Art-Shop Agency

* Art-Shop Agency

The Art-Shop agency got an order from the “Tube Incorporation” company, wishing to beatify its main office with the sculpture of “Young dryad”. Art manager of the agency stated the value of the sculpture at $100 thousand. Tube Incorporation is ready to pay this price.

At the moment the sculpture is displayed for sale at the commercial exhibition/ which will last for 3 weeks.

During the first week the agency can buy the sculpture for $85 thousand, which gives $15 thousand profit. If it is not sold during the first week, the price will go down to $70 thousand, and agency can by the sculpture at this price next week. Art manager estimates the probability of that as 2/3. He estimates the probability that the sculpture will not be sold for $70 thousand during the second week as 50%.

If it is really not sold during the second week, the price will drop to $50 thousand, and agency can buy the sculpture at this final price.

a.  Draw the decision tree.

b.  What is the optimal strategy and Expected Monetary Value for this strategy?

* EBT production

Chief Production Officer of the company considers two different alternatives for the construction of the new production line, which will produce electron-beam tubes for computer workstations. The total sale of EBT during the of the production line’s life cycle are forcasted as pieces

According to alternative A, the outcome of the good tubes will be 59 pieces out of 100 produced pieces for the normal setup (the probability – 80%) or 64 out of 100 for outstanding setup (the probability – 20%). The initial investment for the alternative A is $1 Mio.

According to alternative B, the outcome of the good tubes will be 64 pieces out of 100 produced pieces for the normal setup (the probability – 80%) or 59 out of 100 for bad setup (the probability – 20%). The initial investment for the alternative A is $1.4 Mio.

The cost of any tube (good or bad) is $80. The good tube will be sold for $145.

-  Which alternative to choose? What is the EMV?

-  The chief engineer proposes the additional stage of the production line that makes it possible choose additional 10% of tubes for correction if the outcome is 59 out of 100. Such a correction will cost $40 per tube and gives additional 7% of good tubes to outcome (so that the total outcome of good tubes will be 66 out o 100).Which alternative (A or B) to choose, if this proposal is taken in account? What is the change in EMV compared to the basic case?

* Shoes

A year’s supply of shoes of a certain popular type must be ordered in advance by a large department store. Each pair costs $30, sells for $60, and can be sold to a discount for $15, if unsold at the end of the year. Stock levels of pairs that could be ordered are divisible by 100. How many pairs of shoes should be ordered if the expected profits are to be maximized? The demand levels, along with their associated probabilities, are:

Number of pairs	Probability
From 200 to 250	0.20
From 250 to 300	0.25
From 300 to 350	0.20
From 350 to 400	0.15
From 400 to 450	0.10
From 450 to 500	0.05
From 500 to 550	0.05

What would you suggest if maximin or minimax regret criteria are preferable for the management of the store?

a.  Which criterion would you prefer? Would it be worth doing to use a consultant for conducting a special marketing research, if the cost of it is $1500?

b.  Will your recommendations change if you take into account that the probabilities are known with the mean relative errors of about 10%?

* New business

You consider creating new consulting firm. The initial investment will be $300 thousand. There is a probabilit of 66% that the demand will high in the first year of operation. If it is so, then experts estimate the probabilities of the high, medium, and low demand in the following years as 60%, 10% and 30% correspondingly. If the demand is law in the first year, then the probabilities of the high, medium, and low demand in the following years will be 20%, 30% and 50% correspondingly.

If the demand is high, then the revenue will be $600 thousand a year; for the law demand the revenue will be $300 thousand a year, and for the medium demand - $450 thousand.

The fixed costs of operaitions (beside of the computer costs) are forcasted at the level of $160 thousand a year, no matter what the level of demand is. You can stop operations at any moment.

If you deceide to start consulting service, you need to solve the problem with computer calculations and simulations, which is the essence of your consulting business. One possible alternative is buying the server at the price $150 thousand. The cost of operations will be $22 thousand per year. The period of obsolescense of the server is 5 years. The other alternative is to rent the computer resources when needed. In this case the variable computer costs will be propotional to the demand and will come to 28% of the difference between revenue and fixed costs ($160 thousand).

If you don’t start consulting business you can invest money in the conpany of your friend. This investmebt is almost free of risk with the interest of 21% per year and with no costs.

