Net book value and Net present value: Difference between pages

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''Accounting''.
(NPV).  


(NBV).
Net present value is the total present value of all of the cash flows of a proposal - both positive and negative - netting off negative present values against positive ones.  
 
The net value of a fixed asset reported in financial statements.


For example, its historical cost purchase price LESS the accumulated provision for depreciation.
For example, the expected future cash inflows from an investment project LESS the initial capital investment outflow at Time 0.
 
 
Each present value (PV) is calculated as:
 
PV = Future value x Discount factor (DF)
 
Where:
 
DF = (1 + r)<sup>-n</sup>
 
:r = cost of capital per period; ''and''
:n = number of periods into the future that the cash flow is expected
 
 
<span style="color:#4B0082">'''Example 1: cost of capital 10%'''</span>
 
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<sup>-1</sup>
 
= $109.09m
 
 
NPV = -$100m + $109.09m
 
= '''+$9.09m'''
 
 
<span style="color:#4B0082">'''''Decision rule'''''</span>
 
In very 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 the basis of this simple form of the NPV decision rule) 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:
 
#All negative NPV opportunities should still be rejected; while
#All positive NPV opportunities remain eligible for further consideration (rather than automatically being accepted).
 
 
<span style="color:#4B0082">'''''NPV drivers'''''</span>
 
NPV is driven by the amounts of expected cash flows, their timing, and the cost of capital.
 
 
<span style="color:#4B0082">'''Example 2: cost of capital rises to 20%'''</span>
 
Taking the same example of a project requiring an investment today of $100m, with $120m being receivable one year from now.
 
The cost of capital (r) rises to 20% per annum.
 
 
The NPV of the project is now calculated as follows:
 
 
PV of Time 0 outflow $100m
 
= $(100m)
 
 
PV of Time 1 inflow $120m
 
= $120m x 1.2<sup>-1</sup>
 
= $100m
 
 
NPV = -$100m + $100m
 
= '''$NIL'''
 
Now the project decision is marginal, following the change in the cost of capital assessment.
 
 
 
<span style="color:#4B0082">'''Example 3: cost of capital rises further to 30%'''</span>
 
Continuing with the same example of a project requiring an investment today of $100m, with $120m receivable one year from now.
 
The cost of capital (r) rises further to 30% per annum.
 
 
The NPV of the project would now be calculated as follows:
 
 
PV of Time 0 outflow $100m
 
= $(100m)
 
 
PV of Time 1 inflow $120m
 
= $120m x 1.3<sup>-1</sup>
 
= $92.3m
 
 
NPV = -$100m + $92.3m
 
= '''-$7.7m'''
 
Now the project would be rejected, following the further rise in the cost of capital evaluation.




== See also ==
== See also ==
* [[Amortisation]]
* [[Capital rationing]]
* [[Book value]]
* [[Discounted cash flow]]
* [[Cost]]
* [[Economic value added]]
* [[Depreciation]]
* [[Future value]]
* [[Fixed assets]]
* [[Internal rate of return]]
* [[Impairment]]
* [[Investment appraisal]]
* [[Net realisable value]]
* [[Present value]]
* [[Provision]]
* [[Residual theory]]
* [[Residual value]]
* [[Weighted average cost of capital]]
* [[Revaluation]]
* [[Useful economic life]]


[[Category:Accounting,_tax_and_regulation]]
[[Category:Corporate_finance]]

Revision as of 11:18, 3 March 2019

(NPV).

Net present value is the total present value of all of the cash flows of a proposal - both positive and negative - netting off negative present values against positive ones.

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


Each present value (PV) is calculated as:

PV = Future value x Discount factor (DF)

Where:

DF = (1 + r)-n

r = cost of capital per period; and
n = number of periods into the future that the cash flow is expected


Example 1: cost of capital 10%

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


Decision rule

In very 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 the basis of this simple form of the NPV decision rule) 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).


NPV drivers

NPV is driven by the amounts of expected cash flows, their timing, and the cost of capital.


Example 2: cost of capital rises to 20%

Taking the same example of a project requiring an investment today of $100m, with $120m being receivable one year from now.

The cost of capital (r) rises to 20% per annum.


The NPV of the project is now calculated as follows:


PV of Time 0 outflow $100m

= $(100m)


PV of Time 1 inflow $120m

= $120m x 1.2-1

= $100m


NPV = -$100m + $100m

= $NIL

Now the project decision is marginal, following the change in the cost of capital assessment.


Example 3: cost of capital rises further to 30%

Continuing with the same example of a project requiring an investment today of $100m, with $120m receivable one year from now.

The cost of capital (r) rises further to 30% per annum.


The NPV of the project would now be calculated as follows:


PV of Time 0 outflow $100m

= $(100m)


PV of Time 1 inflow $120m

= $120m x 1.3-1

= $92.3m


NPV = -$100m + $92.3m

= -$7.7m

Now the project would be rejected, following the further rise in the cost of capital evaluation.


See also