current
expenditures by $1000/yr. The tax rate is 25%. Also there is one other machine that has
depreciation of $20,000/yr, no salvage value.
Depreciation
Yr Cost * Schedule = DEP
1 $100,000 .2 $20,000
2 $100,000 .32 $32,000
3 $100,000 .192 $19,200
4 $100,000 .1152 $11,520
5 $100,000 .1152 $11,520
6 $100,000 .0576 $5,760
Now putting together the OCFs:
OCF
0
= =-$100,000
OCF
1
= (11000-1000)*(1-.25) + 20000*.25=$12,500
OCF
2
= (11000-1000)*(1-.25) + 32000*.25=$15,500
OCF
3
= (11000-1000)*(1-.25) + 19200*.25=$12,300
OCF
4
= (11000-1000)*(1-.25) + 11520*.25=$10,380
OCF
5
= (11000-1000)*(1-.25) + 11520*.25=$10,380
OCF
6
= (11000-1000)*(1-.25) + 5760*.25=$8,940
Then entering all these in the cash flow keys and i=6% we get:
NPV= -$41,804, REJECT; IRR= -9.97, again REJECT
Unequal Lives of Projects
So far we have considered projects with equal lives. Now let’s look at unequal lives. NPV
depends on the length of the life of the project. This doesn't matter for independent projects but
for mutually exclusive projects it does.
Say we have 2 mutually exclusive projects of 2 machines with the same function. Machine 1 has
a 5yr life, machine 2 has a 10yr life. If we used the same discount rate (which we should) then
we could calculate the NPV's of both projects. Let’s say NPV1<NPV2.