Draw the decision tree, which presents all the variants for the next 5 years.

a.  Is it worth starting consultine firm (give the possible outcomes for the periods of 2, 3, 4, and 5 years)

b.  What is better to buy or to rent the computer?

* Palace Construction

General Director of “Palace Construction” company considers business plan of reconstruction old county estate. Tumbledown palace of the country estate is situated in the scenic place on the river bank. It is on sale with a big piece of land for $800 thousand.

Real estate market analysis shows that the old palace can be renovated either as a big mansion for one owner, or as a townhouse for 8 families with luxury apartments on three levels.

The alternative “Mansion” requires $600 thousand investment and, most likely, could be sold for $2 Mio. There is 20% probability that the price can be $2.5 Mio. Although, if the scandal with one of Russian big companies, arisen recently, will not be settled down quickly, the demand for expensive real estate can drop down. In this scenario, the probability of which is estimated as 10% by the experts, the mansion could be sold only in 2 years for $1.5Mio. Besides the conservation of this object will cost $40 thousand per year.

The alternative « Townhouse of 8 apartments» requires $750 thousand investment. All the apartments in the townhouse are going to be sold for $300 thousand each. Those apartments which were not sold immediately could be rent with the marginal profit at $4 thousand per month till the moment of sale. Analyst of the company estimates that 3 apartments will be sold right after the renovation, the other 3 – in 6 months, and the rest of them – in a year.

Commercial manager of the “Palace Construction” company has private information that top managers of various big corporations consider investing money in small hotels or pensions in beautiful places not far from the capital. So he proposed the third alternative of reconstruction.

Alternative “Hotel” for 12 luxury suites requires $1 Mio investment with selling price at $2.4 Mio. Because the piece of land borders with river, the architecture of the company proposes to construct a small wharf with boats and cutter. This requires additional $100 thousand investment, but with the probability 70% will increase the price of the hotel to $2.6 Mio. And to all appearances such a hotel could be sold right after the reconstruction, if salesmen of the company will start looking for a client immediately.

The decision has been made to buy the tumbledown palace with land. The company has $500 thousand available. The rest of money will be taken from the bank as a credit with 12% interest per annum for half a year. The reconstruction will take 6 months.

a.  Draw the decision tree and find the best alternative, if all future cash flows should be discounted with the rate 22% (company’s WACC).

b.  What will be the return on invested capital for the best alternative?

* Big Oil

A “Big Oil” company would like to estimate if it is worth doing to drill an oil well at the lot the company bought earlier in the region that considered being oil bearing one. The drilling made at some neighbour lots showed that the prospects to find out the oil are not so good. The estimated probability to discover oil at a depth of less then 400 meters is just 50%. At that the cost of drilling will be $1.5 mln, and the discounted cash flow from the oil production шы estimated as $ 6 mln (the cost of drilling is not included).

If there is no oil at a depth less then 400 meters, there is a possibility to find it out if we continue to drill. The costs of drilling, depending on depth, and the conditional probabilities to find out oil at next level of depth, if it has not been found at this depth are presented in the Table.

Depth of drilling (meters)	Total cost ($ Mio)	Conditional probabilities	The sum of discounted cash flows from oil production ($ Mio)
400	1.5	50%	6
800	2.0	40%	5
1200	2.6	30%	4
1500	3.3	20%	3

a.  Draw a decision tree, presenting the sequence of decisions the “Big Oil” company has to make.

b.  What depth of the oil well the company should be ready to drill? Is it worth doing to drill till the maximum depth of 1500 meters, or stop at some intermediate depth? What is the expected monetary value of the best decision?

What is the total probability to find out oil by the drillilng till the limit of depth you have choosen? What is the total probability to find out oil by the drillilng till the maximum depth – 1500 meters?

* City Footwear

“City Footwear” company, owns a chain of footwear stores is going to make an order for prospective fall season. In the fall boots, lace-boots and fall shoes give the main part of sales. Director of Marketing & Sales department plans to sell 1 Mio. pairs of woman('s) footwear. He has three different demand estimations for different weather. If the prospective fall is dry, then 200 thousand of boots, 500 thousand of lace-boots and 300 thousand of fall shoes will be sold. If it is wet, then then 600 thousand of boots, 300 thousand of lace-boots and 100 thousand of fall shoes will be most likely sold. For medium scenario the following sales are expected: 300 thousand of boots, 500 thousand of lace-boots and 200 thousand of fall shoes. Which plan should be accepted?

