Net Present Value

1
Net Present Value

• Money invested now is weighed against the value
  in current terms of both the savings and
  equipment disposal money received in future
  years.
• Need to ensure the appropriate rates are used for
  estimating and discounting future returns and
  expenses

Dr Alan J. R. Smith Mechanical and Manufacturing
Engineering
2
Net Present Value

• If all inflation rates (for wages, materials,
  prices obtained, etc) are the same, then can
  simply use real interest rate for discounting,
• i.e. (1 i - cpi)-1 is the discount factor
• more correctly (1 cpi)/(1 i)
• Need to use i appropriate to source of funding

Dr Alan J. R. Smith Mechanical and Manufacturing
Engineering
3
Net Present Value

• In summary a project changes the wealth
  of a company either by the NPV at the start or by
  the NTerminalV on cessation. Only projects with a
  positive NPV are acceptable.There is an explicit
  assumption that the cost of capital is charged at
  the rate i, and an implicit assumption that
  project returns are invested at the same rate

Dr Alan J. R. Smith Mechanical and Manufacturing
Engineering
4
Internal Rate of Return

• Sometimes simply Rate of Return (RoR)
• Similar to NPV except that i (the rate of return)
  is calculated to reduce NPV to zero
• The calculated i is then compared with the
  company criterion
• usually the borrowing rate or the investment
  rate if the capital is to found from reserves

Dr Alan J. R. Smith Mechanical and Manufacturing
Engineering
5
Internal Rate of Return

• Need to search for i
• Wide acceptance being a relative measure
• Implicit assumptions
• a (unique) value for i can be calculated
• any surplus cash generated will be used to reduce
  debt or is invested at i
• all cash outflows (other than the initial
  outflow) are discounted at i

Dr Alan J. R. Smith Mechanical and Manufacturing
Engineering
6
IRR for Investment

• A refinement of IRR to overcome problems such as
  there not always being a solution
• IRRI uses the known cost of capital to discount
  all (net) outflows of capital and then finds an i
  for all inflows of cash to yield a zero NPV
• Not widely used, although has desirable features

Dr Alan J. R. Smith Mechanical and Manufacturing
Engineering
7
Uniform Annual Cost

• Recommended in some engineering texts to evaluate
  projects with different time horizons
• Basically converts the NPV into an equivalent
  annuity
• When making comparisons it implicitly assumes
  that at the end of the (shorter) project, a new
  project will be started with at least equal
  returns.

Dr Alan J. R. Smith Mechanical and Manufacturing
Engineering
8
Pay-back Period

• One of the simpler methods
• Was the most common method and still is widely
  used
• In its basic form ignores the time value of money
• The method is to determine when the initial
  investment is paid back by the net savings in
  later years

Dr Alan J. R. Smith Mechanical and Manufacturing
Engineering
9
Pay-back Method

• If savings in future years will be approximately
  constant, then can simply take the total capital
  investment and divide it by the total expected
  annual gain
• gain calculated gross or net of tax
• The exclusion of the time value of money is
  reasonable when interest rates are the same as
  inflation

Dr Alan J. R. Smith Mechanical and Manufacturing
Engineering
10
Pay-back Method

• Acceptable pay-back periods will be determined by
  company policy
• generally a period of five years is too long,
  typically three years is used as a criterion
• lower during high inflation or a depression
• it can vary for different types of investment
• large petrochemical plants can have pay-back
  periods of decades
• hand tools can pay-back in six months

Dr Alan J. R. Smith Mechanical and Manufacturing
Engineering
11
Pay-back Method

• The method could be improved by allowing for the
  time value of money, but it then loses its
  simplicity
• In an attempt to make the estimates more
  realistic, Colville suggests including interest
  charges and depreciation in the annual costs
• there are fundamental problems with this approach

Dr Alan J. R. Smith Mechanical and Manufacturing
Engineering
12
Pay-back Method

• By other criteria, pay-back method can make a bad
  decision appear good and visa versa
• Paradoxically, is usually a safe method
• because it usually operates over a short time
  frame, hence predictions of future returns will
  be reasonable
• Ignores returns after pay-back period

Dr Alan J. R. Smith Mechanical and Manufacturing
Engineering
13
Accounting Rate of Return

• ARR profit / capital_outlay
• several practical variations
• profit may be calculated as an annual average
• often net of accounting depreciation
• introduces a subjective component
• capital_outlay may be the initial capital sum, or
  an annual average with or without the working
  capital

Dr Alan J. R. Smith Mechanical and Manufacturing
Engineering
14
Accounting Rate of Return

• Fundamentally flawed by not including the time
  value of money
• Regardless of the above choices the ARR cannot be
  compared to true rates
• When based on initial capital tends to over
  estimate the true rate and conversely when based
  on average capital employed
• Erroneous to use an accounting profit to
  discriminate between projects

Dr Alan J. R. Smith Mechanical and Manufacturing
Engineering
15
Other Methods

• Some equipment suppliers have developed rules of
  thumb which can be quickly applied to encourage
  customers to purchase
• major problem is when these are based on outdated
  figures for inflation and interest, depreciation
  and tax
• Profitability Index NPV / sum_of_net_ outflows

Dr Alan J. R. Smith Mechanical and Manufacturing
Engineering