Expected valuePossible outcome NPV Probability (p) NPV×p
££
C −19,672 0.04 − 787
F −15,881 0.10 −1,588
I −12,090 0.06 − 725
B −4,508 0.14 − 631
E +1,179 0.35 + 413
H +6,865 0.21 +1,442
A +10,656 0.02 + 213
D +18,238 0.05 + 912
G +25,820 0.03 + 775
Expected value + 24Incidentally, if the decision maker were not interested in the individual outcomes
(A to I), there is a much more direct approach to arriving at the expected value. This
is to calculate the expected value of the risky factors and then to calculate the NPV,
incorporating these expected values.
Expected sales volume=(4,000 ×0.2) +(4,500 ×0.5) +(5,000 ×0.3)
=4,550 unitsExpected labour cost =(£3 ×0.1) +(£4 ×0.7) +(£5 ×0.2) =£4.10NPV =−50,000 +{4,550 ×[10 −(4.1 +3)] ×3.791} =+£22The difference between this figure and the original expected NPV (+£24) is entirely
due to rounding errors in the original calculation.
We now have one single factor to which we could apply the NPV rule. (In this case
the expected NPV (ENPV) is very close to zero and thus the project would be on the
margin between acceptance and rejection if ENPV were the decision criterion.)
There are some obvious weaknesses in the ENPV approach.
l As with all averaging, information is lost. The figure of +£24 for the ENPV of the
project in the example does not tell us that there is a 4 per cent chance of the project
yielding a negative NPV of £19,672. It also fails to tell us that the single most likely
outcome, outcome E, gives a positive NPV of £1,179.
How could we distinguish between this project and one with a certain NPV of
+£24? We need some measure of dispersion, such as range or standard deviation.
l The ENPV is likely to represent a value that could not possibly exist. In our exam-
ple an NPV of +£24 is certain not to occur: the possible outcomes are A to I, one of
which must occur, and +£24 is not among these. In this sense, expected value is a
misnomer as it could not possibly occur, let alone be expected in the normal mean-
ing of the word. Does this invalidate ENPV as a decision-making criterion?
We know that the probability of a fair coin landing heads up is 0.5. If we were
offered a wager such that we should gain £1 if a coin landed heads up and nothing if
it landed tails up, one such throw would have an expected value of £0.50 (despite the
fact that the outcome could only be £1 or nothing). If the wager were repeated 100
times we should be very surprised if the expected value (£50) and the actual outcome