Statistics says that in the region where the company works, wet fall is one case of 10 years, medium conditions happen 3 times for 10 years, and dry fall happens 6 times of 10 years. The lead time for the order is 6 month, so it is impossible to use weather forecast.

One pair of boots sold in the season brings $20 of marginal profit, while unsold pair brings $2 of loss. For lace-boots the profit and loss are $15 and $1.5, and for shoes -$10 and $1 correspondingly.

a.  Which of three possible plans of purchasing should be accepted? What will be the gross expected profit?

b.  The Head of Startegic Development department claims, that the weather is getting more wet during the last several years, but can not provide any quntitative data on that. How does the decision change if the probability of wet fall has really increased?

c.  Financial Director does not believe in optimistic scenarious. So she asks to estimate the gross profit in pessimistic scenario. What would be the best decision under this constraint? #

* Biochemical Lab.

Small company, working on new detergents adn cleansers has a research lab. Recently the scientists of this lab have found a new cleanser for carpeting. Potentialy, this cleanser can bring a considerable profit, but the company has not enough resources to bring it to market.

Thr President of the company considers 3 alternatives.

1. To follow out the reseacrh and try to bring the cleanser to market, using the own funds of the company. This will require as minimium $2 Mio investment to develop the end product and $500 thousand for promotion. The company can afford it. But then, the outcome will depend on how big competitors act. Market experts estimate that there is 65% probability that the company will earn $12 Mio revenue during the next year from sales. Less favourable scenario (the probability is 25%) brings the revenue $6 Mio during the year. And if the competitors will be very active (10% probability) the company will gain only $2 Mio from sales next year. The exeprts prefer not looking futher then 1 year ahead, because the uncertainty becomes too much.

2. To sell the result of sientific research to a big company. It can bring $5 Mio.

3. To find exterior investor and finance the research program and promotion in full. This will require $5.5 Mio for full program of research and development of the end product and $9 Mio for good promotion. $2.5 Mio will invest the coompany itself and $12 will come from exterior investor. The net profit will go fifty-fifty to each of stakeholders. In this case the net profit from sales will be $35 Mio with the probability 50%, $ 25 Mio – with probability 25%, and in pessimistic scenario it will be only $15 Mio.

a.  Draw the decision tree and find the expected profi for each scenario.

b.  Which the decision will you choose? Why?

c.  Provide a sensitivity analysis, varying the probabilities of best and worst outcomes.

* Gold Mine

Imagine, you are the owner of a virgin gold mine. To start extraction you have to inest $Experts estimate that if you start mining, you will extract 1000 oz of gold during 3 years. After that the mine will be exhausted.

By now the price of gold is $500for 1 ounce. In lonf term perspective the price of gold is certainly growing, but there are some fluctuations against this trend.

Experts estimates there is 37 % probability that the price of gold will grow $50 next year, 33% that it will stand the same, and 30% that it will drop $50 down.

Operational costs are $420 per ounce, and weighted average cost of cpital ( the rate of discount for future cash flows) is 10%.

Is it worth doing to start expoitation of the mine?

-  Draw the decision tree, covered three years

-  Should you start mining right now or wait hoping that the price of gold will grow next year?

-  Imagine you can stop mining any time, but for ever. How your concusion will change?

#

* LCD production

Production manager of Korean company, producing LCD screens for computer monitors, analyses different alternatives of modernization of production equipment.

The cheap plan reqires $10 Mio investment. In this case the new equipment will provided 70% of good screens in outcome with the rpobability 90%, and 80% of good screens in outcome with the probability 10%.

The expensive plan reqires $15 Mio investment. In this case the new and more perfect equipment will provided 77% of good screens in outcome with the rpobability 70%, and 70% of good screens in outcome with the probability 30%.

The company estimates that during the life cycle of the new equipment 1 Mio good screens will be produced.

The production cost for any screen (good or bad) is $110. Average price for such screens during the life cycle of production will be $200.

a.  Which alternative (cheap or expensive) to choose? What will be the exepecte monetary value of the best alternative?

b.  Engeneers of the company propose the technology for choosing some of bad screens in the case when the outcome of good screens is 70% for correction. The cost of correction will be $50, and it will provided additional 5% outcome of good screens (so that the total outcome of good screens will be 75%). Draw the decision tree and decide which alternative to choose in this case. How the expected monetary value will change?

