Net Present Value Question

[dmillionaire]

Hey guys, currently working on a problem and need some second thoughts to see if I am on the right track.

Cost of capital = 15%
GI pays corporate taxes of 35%

Alternative A has initial software development costs
projected at $185,000, while Alternative B would cost $320,000. capital cost allowance (CCA) rate of 30 percent.
In addition, IT would hire a software consultant under either alternative to assist in making
the decision whether to invest in the project for a fee of $16,000 and this cost would be
expensed when it is incurred.

IT department would charge the
production department for the use of computer time at the rate of $375 per hour and
estimates that it would take 182 hours of computer time per year to run the new soft
ware under either alternative. GI owns all its computers and does not currently operate them
at capacity. The information technology (IT) plan calls for this excess capacity
to continue in the future. For security reasons, it is company policy not to rent excess computing capacity to outside users.




Year/ A / B
1 - $82 000 - $112 000
2 - $82 000 - $124 000
3 - $64 000 - $101 000
4 - $53 000 - $93 000
5 - $37 000 - $56 000




1.) Calculate the NPV of each and which would you recommend

2.) The CFO suspects that there is a high risk that new technology will render the
production equipment and this automation software obsolete after only three years.
Which alternative would you now recommend? (Cost savings for Years 1 to 3 would
remain the same.)






MY WORK

So ill just use alternative a as an example but I did:

PV= -185 000
n= 5
i/y= 15

Cfo = -185000
c01 = 82000
c02 = 82000
c03 = 64000
c04 = 53000
c05 = 37000
I = 15

NPV = 39087.63


If that is correct do I just do the same thing for 2.) but just use the first three years?
Thanks!

 

[Ishuda]

Hey guys, currently working on a problem and need some second thoughts to see if I am on the right track.

Cost of capital = 15%
GI pays corporate taxes of 35%

The proposed capital project calls for developing new computer software to facilitate partial
automation of production in GI's plant. Alternative A has initial software development costs
projected at $185,000, while Alternative B would cost $320,000. Software development
costs would be capitalized and qualify for a capital cost allowance (CCA) rate of 30 percent.
In addition, IT would hire a software consultant under either alternative to assist in making
the decision whether to invest in the project for a fee of $16,000 and this cost would be
expensed when it is incurred.

To recover its costs, GI's IT department would charge the
production department for the use of computer time at the rate of $375 per hour and
estimates that it would take 182 hours of computer time per year to run the new soft
ware under either alternative. GI owns all its computers and does not currently operate them
at capacity. The information technology (IT) plan calls for this excess capacity
to continue in the future. For security reasons, it is company policy not to rent excess computing capacity to outside users.




Year a b
1 82000 112000
2 82000 124000
3 64000 101000
4 53000 93000
5 37000 56000




1.) Calculate the NPV of each and which would you recommend

2.) The CFO suspects that there is a high risk that new technology will render the
production equipment and this automation software obsolete after only three years.
Which alternative would you now recommend? (Cost savings for Years 1 to 3 would
remain the same.)






MY WORK

So ill just use alternative a as an example but I did:

PV= -185 000
n= 5
i/y= 15

Cfo = -185000
c01 = 82000
c02 = 82000
c03 = 64000
c04 = 53000
c05 = 37000
I = 15

NPV = 39087.63


If that is correct do I just do the same thing for 2.) but just use the first three years?
Thanks!

That would be the answer if there were no tax benefits [but see Note (1)]. Review how the capital cost allowance (CCA) changes the present value of an investment which will change the Cfo = -185000. The following looks like a good primer on the subject
https://en.wikipedia.org/wiki/Capital_Cost_Allowance

As far as the equipment being obsolete in three years, see Note (2)

Note (1) What you computed was not the total cost of the project even had the present value of the initial investment been used. The fee of $16000 has not been included. But that, and the operating costs, are (assumed) the same for both projects and may be ignored for purposes of computing the best investment value.
Note (2) Nothing has been said about replacing the equipment at some time in the future nor the salvage value of the equipment. This would impact the actual cost and could, if it were replaced at say at the end of year five, you would need to bring the salvage value to a present value and include it in the CCA computations. If the equipment were to become obsolete in three years, what is going to be done and what are the associated costs (and possible income)?

