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Hello Sir,
Extract from the question:
Care Co needs to replace a major piece of office equipment that is in constant use and for
which there is expected to continue to be use for the foreseeable future. Two types of
machine are available with different capital costs, useful lives, scrap values and annual
running costs.
Care Co’s cost of capital is 10%. Assume all cash flows, except the initial capital cost, occur
at the end of the relevant year and assume that taxation and inflation can be ignored.QUESTION:
It is now felt that the final scrap value of the machines depends on two factors:
whether or not a new supplier enters the market (which would reduce the likely
scrap value) and the strength of the dollar against other currencies (since sales of
used machines will be made abroad and invoiced in the foreign currency). Adverse
effects will each reduce the scrap value by 10% of the figure used in the investment
appraisal. The relevant probabilities are as follows.New supplier Probability Strong $ Probability
Yes 0.4 Yes 0.3
No 0.6 No 0.7What is now the expected value of the scrap proceeds from machine 2?
A $106,800
B $109,000
C $111,600
D $113,000ANSWER:
Scrap value Probability Expected value
$120,000 0.6 × 0.7 = 0.42 50,400
£108,000 0.4 × 0.7 + 0.6 × 0.3 = 0.46 49,680
$96,000 0.4 × 0.3 = 0.12 11,520
–––– –––––––
1.00 $111,600
–––– –––––––
Answers B and D ignore joint probabilities; whereas answers A and B misinterpret the
effects of a strong dollar (a strong dollar would make an overseas sale less
attractive).MY DOUBT: I completely didn’t understand the logic behind this question even though I understand the concept of expected values but I just can’t put the knowledge of it in solving this question.
Thank you in advance!
Have a good day 🙂Sorry, I forgot to add in the Machine 2 details given in the question!
Machine 2 will initially cost $540,000, have a life of three years, scrap value of $120,000
and annual running costs of $47,000.There are four possible outcomes :
New supplier and strong dollar
New supplier and not strong dollar
No new supplier and strong dollar
No new supplier and not strong dollarA new supplier will reduce the scrap value by 10%, and so will a strong dollar.
So the final outcome for each of the four possibilities (in the same order in which I have listed them above) will be:120,000 – 10% – 10% = 96,000
120,000 – 10% = 108,000
120,000 – 10% = 108,000
120,000 – 0 = 120,000The probability of each of the 4 outcomes (again, in the same order in which I have listed them above) are:
0.4 x 0.3 = 0.12
0.4 x 0.7 = 0.28
0.6 x 0.3 = 0.18
0.6 x 0.7 = 0.42Therefore the expected value is the total of the following:
96,000 x 0.12 = 11,520
108,000 x 0.28 = 30,240
108,000 x 0.18 = 19,440
120,000 x 0.42 = 50,400$111,600
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