#

* Programming Institute

The Programming Institute is in the business of training computer programmers. They guarantee to find each new graduate a job within one week or less they will refund the entire cost of the training. For every graduate successfully placed, they make a profit of $1,000. If the cost of training must be refunded, they loose $2,000. From past experience and by watching the want ads, the institute managers have determined the demand for programmers during a typical one-week period to be:

Demand level	Probability
10	0.10
11	0.10
12	0.30
13	0.25
14	0.20
15	0.05

How large a group should the institute graduate at any one time?

What criterion would you use?

Imagine, that the institute would like to open a totally new specialisation, what number of students would you recommend to enroll?

The local marketing agency offers to provide a special market research on the demand of this type programming specialists and asks for $3000? Would you buy it? Explain.

* Real Estate company

The owner of a small real estate company got an offer to buy urgently 3 apartments all together. The total amount of the deal is $720 thousand. The owner estimates the selling prices for each of the apartments as follows:

The apartment А will be sold for $ 270 thousand.

There are 20% chances that he sells the apartment B $250 thousand, 60% chances that the outcome will be $260 thousand, and 20% chances that it will be $280 thousand.

For the apartment В there are 30 % chances that outcome will be $250 thousand, 50% - $270 thousand, and 20% - $300 thousand.

The first buyer who will pay not less then the minimum price, estimated for each apartment, will get it.

The cost of sales (preparation the apartments for sale, paperwork e. t.a.) will be $10 thousand for each apartment.

The owner of the company has only $50 thousand available for this deal. So he has to take a short-term credit from bank. The terms of this credit is quite strict: the credit should be paid back in 2 months (not earlier) with 4% above the amount of the credit. If the owner returns the money in three month, he has to pay 7% above the amount of credit.

The owner estimates that the apartment A will be definitely sold during the first month. The probability to sell the apartment B (or C) during the first month is 30%, during the second month – 60%. During three months both the apartments will be sold for sure.

a.  Should the owner accept the offer to buy these three apartments?

b.  Draw the decision tree. How much money the owner could expect to get back during the first, the second and the third month.

c.  What is the probability to pay the credit back in two months?

#

* Buying the shop.

The retail company considers buying a new shop. At the moment, to rent this shop costs $8000 per month. Every half a year the price for rent will increase 20%, if the business has grown. If not – the price will stay the same.

Experts estimate the 80% probability for this business to grow during next several years. At that, if there is a growth during the present period, the probability of growth during the next period is 80%. If there is no growth at the present period, the probability of growth during the next period is 50%. If there is no growth during two periods in a row, the probability of growth during the next period is only 20%.

The company has decided to buy the shop.

What the maximum price the company ready to pay for that, if in two years it can be sold for $210 thousand (with the estimated probability 60%) or $150 thousand (with the probability 40%).

Draw the decision tree for 4 periods, half a year each, to compare the alternative “To buy” with alternative “To rent”. Take into account that re-equipment of the shop will require $5000 at the end of the first half a year period, and provide the increase in profit of the shop by

-  $2000 per month during the second half a year period,

-  $2500 per month during the third half a year period

-  $3000 per month during the fourth half a year period

The discount rate for the future cash flows is 12% per half a year period.

* Lots

A manufacturer produces and sells a certain item in round lots of 50 units each. The items have a very limited shelf-life; therefore if items are made but not sold, they have no value. Conversely, if demand exceeds supply during the week (regular production runs are made on Friday of each week for sales the following week), an extra production run can be made. The cost per unit for a regular run is $5, whereas the cost of an extra production run is $7 per unit. All items are sold for $10 per unit, regardless of production cost. Historically, the demand has been for 50, 100, or 150 units each week, so the company makes one of those run sizes. In the past, the manager of the department has made 100 units per week for regular production.

a) Prepare a payoff table showing profits for each of the lot sizes.

b) If probability of demand for 50 units is 0.40, probability of demand for 100 units is 0.50, probability of demand for 150 units is 0.10, and what lot size would you recommend if the goal is to maximize expected profit?

c) A marketing specialist can be hired for part time job to provide a marketing research on permanent basis to predict a demand for the next week. His salary should be $ 100 per week. Is it worth hiring him?

d) Answer the questions a), b), and c) given that disposal cost for unsold items is $1 per unit.