Net present value: Difference between revisions
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''Project appraisal - discounted cash flow.'' | |||
(NPV). | (NPV). | ||
For example | Net present value is a discounted cash flow technique. | ||
It expressly recognises that the timing of project cash flows is important, as well as the amounts. | |||
It makes future cash flows with different timings directly comparable, by converting them to equivalent ''present values''. | |||
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)<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 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: | ||
PV of Time 0 outflow $100m | |||
In simple ''Net Present Value analysis'' the decision rule would be that | |||
So the project in the example above would be accepted because its NPV is positive, namely +$9.09m. | = $(100m) negative | ||
PV of Time 1 inflow $120m | |||
= $120m x 1.1<sup>-1</sup> | |||
= $109.09m | |||
NPV = -$100m + $109.09m | |||
= '''+$9.09m''' (positive) | |||
<span style="color:#4B0082">'''''Decision rule'''''</span> | |||
In very simple ''Net Present Value analysis'' for investments, the decision rule would be that: | |||
(1) All positive NPV investment opportunities should be accepted. | |||
(2) All negative NPV investment 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. | However this assumes the unlimited availability of further capital with no increase in the cost of capital. | ||
A more refined decision rule is that | |||
A more refined decision rule is that: | |||
#All negative NPV investment opportunities should still be rejected; while | |||
#All positive NPV investment 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 forecast 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> | |||
= $92.31m | |||
NPV = -$100m + $92.31m | |||
= '''-$7.69m''' (negative) | |||
''Now the project would be rejected, following the further rise in the cost of capital evaluation.'' | |||
== See also == | == See also == | ||
* [[Capital rationing]] | * [[Capital rationing]] | ||
* [[Cost of capital]] | |||
* [[Discounted cash flow]] | * [[Discounted cash flow]] | ||
* [[Economic value added]] | |||
* [[Future value]] | |||
* [[Internal rate of return]] | * [[Internal rate of return]] | ||
* [[Investment appraisal]] | * [[Investment appraisal]] | ||
* [[Payback period]] | |||
* [[Present value]] | * [[Present value]] | ||
* [[Profitability index]] | |||
* [[Residual theory]] | * [[Residual theory]] | ||
* [[Time value of money]] | |||
* [[Weighted average cost of capital]] | |||
[[Category:Corporate_finance]] | |||
Latest revision as of 09:03, 8 February 2022
Project appraisal - discounted cash flow.
(NPV).
Net present value is a discounted cash flow technique.
It expressly recognises that the timing of project cash flows is important, as well as the amounts.
It makes future cash flows with different timings directly comparable, by converting them to equivalent present values.
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) negative
PV of Time 1 inflow $120m
= $120m x 1.1-1
= $109.09m
NPV = -$100m + $109.09m
= +$9.09m (positive)
Decision rule
In very simple Net Present Value analysis for investments, the decision rule would be that:
(1) All positive NPV investment opportunities should be accepted.
(2) All negative NPV investment 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 investment opportunities should still be rejected; while
- All positive NPV investment opportunities remain eligible for further consideration (rather than automatically being accepted).
NPV drivers
NPV is driven by the amounts of forecast 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
= $92.31m
NPV = -$100m + $92.31m
= -$7.69m (negative)
Now the project would be rejected, following the further rise in the cost of capital evaluation.