 

[dmillionaire]

That would be the answer if there were no tax benefits [but see Note (1)]. Review how the capital cost allowance (CCA) changes the present value of an investment which will change the Cfo = -185000. The following looks like a good primer on the subject
https://en.wikipedia.org/wiki/Capital_Cost_Allowance

As far as the equipment being obsolete in three years, see Note (2)

Note (1) What you computed was not the total cost of the project even had the present value of the initial investment been used. The fee of $16000 has not been included. But that, and the operating costs, are (assumed) the same for both projects and may be ignored for purposes of computing the best investment value.
Note (2) Nothing has been said about replacing the equipment at some time in the future nor the salvage value of the equipment. This would impact the actual cost and could, if it were replaced at say at the end of year five, you would need to bring the salvage value to a present value and include it in the CCA computations. If the equipment were to become obsolete in three years, what is going to be done and what are the associated costs (and possible income)?

Confused on the tax benefit part, for the $16 000 would you just add that on to the (-185000) to make (-201000) so pv and cfo would change to -201000?

 

[dmillionaire]

Yes, that's correct.
WHY the long boring background story?

haha I dunno, I thought the whole question would help. Do I add the extra $16000 to the PV and Cfo? Which would make it -201000?

Also any thoughts on #2 ?

 

[Ishuda]

Confused on the tax benefit part, for the $16 000 would you just add that on to the (-185000) to make (-201000) so pv and cfo would change to -201000?

Did you review the information for computing the present value of an investment given the information you have? As far as the $16,000, reread my Notes (1) & (2)

 

[dmillionaire]

Did you review the information for computing the present value of an investment given the information you have? As far as the $16,000, reread my Notes (1) & (2)

I looked at the wiki, is there a certain spot exactly too look. By looking at note(1) I ignore the 16000 to find the best investment value and leave it at -185000.
Would I multiply the final npv to the 35% tax and would be the final npv?
Thanks!,

 

[Ishuda]

I looked at the wiki, is there a certain spot exactly too look. By looking at note(1) I ignore the 16000 to find the best investment value and leave it at -185000.
Would I multiply the final npv to the 35% tax and would be the final npv?
Thanks!,

Using the notation in the article,
I = Investment
d = CCA rate per year for tax purposes
t = rate of taxation
n = number of years
i = cost of capital, rate of interest, or minimum rate of return (whichever is most relevant)
and looking under the Full-Year rule
https://en.wikipedia.org/wiki/Capital_Cost_Allowance#Full-year_rule
you find that the net present value of the depreciation is
PV = \(\displaystyle \frac{I\, t\, d}{i\, +\, d}\)
assuming there is no salvage value and the equipment is used 'forever'. You would subtract that from your investment to get the after tax investment present value.

Whether the Full-Year or Half-Year rule should be used is possibly something your should know. There is a table which suggests to me that maybe the Half-Year rule
https://en.wikipedia.org/wiki/Capital_Cost_Allowance#Half-year_rule
should be used

EDIT: It does seem to me though that you just need to compute the depreciation allowance for the 5 years.

 

[dmillionaire]

I thought the cash flow you showed and present-valued correctly
was all you wanted.
You didn't ask that it be checked...

I asked if I was on the right track with the question that I posted. That was the "long back story" you probably skipped over.

 

[dmillionaire]

OK...again, thought you wanted to know if your present value
calculation was correct...hence background not required...my bad;
glad to see that Ishuda s'got you covered!

Im still really confused on the whole tax part and cca, I haven't made it passed the part I've already posted. Any help at all retaining to the question would be very helpful

 

[Ishuda]

Im still really confused on the whole tax part and cca, I haven't made it passed the part I've already posted. Any help at all retaining to the question would be very helpful

Let's use the wiki article symbols
I = $185,000 Investment
d = 0.30 (30%) CCA rate per year for tax purposes
t = 0.35 (35%) rate of taxation
n = 1 through 5 number of years
i = .15 (15%) cost of capital
use the Full-Year rule and assume no salvage value
Future Value of year n depreciation = I d (1-d)^n-1
...For example, the first year is 185000*0.30*0.70⁰ = 55500
Present Value of year n depreciation = I d (1-d)^n-1 / (1+i)ⁿ

Compute PV for n=1, 2, 3, 4, 5; add and you get present value of future tax savings. Subtract than from the investment cost and get the present value of the after tax benefits of your investment.

