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The principle of value additivity means that the value loss to the player must equal the

value gain to the casino. In theory, therefore, there is a gain to the casino owner of one

sixth of a dollar each time the game is played. However, the casino has to incur high costs

and only has limited access to gamblers.

If we define one unit of gambling capacity as one gambler present for one hour, the

casino has a maximum capacity of 12 Ã— 500 Ã— 52 gambling hours per year. This equals

312,000. We know that each individual gamble is worth one sixth of a dollar to the casino

operator. The required gain per gambling hour is $1m divided by 312,000, which equals

$3.205. Finally we multiply this by six to get to the minimum number of games per hour.

The answer is 19.2.

So simply to break even each and every gambler in the casino must play about one game

every three minutes throughout their time in the casino and the casino must always be

full. Now I am not a gambler but I doubt that those are good enough conditions to make

it worth operating the casino. I would not, however, give up straight away. If the gam-

bling regulations could be relaxed or if the size of bets could be increased it might well be

worthwhile opening a casino.

4. Here are six different types of probability distribution and ten situations. Match the situ-

ations to the distributions.

Distributions

â€¢ Symmetrical, narrow range

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595 Building block 5: Risk

Symmetrical, wide range

â€¢

Skewed with heavy upside

â€¢

Skewed with heavy downside

â€¢

Bimodal

â€¢

Substantially flat

â€¢

Situations

â€¢ The quantity of cash being carried by an individual selected at random at a shopping

centre. I would suggest skewed with heavy upside. Most people will have some cash

but some will have a lot. You cannot have less cash than zero. One could also suggest a

bimodal distribution with all very young children having no cash and grown-ups hav-

ing more.

â€¢ The height of the people present at an infantsâ€™ school. This would be bimodal with, in

effect, two groups present â€“ the infants and the adults. Each of these two groups would

have its own distribution.

â€¢ The price of a particular share tomorrow in relation to its price today (ignoring complica-

tions such as days when the markets are not open or the effect of any dividends that are

paid). This would be symmetrical with a narrow range.

â€¢ The corporate tax rate in your home country in five yearsâ€™ time compared with the current

rate. With tax rates there is always a possibility that there might be some major reform

within a five year period. One would need to know which country before one guessed

whether this could give a downside or an upside skew. If this possibility was ignored

one would usually assume a symmetrical distribution with a narrow range.

â€¢ The price of a TV set in ten yearsâ€™ time. This is difficult to answer because with the pace

of technological change, who can be sure exactly what functions will be present in a TV

ten years in the future? My perception is that the trend has been that on a like-for-like

basis TV prices have come down but technology changes have resulted in substantial

overall rises in the headline price of a TV. Lacking any better basis I would suggest a

symmetrical distribution with a wide range.

â€¢ The exchange rate between US dollars and the euro in one yearâ€™s time. I have no real

reason to expect any significant changes or skews and so would go for symmetrical,

narrow range.

â€¢ The cost of building the stadia required for the London Olympics compared with the ini-

tial estimate made when the Olympic bid was submitted. This would be a classic skewed

distribution with heavy upside (always assuming that the term â€˜upsideâ€™ means higher

cost and not a better outcome).

â€¢ The amount of rainfall in London on a particular day in July relative to the average

daily rainfall for July. This is a success or failure situation. The way to model rainfall is

through whether or not it rains and then the average rain on days when it does rain.

Even on the days when it does rain, I would expect a wide range of outcomes.

â€¢ The closing price of gold on the London futures market relative to the closing price on

the US market on the same day. International markets are connected and so the only

difference that I would anticipate would be due to the time difference between the two

countries. This would drive a small and symmetrical distribution.

â€¢ The average wage rate in the US in five yearsâ€™ time. It is a fair bet that wages will be higher

but even this is not certain because the national average will be affected by several

596 Individual work assignments: Suggested answers

factors and not just inflation. However, the overall uncertainty is probably not very

great. So I would suggest a slight upward skew.

Note that my answers to these questions have tended to be very imprecise. This uncer-

tainty about uncertainty is fairly typical!

5. A business opportunity exists to sell replica sports shirts outside a stadium. You have two

choices. You can go for the minimal overheads approach and carry 50 shirts to the ground

for each home game, held over your arm and in a large holdall bag. You would expect to

sell at least 40 of these every game for $20 each while the cost to you is just $10 per shirt.

