Decision Tree Questions

DECISION TREE QUESTIONS
Question 1
A firm has developed a new product X. they can either test the market or abandon the project. The
details are set out below:
Test market cost N 50,000; likely outcomes are: favourable (p = 0.7) or failure (p = 0.3). If
favourable they could either abandon or produce it when demand is anticipated to be:
Low P = 0.25 Loss N100,000
Medium P = 0.6 Profit N150,000
High p = 0.15 Profit N450,000
If the test market indicates failure, the project would be abandoned. Abandonement at any stage
results In gain of N 30,000 from the special machinery used. Draw the decision tree showing the
nodes and probabilities.
Question 2
Hadex Limited has a new wonder product of which it expects great things. At the moment, the
company has two courses of action open to it to test-market the product or abandon it.
If the company test-markets it, the cost will be N100,000 and the market response would be
positive or negative with probabilities of 0.60 and 0.40 respectively.
If the response is positive, the company could either abandon the product or market it full scale.
If it markets the product full scale, the outcome might be low, medium or high demand and the
respective net gains/(losses) would be (200), 200 or 1,000 in units of N 1,000 (the result could
range from a net loss of N 200,000 to a gain of N 1,000,000). These outcomes have probabilities
of 0.20, 0.50 and 0.30 respectively.
If the result of the test marketing is negative and the company goes ahead and markets the product,
estimated losses would be N 600,000.
If at any point, the company abandons the product, there would be a net gain of N 50,000 from the
sale of the scrap. All the financial values have been discounted to the present value.
You are required to:
a) Draw a decision tree to illustrate the above scenario.

b) Advise the company on the option to be selected.
Question 3
A software company has just won a contract worth N80,000,000 if it delivers a successful product
on time, but only N40,000,000 if this is late. It faces the problem on whether to produce the work
in house or subcontract it. To subcontract the work would cost N 50,000,000, but the local
subcontractor is so fast and reliable as to make it certain that successful software is produced on
time.
If the work is produced in-house, the cost would be only N20,000,000 but based on past
experience, it would have a 90% chance of being successful. In the event of the software not being
successful, there would be insufficient time to re-write the whole package internally, but there
would still be the options of either a late rejection of the contract (at a further cost of N10,000,000)
or subcontracting the job on the same terms as before. With this late start, the local subcontractor
is estimated to have a 50/50 chance of producing the work on time or producing it late. In this case,
the subcontractor still has to be paid N50,000,000 regardless of whether he meets the deadline or
not.
You are required to:
a) Draw a decision tree for the software company using squares for decision points and circles
for chance points including all relevant data on the diagram.
b) Calculate expected values as appropriate and to recommend a course of action to the software
company.
Question 4
Your company is considering whether it should tender for two contracts (MS1 and MS2) on offer
from a government department for the supply of certain components. The company has three
options:
 tender for MS1 only; or
 tender for MS2 only; or
 tender for both MS1 and MS2.
If tenders are to be submitted the company will incur additional costs. These costs will have to be
entirely recouped from the contract price. The risk, of course, is that if a tender is unsuccessful the
company will have made a loss.
The cost of tendering for contract MS1 only is N50,000. The component supply cost if the tender
is successful would be ₦18,000.
The cost of tendering for contract MS2 only is ₦14,000. The component supply cost if the tender
is successful would be ₦12,000.
The cost of tendering for both contract MS1 and contract MS2 is ₦55,000. The component supply
cost if the tender is successful would be ₦24,000.
For each contract, possible tender prices have been determined. In addition, subjective assessments
have been made of the probability of getting the contract with a particular tender price as shown
below. Note here that the company can only submit one tender and cannot, for example, submit
two tenders (at different prices) for the same contract.
Option Possible Probability
tender of getting
prices (₦) contract
MS1 only 130,000 0.20
115,000 0.85
MS2 only 70,000 0.15
65,000 0.80
60,000 0.95
MS1 and MS2 190,000 0.05
140,000 0.65
In the event that the company tenders for both MS1 and MS2 it will either win both contracts (at
the price shown above) or no contract at all.
 What do you suggest the company should do and why?
 A consultant has approached your company with an offer that in return for ₦20,000 in cash
she will ensure that if you tender ₦60,000 for contract MS2 only your tender is guaranteed to
be successful. Should you accept her offer or not and why?
Question 5
A large steel manufacturing company has three options with regards to production: (i) produce
commercially (ii) build pilot plant (iii) stop producing steel. The management has estimated that
their pilot plant, if built, has 0.8 chance of high yield and 0.2 chance of low yield. If the pilot plant
does show a high yield, management assigns a probability of 0.75 that the commercial plant will
also have a high yield. If the pilot plant shows a low yield there is only a 0.1 chance that the
commercial plant will show a high yield. Finally, management’s best assessment of the yield on a
commercial –size plant without building a pilot plant first has a 0.6 chance of high yield. A pilot
plant will cost N300,000. The profits earned under high and low yield conditions are N12,000,000
and N1,200,000 respectively. Find the optimum decision for the company.

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DECISION TREE QUESTIONS

You are required to:

a) Draw a decision tree to illustrate the above scenario.

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