Net present value: Difference between revisions

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(NPV).  
(NPV).  


'''1.'''
1.


The total [[present value]] of all of the cash flows of a proposal - both positive and negative.  
The total [[present value]] of all of the cash flows of a proposal - both positive and negative.  
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'''''Example'''''
'''Example'''


For example, a project requires an investment today of $100m, with $120m being receivable one year from now.
A project requires an investment today of $100m, with $120m being receivable one year from now.


The cost of capital (r) is 10% per annum.


The cost of capital (r) is 10% per annum.


The NPV of the project is calculated as follows:
The NPV of the project is calculated as follows:
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= $(100m)
= $(100m)


PV of Time 1 inflow $120m = $120m x 1.1<sup>-1</sup>  
 
PV of Time 1 inflow $120m  
 
= $120m x 1.1<sup>-1</sup>  


= $109.09m
= $109.09m


NPV = -$100m +$109.09m  
NPV = -$100m +$109.09m  


= '''+$9.09m'''
= +$9.09m
 




'''2.'''
2.


In simple ''Net Present Value analysis'' the decision rule would be that:
In simple ''Net Present Value analysis'' the decision rule would be that:

Revision as of 16:47, 16 March 2015

(NPV).

1.

The total present value of all of the cash flows of a proposal - both positive and negative.

For example, the expected future cash inflows from an investment project LESS the initial capital investment outflow at Time 0.


Example

A project requires an investment today of $100m, with $120m being receivable one year from now.

The cost of capital (r) is 10% per annum.


The NPV of the project is calculated as follows:


PV of Time 0 outflow $100m

= $(100m)


PV of Time 1 inflow $120m

= $120m x 1.1-1

= $109.09m


NPV = -$100m +$109.09m

= +$9.09m


2.

In simple Net Present Value analysis the decision rule would be that:

(1) All positive NPV opportunities should be accepted.

(2) All negative NPV opportunities should be rejected.


So the project in the example above would be accepted - on this basis - because its NPV is positive, namely +$9.09m.


However this assumes the unlimited availability of further capital with no increase in the cost of capital.

A more refined decision rule is that:

(1) All negative NPV opportunities should still be rejected; while

(2) All positive NPV opportunities remain eligible for further consideration (rather than automatically being accepted).


See also