Year   Project A     Project B
0       -30000         -60000
1        10000          20000
2        10000          20000
3        10000          20000
4        10000          20000
5        10000          20000

This project has a required 14% rate of return
1.  Compare the NPV of both projects
2.  Compute the IRR on both projects

Show work

Hi!!


Present Value (PV):

         CF1           CF2                    CF5  
PV  = ---------  +  ----------  +  ...  +  ----------
      (1 + r)^1     (1 + r)^2	          (1 + r)^5  

Where r is the required return.


If all the cash flows are equal (like in this problem):

      CF             1
PV = ---- * [1 - ---------] 
       r          (1+r)^5

Net Present Value (NPV):

NPV = PV - I         where I = Total Initial Investment


For reference see:
"Annuities":
http://www.netmba.com/finance/time-value/annuity/


Now we can calculate both NPV:

-Project A NPV:

PV(A) = 10,000/0.14 * [1 - 1/(1.14)^5] =
      = 37,097.76

NPV(A) = 34,330.81 - 30,000 =
       = 4,330.81


-Project B NPV: 

PV(B) = 20,000/0.14 * [1 - 1/(1.14)^5] =
      = 68,661.62

NPV(B) = 68,661.62 - 60,000 =
       = 8,661.62


The NPV of the project B is greater than the NPV of the project A,
exactly the double as you expect after a first look of the cash flows.

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IRR:

IRR is the discount rate r at which the NPV equals zero, in other
words it is the rate that satisfies:

NPV = PV - I = 0


Then IRR is the discount rate r at which:

PV = I


So you must find the r that solves the following equation:


      CF             1
PV = ---- * [1 - ---------] = I
       r          (1+r)^5


You can use different ways to calculate the IRR, for example:
-Trial & Error
-Calculator
-Computer (Excel spreadsheet)

Here is a brief guide to do this using an MS Excel spreadsheet for this problem:
1) Select a column for the project's Cash flows (for example column "A").
2) Input the project's Cash Flows starting from the initial investment
(this is a negative input) and followed by the CF1 to CF4 cash flows,
each one in one cell of the column.
3) Click on the cell where you want your IRR calculated (say B1). 
4) Enter "=IRR(" (without the quotes) and then highlight the column A
then close the parenthesis and hit enter.

For the project A the column A will have:
A1: -30,000 ; A2: to A6: 10,000 ;
B1: =IRR(A1:A6)

You will find that IRR(A) = 19.858%


For the project B the column A will have:
A1: -60,000 ; A2: to A6: 20,000 ;
B1: =IRR(A1:A6)

You will find that IRR(B) = 19.858%

Both IRR are equal.

This problem shows that IRR and NPV are independent ways to decide if
a project is eligible or not.

----------------------------------------------------------

I hope that this helps you. If you find something unclear or need
further assistance, please post a request for an answer clarification
before rate this answer. I will be glad to respond your requests.

Best regards.
livioflores-ga

IRR is same for both projects. as project B is just double the size of
project A. NPV of B will be double of A.

But how do you calculate that?

NPV, you can calculate in similar fashion as in your previuos
question. i.e. cashflow/(1+discount rate)^no. of year to cash flow -
reapeat the PV for all years taking year of investment as year 0 - sum
of these PVs is your NPV (N for net as its sum of - and + values)

For IRR, you need to do trial and error. say, assume a discount rate
and calculate NPV. if its greater than 0, increase discount rate and
if its less than 0, decrease discount rate. keep adjusting it till you
get NPV of 0 - that's your IRR. (you can use worksheet function irr()
to crosscheck your answer.

Alternatively, if you have taken two discount rates which are giving
small positive and small negative NPVs, you can use interpolation to
find out rate at which NPV should be zero - the approximation will not
be very far from exact answer.