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Print UKCAT Practice Series #002: A Fair Trade for All?

In this second part of our series, we provide a UKCAT-style Quantitative Reasoning problem that you will encounter at the UKCAT exam. We offer a detailed solution so you can learn practical insights and lessons that will help you score higher than anyone else!





  - the purchase price is 1p above mid price
  - the sale price is 1p below mid price
  - commission is £11.95 for every trade
  - stamp duty is 0.5% on purchases only.

In our example, we take the following question:

Bob has never traded shares before and decides to try it out by buying 100 Acme shares on Tuesday and then sells them on Friday. As a percentage of his outlay, how much did he get back?

I’ve chosen this problem because it incorporates several points that I want to make. It is a realistic scenario with fictitious though realistic data; there is a lot of information to sort through, and there are several calculations that need to be made to get to the answer.

Analysing the graph

The graph shows the trading prices of the shares and is known as the mid value because the actual purchase and sale price is just above or below this price. This is known as ‘the spread’ and keeps the market makers in business.

The figures

There is an overhead with each trade of £11.95 known as the commission and this keeps the brokers in business. There is a further 0.5% stamp duty, technically known as ‘the rip off’, and this keeps the chancellor in clover.

The calculation method

So, Bob buys 100 Acme shares on Tuesday. From the graph we can see that the mid value for Acme shares is £1.20 (the dark line) and the spread is 1p making the purchase price £1.21. One hundred shares at £1.21 is £121. There is stamp duty to pay at 0.5% so we multiply by 0.5 and divide by 100 giving 0.605 or 61p and then there is the £11.95 commission to add on. This gives a total cost of 121+11.95+0.61 or £133.56.

On Friday he sells when the mid price has risen to £1.24 (this is a 3.3% rise in share value) but the spread brings this down to £1.23. One hundred shares at £1.23 generates £123 but there is also the commission to pay of £11.95 bringing it down to £111.05 which is £22.51 less than they cost him despite the rise in share price.

The result

So, Bob has lost £22.51 from an initial investment of £133.56 which as a percentage is:



If he has lost 16.9% then he has 100-16.9=83.1% of his money left.

The conclusion

The lesson to be learned is not to deal in small numbers of shares as the dealing costs will wipe out all modest gains.

Was it hard? Easy? Add some comments and let us know!

(If you’d like to get more practice, check the free demo tests now.)

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