In order to evaluate decision 1, decision 2 needs to be evaluated first. In other words, the values we use in decision 1 need to be determined by the decision we take in decision 2.

### Decision 2

The net present value ($000s) on the 75% path is

1,686 – 300 = 1,386.

Taken together with the net present value ($000s) on the 25% path of

(211) – 300 = (511)

there is an expected net present value of choosing to market the component of ($000s):

[0.75 x 1,386] + [0.25 x (511)]

= 1,040 – 128

= 912

This is a higher value than the option of selling the design and the rights to sell the developed component for a net present value of $594,000 ($894,000 – $300,000). Therefore, if the development goes ahead, it will be more beneficial to market the product.

Of course, we still need to evaluate decision 1, whether to develop at all. The ‘success’ of the expected present value of $912,000 in decision 2 has an 80% chance of arising, but there is a 20% chance of the development not succeeding and recouping just half of the initial market value, that being $187,000 in present value terms, resulting in the company being worse off by $113,000 in present value terms after taking the development costs into account.

Hence, the expected net present value of the development option of decision 1 can be calculated ($000s):

= [0.80 x 912] + [0.20 x (113)]

= 730 – 23

= 707

Since this is higher than the option to sell the design at time 0, $400,000, on an expected value basis, the component should be developed and marketed.

### Attitude to risk

The expected value approach assumes risk neutrality, but not all management decision makers are risk neutral. A risk averse management would, in this scenario, be concerned with the 20% probability of being $113,000 worse off in present value terms should the development decision go on to fail.

Furthermore, having taken the decision (at node 2) that marketing the component is preferred to selling both the design and developed component there is a further risk of losses, since there is a 25% chance of the component being unpopular leaving the company worse off by $511,000 in present value terms.

Combined with the 80% probability of the development being successful, there is an overall 20% chance of this $511,000 loss. This 20% is known as a conditional probability since it depends upon the 80% (0.80) success rate firstly and then depends on the 25% (0.25) unpopularity chance.

Hence,

0.80 x 0.25 = 0.20 ie 20%

For completeness, there is of course a 75% chance of the component being popular if marketed, and hence the overall combined probability of a successful development together with a marketing campaign which results in popularity is:

0.80 x 0.75 = 0.60

ie 60%

### Summary