Assignment:
Problem 1. A pharmaceutical firm is thinking of marketing a new drug, and they want to evaluate the profitability of the project after five years. At the beginning of the current year, there are 1,000,000 potential users (customers) of the product. Each customer will use the drug (or a competitor's drug) at most once a year. The number of potential users is forecasted to grow by an average of 5% per year, and they are about 95% confident that the number of potential users will grow each year by between 3% and 7% (this variability can be modeled with a normal random variable).
They are not sure what proportion of potential customers will use the drug during year 1, but their worst-case guess is 20%, most likely 40% and best case use is 70% (model this variability with a triangular random variable). In later years, they feel that the fraction of potential customers using their drug (or a competitor's) will remain the same, but in the year after a competitor enters, they lose 5% of their share for each competitor who enters.
Thus, if in Year 1 two competitors enter the market, in Year 2 the firm's market share will be reduced by 10%. There are ten potential entrants (in addition to the firm). At the beginning of each year, each entrant who has not already entered the market has a 40% chance of entering the market. Each unit of the drug is sold for $2.20 and incurs a variable cost of $0.40. Profits are
discounted by 10% (risk-adjusted rate) annually.
Before marketing the drug, the firm needs to decide on their annual capacity level; that is, the maximum number of units of the drug they will be able to produce per year. Suppose it costs $3.50 to build one unit of annual capacity (up-front cost) and $0.30 per year to operate one unit of capacity (whether or not they use the capacity to produce the drug).
a) Determine the capacity level that maximizes risk-adjusted NPV
b) At the capacity level determined in a), provide a 95% confidence interval for the NPV of the project.
c) At the capacity level determined in a) construct a graph showing the distribution of the NPV.
Problem 2. A highly perishable drug spoils after three days. A hospital estimates that they are equally likely to need between 1 and 9 units of the drug daily. Each time an order for the drug is placed, a fixed cost of $200 is incurred as well as a purchase cost of $50 per unit. Orders are placed at the end of each day and arrive at the beginning of the following day. It costs no money to hold the drug in inventory, but a cost of $100 is incurred each time the hospital needs a unit of the drug and does not have any available. The following policy is being considered:
If we end the day with less than X units (Reorder Point), order enough to bring next day's beginning inventory up to Y (Ceiling Quantity) units.
Develop a Monte Carlo simulation model that describes 30 days of operations. Assuming that X = 4 units, you are to determine a 'good' value for Y to minimize expected monthly costs.
Analyze the model using 5,000 replications per simulation. Assume that there are five units of the drug on hand at the beginning of day 1 and that they were all received that same day. (Hint: you will need to keep track of the age distribution of the units on hand at the beginning of each day. Assume that the hospital uses a FIFO inventory policy. The trick is to get formulas that relate the age of each unit of the drug you have at the beginning of the day to the age of each unit you have at the end of the day.)
Problem 3. Bullock County has never allowed liquor to be sold in restaurants. However, in three months, county residents are scheduled to vote on a referendum to allow liquor to be sold by the drink.
Currently, polls indicate there is a 60% chance that the referendum will be passed by voters. Phil Jackson is a local real estate speculator who is eyeing a closed restaurant building that is scheduled to be sold at a sealed bid auction. Phil estimates that if he bids $1.25 million, there is a 25% chance he will obtain the property; if he bids $1.45 million, there is a 45% chance he will obtain the property; and if he bids $1.85 million, there is an 85% chance he will obtain the property. If he acquires the property and the referendum passes, Phil believes he could then sell the restaurant for $2.2 million. However, if the referendum fails, he believes he could sell the property for only $1.15 million.
a. Develop a decision tree for this problem
b. What is the optimal decision according to the EMV criterion?
c. Create a strategy chart (and table) showing how the optimal decision might change if the probability of the referendum passing varies from 0% to 100% in steps of 10%. Provide (in words) an interpretation of the chart.
d. To which financial estimate in the decision tree is the EMV most sensitive?
Problem 4. During the next two months, an automobile manufacturer must meet (on time) the following demands for trucks and cars: month 1, 400 trucks and 800 cars; month 2, 300 trucks and 300 cars. During each month, at most 1000 vehicles can be produced. Each truck uses two tons of steel, and each car uses one ton of steel. During month 1, steel costs $700 per ton; during month 2, steel is projected to cost $800 per ton. At most 2500 tons of steel can be purchased each month. (Steel can be used only during the month in which it is purchased.) At the beginning of month 1, 100 trucks and 200 cars are in inventory. At the end of each month, a holding cost of $200 per vehicle is assessed. Each car gets 20 miles per gallon (mpg), and each truck gets 10 mpg. During each month, the vehicles produced by the company must average at least 16 mpg.
a. Determine how to meet the demand and mileage requirements at minimum total cost.
b. Use SolverTable to see how sensitive the total cost is to the 16 mpg requirement.
Specifically, let the requirement vary from 14 mpg to 18 mpg in increments of 0.25 mpg.
Explain intuitively what happens when the requirement is greater than 17 mpg.
Problem 5. Kelly Jones is a financial analyst for Wolverine Manufacturing, a company that produces engine bearings for the automotive industry. Wolverine is hammering out a new labor agreement with its unionized workforce. One of the major concerns of the labor union is the funding of Wolverine's retirement plan for their hourly employees. The union believes that the company has not been contributing enough money to this fund to cover the benefits it will need to pay to retiring employees. Because of this, the union wants the company to contribute approximately 1.5 million dollars in additional money to this fund over the next 20 years. These extra contributions would begin with an extra payment of $20,000 at the end of one year with annual payments increasing by 12.35% per year for the next 19 years.
The union has asked the company to set up a sinking fund to cover the extra annual payments to the retirement fund. Wolverine's Chief Financial Officer and the union's chief negotiator have agreed that AAA-rated bonds recently issued by three different companies may be used to establish this fund. The following table summarizes the provision s of these bonds.
|
Company
|
Maturity
|
Coupon payment
|
Price
|
Par value
|
|
AC&C
|
15 years
|
$80
|
$847.88
|
$1.00
|
|
IBN
|
10 years
|
$90
|
$938.55
|
$1.00
|
|
Micro Hard
|
20years
|
$85
|
$872.30
|
$1.00
|
According to this table, Wolverine may buy bonds issued by AC&C for $847.88 per bond. Each AC&C bond will pay the bondholder $80 per year for the next 15 years, plus an extra payment of $1,000 (the par value) in the fifteenth year. Similar interpretations apply to the information for the IBN and MicroHard bonds. A money market fund yielding 5% may be used to hold any coupon payments that are not needed to meet the company's required retirement fund payment in any given year.
Wolverine's CFO has asked Kelly to determine how much money the company would have to invest and which bonds the company should buy to meet the labor union's demands.
a) If you were Kelly, what would you tell the CFO?
b) Suppose that the union insists on including one of the following stipulations into the agreement:
1. No more than half of the total number of bonds purchased may be purchased from a single company.
2. At least 10% of the total number of bonds must be purchased from each of the companies.
To which stipulation should Wolverine agree?