Introduction to Corporate Finance

PART 3: CAPITAL BUDGETING

9-4 NET PRESENT VALUE

The net present value (NPV) of a project is the sum of the present values of all its cash flows, both inflows

and outflows. In this section we discuss the logic, calculation and pros and cons of the NPV method, as

well as a variant of this, the economic value added (EVA) method.

9-4a NET PRESENT VALUE CALCULATIONS

The net present value (NPV) of a project is the sum of the present values of all its cash flows, both

inflows and outflows. The rate used to discount the cash flows must be consistent with the project’s

risk. Calculating an investment project’s NPV is relatively straightforward. First, write down the net

cash flows that the investment will generate over its life. Second, discount these cash flows at a rate

that reflects the degree of risk inherent in the project. (Note: the choice of discount rate is discussed in

Chapter 11.) Third, add up the discounted cash flows to obtain the NPV, and invest in the project only

when that value exceeds zero.

Eq. 9.1 NPV CF

CF

r

CF

r

CF

r

CF

111 r

....

1

n

(^0) n
1
1
2
2
3
3
()()() ()
=+

• 
  


• 
  


• 
  


• 
  


• 
  

  ++

  
  


• 
  

  In this expression, CFt represents net cash flow in year t, r is the discount rate, and n represents the
  project’s life. Each year’s cash flows could be positive or negative, although typically projects generate cash
  outflows initially and cash inflows later on. For example, suppose that the initial cash flow, CF 0 , is a negative
  number representing the outlay necessary to get the project started, and suppose that all subsequent cash
  flows are positive. In this case, the NPV can be defined as the present value of future cash inflows minus the
  initial outlay. The NPV decision rule says that companies should invest when the sum of the present values
  of future cash inflows exceeds the initial project outlay. That is, NPV > $0 when the following occurs:
  CF
  CF
  r
  CF
  r
  CF
  r
  CF
  111 r
  ...
  1
  n
  (^0) n
  1
  1
  2
  2
  3
  3
  ()()() ()
  − <

  
  


• 
  


• 
  


• 
  


• 
  


• 
  

  ++

  
  


• 
  

  Simply stated, the NPV decision rule is:
  NPV > $0 invest
  NPV < $0 do not invest
  Notice that for a project to have a positive NPV, the present value of its cash inflows must exceed the
  present value of its cash outflows. Therefore, any project that meets the discounted payback criterion
  will generally have a positive NPV (unless it suffers from massive negative cash flows after the payback
  period). But is the opposite true? Some projects with positive NPVs have large cash flows beyond the
  payback cutoff period. So we can say that a company using the discounted payback method will never
  accept a project with a negative NPV, and it may reject some projects with positive NPVs. Another way
  to say this is that the discounted payback approach is overly conservative, relative to the NPV method.
  Why Does the NPV Rule Generally Lead to Good Investment Decisions?
  Remember that the company’s goal in choosing investment projects is to maximise shareholder wealth.
  Conceptually, the discount rate, r, in the NPV equation represents an opportunity cost, the highest
  return that investors can obtain in the marketplace on an investment with risk equal to the risk of the
  LO9.3
  net present value (NPV)
  The sum of the present values
  of all of a project’s cash flows,
  both inflows and outflows,
  discounted at a rate consistent
  with the project’s risk. NPV is
  also the preferred method for
  valuing capital investments
  economic value added
  (EVA)
  A method of analysing
  capital investments which
  determines whether an
  investment produces net cash
  flow sufficient to cover the
  company’s cost of capital