Question

Determine the Net Present Value for the following: An information system will
cost $95,000 to implement over a one-year period and will produce no savings during
that year. When the system goes online, the company will save $30,000 during
the first year of operation. For the next four years, the savings will be $20,000 per
year. Assuming a 12% discount rate, what is the NPV of the system? um stuck here...

Answer 1

Outflow :
95000 during 0th year

Answer 2

Inflow :
30,000 during 1st year
20,000 during 2nd year
20,000 during 3rd year
20,000 during 4th year
20,000 during 5th year

Answer 3

right ?

Answer 4

yes

Answer 5

what would be next?

Answer 6

we need to calculate the present value for all these inflow payments
and add them

Answer 7

how would i do that?

Answer 8

do you have the present value of annuity formula ?

Answer 9

but first i need the present value factor for12%

Answer 10

i did search but didnt understand the formula to a great extent...

Answer 11

its easy, lets first take a moment to interpret the question

Answer 12

the exact problem at hand is this :
how much a certain amount of money values NOW compared to the same amount of money in future.

Answer 13

we're given the interest rate(discount) is 12%

Answer 14

the spreadsheet i need to fill out has the following rows...
year 0 year 1 year 2 year 3 year 4 year 5
Benefits
present value factor 12%
present value
costs
present value factor 12%
present value
Net present value

Answer 15

yeah the discount is 12%

Answer 16

how would i calculate thr present value factor for 12% first?

Answer 17

and why does it require me to make the value of year 0 to be -95,000? wouldnt that cause the net value to be a negative answer?

Answer 18

\[
\begin{array}{|l|l|l|l|l|}
\hline
&\text{year 0}&\text{year 1}&\text{year 2}&\text{year 3}&\text{year 4}&\text{year 5}\\
\hline
\text{Benefits }\\
\text{present value factor 12%}& \\
\text{present value} & \\
\text{costs} & \\
\text{present value factor 12%}& \\
\text{present value} \\
\text{Net present value} \\
\hline

\end{array}
\]

Answer 19

year0 was filled already is it ?

Answer 20

no it wasnt but we do get from the data that its value is got to be $
95,000

Answer 21

that would be in front of benefits

Answer 22

95,000 is the outflow / cost/expense
so you need to use negative sign

Answer 23

ok and then what would be the formula to calculate its present value for 12%?

Answer 24

\[
\begin{array}{|l|l|l|l|l|}
\hline
&\text{year 0}&\text{year 1}&\text{year 2}&\text{year 3}&\text{year 4}&\text{year 5}\\
\hline
\text{Benefits } & \color{Red}{-95,000}\\
\text{present value factor 12%}& \\
\text{present value} & \\
\text{costs} & \\
\text{present value factor 12%}& \\
\text{present value} \\
\text{Net present value} \\
\hline

\end{array}
\]

Answer 25

like that ?

Answer 26

yeah thats how i'd consider it to be

Answer 27

\[
\begin{array}{|l|l|l|l|l|}
\hline
&\text{year 0}&\text{year 1}&\text{year 2}&\text{year 3}&\text{year 4}&\text{year 5}\\
\hline
\text{Benefits } &\\
\text{present value factor 12%}& \\
\text{present value} & \\
\text{costs} & \color{Red}{95,000} \\
\text{present value factor 12%}& \\
\text{present value} \\
\text{Net present value} & \color{Red}{-95,000} \\
\hline

\end{array}
\]

Answer 28

In the 0th year, I think we should not discount anything. the net present value will be simply -95,000. what do you think ?

Answer 29

aaahhh ok but we don't calculate the net present value for each cost..right?
because the NPV is just supposed to be one value...

Answer 30

I'm not really sure yet, lets see if it becomes clear as we work on it :)

Answer 31

that would be 30,000*12% right?

Answer 32

yep $30,000 after 1 year is same as
$26,400 NOW.

Answer 33

there are no costs in year1, right ?

Answer 34

can i get how you calculated the PV?

Answer 35

PV = Benifits - (discount factor)

Answer 36

PV = 30,000 - (12% of 30,000)

Answer 37

oh ok that makes sense

Answer 38

and what would be the 2nd 12% factor values? if they end up to be the same that wouldn't lead us to the value.

Answer 39

let me think a bit

Answer 40

ok take your time

Answer 41

i have this example

Answer 42

which is confusing me more

Answer 43

yeah ?

Answer 44

year 0 year 1 year 2 year 3 year 4 year 5 year 6
benefits 6,000 28,000 54,000 70,000 82,000 82,000
present value 12% 0.893 .797 .712 .636 .567 .567
present value
costs 80,000
present value 12%
present value
Net present value

Answer 45

i wonder how they calculated the present factor 12% to be in decimals?

Answer 46

ahh ok got it :)

Answer 47

you remember the FV formula ?

FV = PV(1+r)^n ?