There are 20 home games in a season. The alternative is to rent a small lock-up stall by the

entrance to the ground. This would then allow you to hold a more substantial stock of shirts

and win many more sales. The stall costs $2,000 to rent for the season and you would hold a

stock of 400 shirts. Your best estimate of sales would then be 150 per game again at a price of

$20 per shirt and with a variable cost to you of $10 per shirt. Which would be the best thing

to do and how might a risk review make you change this view?

The first stage in the analysis is to carry out a first-cut analysis of the economics given the

stated assumptions. The so-called minimal overheads approach looks as follows:

The outlay per game is $500 (50 shirts bought for $10 each) and the minimum return

is $800 cash plus $100 towards next weekâ€™s shirt purchases. This is a minimum profit of

$400 per game. With 20 home games per season the anticipated profit is $8,000 per year.

We should not forget the need to fund the inventory (i.e. any unsold shirts that we own).

For our base case assumptions we would finish the year with ten shirts in stock. These

would have cost $100. So the overall return is $7,900 of cash and $100 in unsold shirts

valued at cost. In addition to this if you are able to sell all 50 shirts each game then the

cash gain increases to $10,000 per year and there would be no unsold shirts at the end

of the year.

The alternative approach involves an initial outlay on shirts of $4,000 and a commit-

ment to pay rent of $2,000. The contribution to profit per week from shirt sales is $1,500.

So the profit per season is $30,000 less $2,000 equals $28,000. The closing inventory would

be 250 shirts (I am assuming that we start each match day with 400 shirts and since we

sell 150 we must finish with 250). The book value of the unsold shirts would be $2,500.

Hence if we start from scratch the cash generation would be $25,500 over the season and

we would also have 250 unsold shirts.

If we accept the numbers at face value and if we can afford the initial outlay to purchase

shirts then it is clear that the stall approach is preferable.

What might a risk review surface? Well, there are plenty of thoughts that come to mind.

I will put to one side the questions of whether it is legal to sell shirts from a holdall bag

outside a stadium and whether any tax would be payable.

My risk review on the minimal overheads approach highlights two key factors. First, I

do not see how it is reasonable to assume the same selling price for shirts sold from over

the arm compared with shirts sold via a well stocked and clearly officially endorsed stall.

I would assume that the $20 was a stall price and that the over-the-arm approach would

have to be lower. If the selling price was $16 per shirt the profit would fall by $160 per game

or $3,200 per season. The second risk would be that of lost or stolen shirts. I think that I

would need a partner to help me with the selling and to look after the holdall when I was

busy selling. My financial result would be obvious to the partner and so I would assume

597 Building block 5: Risk

that I would have to share the profit with him (or her). Even with a partner I would still

expect some losses, say two shirts per game which cost $20 per game or $400 per sea-

son. So the overall effect of the risk review is to suggest that the profit estimate should be

approximately halved and that I would need to share this with a partner.

With the stall approach my big risk questions concern the lack of allowance for other

costs. I cannot imagine that a stall selling $3,000 worth of shirts in the period around a

game could have no overheads and would not suffer from some degree of theft. At the very

least it would need a second person to help run it. There may also be days when the owner

was unwell and could not be there. The stock would also need to be taken to and from

the stall on match days. If it was left at the stall there would be too big a chance of all the

shirts being stolen (perhaps to be sold over the arm at a subsequent game!). I would allow

$200 per game for two helpers on the stall and $50 per game to bring the stock to the sta-

dium and then keep it stored safely between games. Other overheads would also have to

be allowed for. Even if the owner did the work for no charge there would be an opportun-

ity cost to consider. Overheads would cover things like insurance, accounting costs and

stall fitting-out costs. My guess is for something like 10% of turnover or $6,000 per year.

Finally, I would also make a guess about how many shirts would still be stolen per game.

If I allow for five shirts stolen per game the cost per season is $1,000. The total effect of all

of these costs is to lower profit by $12,000 per season.

Provided the potential owner has the capital available to fund the purchase of stock this

still looks a very profitable opportunity. So profitable, in fact, that I would still be wonder-

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