Note: If we let
x = (1-d)/(1+i)
then each years pv would be
pv(n) = \(\displaystyle \frac{I\, d}{1+i}\, x^{n-1}\)
If we do this for N years then the total is
PV = \(\displaystyle \underset{n=0}{\overset{n=N-1}{\Sigma}}\, pv(n+1)\, =\, \frac{I\, d}{1+i}\, \underset{n=0}{\overset{n=N-1}{\Sigma}}\, x^n\)
which is a geometric series and can be solved in closed form.

 

[dmillionaire]

Let's use the wiki article symbols
I = $185,000 Investment
d = 0.30 (30%) CCA rate per year for tax purposes
t = 0.35 (35%) rate of taxation
n = 1 through 5 number of years
i = .15 (15%) cost of capital
use the Full-Year rule and assume no salvage value
Future Value of year n depreciation = I d (1-d)^n-1
...For example, the first year is 185000*0.30*0.70⁰ = 55500
Present Value of year n depreciation = I d (1-d)^n-1 / (1+i)ⁿ

Compute PV for n=1, 2, 3, 4, 5; add and you get present value of future tax savings. Subtract than from the investment cost and get the present value of the after tax benefits of your investment.

Note: If we let
x = (1-d)/(1+i)
then each years pv would be
pv(n) = \(\displaystyle \frac{I\, d}{1+i}\, x^{n-1}\)
If we do this for N years then the total is
PV = \(\displaystyle \underset{n=0}{\overset{n=N-1}{\Sigma}}\, pv(n+1)\, =\, \frac{I\, d}{1+i}\, \underset{n=0}{\overset{n=N-1}{\Sigma}}\, x^n\)
which is a geometric series and can be solved in closed form.

amazing!! Thank you i really appreciate you going out of your way, I am at work but this is exactly what I needed to continue on with the question when I get home.

 

[dmillionaire]

Let's use the wiki article symbols
I = $185,000 Investment
d = 0.30 (30%) CCA rate per year for tax purposes
t = 0.35 (35%) rate of taxation
n = 1 through 5 number of years
i = .15 (15%) cost of capital
use the Full-Year rule and assume no salvage value
Future Value of year n depreciation = I d (1-d)^n-1
...For example, the first year is 185000*0.30*0.70⁰ = 55500
Present Value of year n depreciation = I d (1-d)^n-1 / (1+i)ⁿ

Compute PV for n=1, 2, 3, 4, 5; add and you get present value of future tax savings. Subtract than from the investment cost and get the present value of the after tax benefits of your investment.

Note: If we let
x = (1-d)/(1+i)
then each years pv would be
pv(n) = \(\displaystyle \frac{I\, d}{1+i}\, x^{n-1}\)
If we do this for N years then the total is
PV = \(\displaystyle \underset{n=0}{\overset{n=N-1}{\Sigma}}\, pv(n+1)\, =\, \frac{I\, d}{1+i}\, \underset{n=0}{\overset{n=N-1}{\Sigma}}\, x^n\)
which is a geometric series and can be solved in closed form.

So what i did was
185000*0.30*0.70⁰ = 55 500
185000*0.30*0.70^1 = 38 850
185000*0.30*0.70^2 = 26 950
185000*0.30*0.70^3 = 18 865
185000*0.30*0.70^4 = 13 205.5

= 152 870.50

= 185 000 - 152 870.50
=32 129.5

I should of mentioned there is a 3rd question , ( I didn't wanna put too much in the question when I was asking ) that is regarding salvage value. So the salvage part will be for that.

That question is:
GI could use excess resources in its Engineering department to develop a way to
eliminate this step of the manufacturing process by the end of year 3. The salvage
value of the equipment (including any CCA and tax impact) would be $50,000 at the
end of Year 3, $35,000 at the end of Year 4, and zero after five years. Should
Engineering develop the solution and remove the equipment before the five years
are up? Which alternative? When?

 

[Ishuda]

So what i did was
185000*0.30*0.70⁰ = 55 500
185000*0.30*0.70^1 = 38 850
185000*0.30*0.70^2 = 26 950
185000*0.30*0.70^3 = 18 865
185000*0.30*0.70^4 = 13 205.5

= 152 870.50

= 185 000 - 152 870.50
=32 129.5

You have computed the actual tax relief for years 1-5 but, like your values in your table for Year/ A / B you have to compute the present value of the tax reliefs.

I should of mentioned there is a 3rd question , ( I didn't wanna put too much in the question when I was asking ) that is regarding salvage value. So the salvage part will be for that.