Answer 48

plugin FV = 1, and solve for PV :

1 = PV(1+r)^n

Answer 49

PV = 1/(1+r)^n

Answer 50

plugin r = 0.12, n = 1 above ^

Answer 51

n= 1 :
PV = 1/(1+0.12)^1 = 1/(1.12) = 0.893

Answer 52

getting ?

Answer 53

yeps now got it

Answer 54

n= 2 :
PV = 1/(1+0.12)^2 = 1/(1.12)^2 = 0.787

Answer 55

lets change our table :)

Answer 56

ok

Answer 57

\[
\begin{array}{|l|l|l|l|l|}
\hline
&\text{year 0}&\text{year 1}&\text{year 2}&\text{year 3}&\text{year 4}&\text{year 5}\\
\hline
\text{Benefits } &&\color{red}{30,000}&\color{red}{20,000}\\
\text{present value factor 12%}&&\color{red}{0.893}&\color{red}{0.797} \\
\text{present value} &&\color{red}{26,790}&\color{red}{15,940} \\
\text{costs} & \color{Red}{95,000} \\
\text{present value factor 12%}& \\
\text{present value} \\
\text{Net present value} & \color{Red}{-95,000}&\color{red}{26,790}&\color{red}{15,940} \\
\hline

\end{array}
\]

Answer 58

see if that looks okay so far

Answer 59

yeah it looks okay um still checking too

Answer 60

\[
\begin{array}{|l|l|l|l|l|}
\hline
&\text{year 0}&\text{year 1}&\text{year 2}&\text{year 3}&\text{year 4}&\text{year 5}\\
\hline
\text{Benefits } &&\color{red}{30,000}&\color{red}{20,000}&\color{red}{20,000}\\
\text{present value factor 12%}&&\color{red}{0.893}&\color{red}{0.797}&\color{red}{0.712} \\
\text{present value} &&\color{red}{26,790}&\color{red}{15,940}&\color{red}{14,240} \\
\text{costs} & \color{Red}{95,000} \\
\text{present value factor 12%}& \\
\text{present value} \\
\text{Net present value} & \color{Red}{-95,000}&\color{red}{26,790}&\color{red}{15,940}&\color{red}{14,240} \\
\hline

\end{array}
\]

Answer 61

good, see if you can fill in the remaining two columns

Answer 62

they would be the same as year 3

Answer 63

but we also have to calculate the 2nd present value factors

Answer 64

in order to determine the NPV

Answer 65

benefits will be same,
but the present values will not be same

Answer 66

yeah the present values would be .636 and .567

Answer 67

use the formula :

PV = 1/(1+r)^n

Answer 68

plugin r = 0.12
n = year number

Answer 69

year4 :
1/(1+0.12)^4 = 0.636

year 5 :
1/(1+0.12)^5 = 0.567

Answer 70

so you're right:) just fill in the columns

Answer 71

yeah and how did you calculate the present value to be 26,790? what formula would be used now?

Answer 72

simply multilply `Benifits` and the `present value factor`

Answer 73

the `present value factor` represents the value of `1 dollar`

Answer 74

so, to get the `present value` of 30,000 dollars, you simply multiply 30000 and the factor

Answer 75

30,000 x 0.893 = 26790

Answer 76

12720 and 11340

Answer 77

\[
\begin{array}{|l|l|l|l|l|}
\hline
&\text{year 0}&\text{year 1}&\text{year 2}&\text{year 3}&\text{year 4}&\text{year 5}\\
\hline
&&\color{red}{30,000}&\color{red}{20,000}&\color{red}{20,000}&\color{red}{20,000}&\color{red}{20,000}\\
&&\color{red}{0.893}&\color{red}{0.797}&\color{red}{0.712} &\color{red}{0.636}&\color{red}{0.567} \\
&&\color{red}{26,790}&\color{red}{15,940}&\color{red}{14,240}&\color{red}{12,720}&\color{red}{11,340} \\
& \color{Red}{95,000} \\
& \\
\\
& \color{Red}{-95,000}&\color{red}{26,790}&\color{red}{15,940}&\color{red}{14,240}&\color{red}{12,720}&\color{red}{11,340} \\
\hline

\end{array}
\]

Answer 78

like above ^ ?

Answer 79

Net present value of cash inflows = `26,790 + 15,940 + 14,240 + 12,720 + 11,240`
= ?

Answer 80

lemme check on that one

Answer 81

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Benefits 3,000 28,000 31,000 34,000 36,000 42,000
Present Factor Value12% 1.000 0.893 0.797 0.712 0.636 0.507
Present Value 3,000 25,004 24,707 24,208 22,896 21,294
Costs 60,000 17,000 18,500 19,200 21,000 23,300
Present Value Factor 12% 1.000 0.893 0.797 0.712 0.636 0.507
Present Value 60,000 15,181 14,745 13,670 13,356 11,813
Net Present Value 1,983

Answer 82

they manage to change the present values here? then we have to sum the present values and subtract the present and future values?

Answer 83

gone?

Answer 84

:(