That question is:
GI could use excess resources in its Engineering department to develop a way to
eliminate this step of the manufacturing process by the end of year 3. The salvage
value of the equipment (including any CCA and tax impact) would be $50,000 at the
end of Year 3, $35,000 at the end of Year 4, and zero after five years. Should
Engineering develop the solution and remove the equipment before the five years
are up? Which alternative? When?

If I am understanding this correctly and since the numbers include any CCA and tax impact (and the other numbers like cost of capital don't change), all you need to do is bring the salvage value up to a present value and include it. If you salvage the equipment in a particular year, you do not get the saving for that year, i.e. if you decide you salvage the equipment in year 4 (the end of year 3), you would need to include the pv of the salvage but would not get the benefit of the $53000 ($93000 for B).

However, I'm not sure I understand what you are saying. Does 'GI could use excess resources in its Engineering department to develop a way to
eliminate this step of the manufacturing process ...' mean they would be doing away with both options A & B? Or does it mean that they would salvage the equipment purchased in either option A or B at the end of a particular year and that both options had the same salvage value? Or is this salvage values just for option A (B) and you have a different one for Option B (A)? Or ...

 

[dmillionaire]

You have computed the actual tax relief for years 1-5 but, like your values in your table for Year/ A / B you have to compute the present value of the tax reliefs.

year - cash flow - present value
0 - (185000) - (185000)
1 - 82000 - 71304.35 - -82000/(1+0.15)^1
2 - 82000 - 62003.78
3 - 64000 - 42080.35
4 - 53000 - 30303.30
5 - 37000 - 18395.15
=224086.66

224086.66 - 185000 = 39086.66

Would it be easier for me to look at it this way?, this is exactly where I am stuck. If you've had enough of this question I understand haha

 

[Ishuda]

...Would it be easier for me to look at it this way?, this is exactly where I am stuck. If you've had enough of this question I understand haha

yes, this is the kind of table you need but year 0 is still incorrect. You have three basic tables. The initial benefit table
year - benefit - pv of benefit
1 - 82000 - 71304.35 = 82000/(1+0.15)^1
2 - 82000 - 62003.78
3 - 64000 - 42080.35
4 - 53000 - 30303.30
5 - 37000 - 18395.15
The tax credit table
Year/tax credit/pv of tax credit
1 - 55 500 - 55500/(1+.15)^1 = 48261
2 - 38 850 - 38 850/(1+.15)^2 = 29376
3 - 26 950 - ...
4 - 18 865 - ...
5 - 13 205.5 - ...
And, depending on just what was meant by the salvage part of the question, the salvage table
Year/Salvage/pv of salvage
1 - 0 - 0
2 - 0 - 0
3 - 0 - 0
4 - 50000 - 50000/(1+.15)^4
5 - 35000 - 35000/(1+.15)^5

For one year you would have
PV tax credit = 48261
PV Initial investment = -185000
PV year one benefits = 71304
PV salvage = 0
Total = -185000 + 48261 + 71304 + 0 = -65435
or include the tax benefits as an
after tax initial investment = -(185000 - 48261) = -136739
for the same total
Total = -136739 + 71304 + 0 = -65435
If you keep the system for only 1 year (and there is 0 salvage) you are throwing money away

For two years you would have
PV tax credit = 48261 + 29376 = 77636
PV Initial investment = -185000
PV year one benefits = 71304 + 62004 = 113308
PV salvage = 0 + 0 = 0
Total = 25944
If you keep the system for 2 years (and there is 0 salvage) you would earn $25 944 in value for the company.

etc.



Note that the way the problem has been stated, a salvage of 0 appears to be assumed for parts (1) and (2) and the salvage table is used for part (3). But you would need to make sure this is the way the question is meant.

 

[dmillionaire]

For two years you would have
PV tax credit = 48261 + 29376 = 77636
PV Initial investment = -185000
PV year one benefits = 71304 + 62004 = 113308
PV salvage = 0 + 0 = 0
Total = 25944
If you keep the system for 2 years (and there is 0 salvage) you would earn $25 944 in value for the company.

etc.

Note that the way the problem has been stated, a salvage of 0 appears to be assumed for parts (1) and (2) and the salvage table is used for part (3). But you would need to make sure this is the way the question is meant.[/QUOTE]



I am trying to figure out how you got that 25 944, anyway you could break that down ?




EDIT: nevermind haha, literally figured it out 2 secs after posting this...

 

[Ishuda]

****** should be 133308 (to the corner, Ishuda!)

77636 + 133308 - 185000 = 25944

Off to the corner I go for 133308 centiseconds