Question 3

Again ignore any trend or seasonality in the data.  Suppose the company uses exponential smoothing to make forecasts.  

1. What are the forecasts for periods Q2 Year 1 through Q4 Year 5 assuming alpha = 0.3. Assume that the forecast for Q1 Year 1 was 25 units.
2. What are the forecasts for periods Q2 Year 1 through Q4 Year 5 assuming alpha = 0.8.  Assume that the forecast for Q2 Year 1 was 25 units.
3. Compare the accuracies of the forecasts in (a) and (b) using Mean Absolute Percent Error.  Which value of alpha gives us the better forecasts?

Question 4

Now make adjustments for trend and seasonality.

1. Quantify the trend in the time series.  What does the trend equation tell you?  
2. Quantify the seasonality in the time series by calculating seasonality indexes.  What do these indexes tell you?
3. Using the trend and the seasonality information from (a) and (b) make forecasts from Q1 Year 1 through Q4 Year 5.  
4. Use MAPE to calculate the accuracy of your forecasts.

Question 5

1. Compare the preferred method in Question 2, the preferred method in Question 3, and the method in Question 4.  Which one would you choose on the basis of MAPE?
2. Using the method in Question 4 make forecasts for the 4 quarters of Year 6.

The following table lists a portion of Major League Baseball’s (MLB’s) leading pitchers, each pitcher’s salary (In $ millions), and earned run average (ERA) for 2008.

a-1. Estimate the model: Salary = β₀ + β₁ERA + ε. (Negative values should be indicated by a minus sign. Enter your answers, in millions, rounded to 2 decimal places.)Click here for the Excel Data File

Salaryˆ=Salary^=    +  ERA

a-2. Interpret the coefficient of ERA.

• A one-unit increase in ERA, predicted salary decreases by $6.37 million.

• A one-unit increase in ERA, predicted salary increases by $6.37 million.

• A one-unit increase in ERA, predicted salary decreases by $16.70 million.

• A one-unit increase in ERA, predicted salary increases by $16.70 million.

b. Use the estimated model to predict salary for each player, given his ERA. For example, use the sample regression equation to predict the salary for J. Santana with ERA = 2.25. (Round coefficient estimates to at least 4 decimal places and final answers, in millions, to 2 decimal places.)

c. Derive the corresponding residuals. (Negative values should be indicated by a minus sign. Round coefficient estimates to at least 4 decimal places and final answers, in millions, to 2 decimal places.)

Measure Maps

Silver Lining Inc. has a balanced scorecard with a strategy map that shows that delivery time and the number of erroneous shipments are expected to affect the company’s ability to satisfy the customer. Further, the strategy map for the balanced scorecard shows that the hours from ordered to delivered affects the percentage of customers who shop again, and the number of erroneous shipments affects the online customer satisfaction rating. The following information is also available:

• The company’s target hours from ordered to delivered is 20.
• Every hour over the ordered-to-delivered target results in a 0.5% decrease in the percentage of customers who shop again.
• The company’s target number of erroneous shipments per year is no more than 65.
• Every error over the erroneous shipments target results in a 0.5 point decrease in the online customer satisfaction rating and an added future financial loss of $700.
• The company estimates that for every 1% decrease in the percentage of customers who shop again, future profit decreases by $3,000 and market share decreases by 0.3%.
• The company also estimates that for every 1 point decrease in the overall online customer satisfaction rating (on a scale of 1 to 10), future profit decreases by $2,000 and market share decreases by 0.6%.

Using these estimates, determine how much future profit and future market share will change if:

• Average hours from ordered to shipped is 28.5.
• Average shipping time (hours from shipped to delivered) is 14.3.
• Number of erroneous shipments is 80.

Total decrease in future profit $

Round your answer to two decimal places.

Total decrease in future market share %

TOPIC: PORTFOLIO ANALYSIS

show all workings step by step

Question 1

M & M (Pvt) Ltd, a small entity in the mining industry is involved in operations that result in the company having stocks of cash resource. The company has thus decided to create a portfolio of investments comprising of agriculture notes, a debt instrument, and ordinary shares of a company that is into telecommunications. The intended investment in Agriculture Notes is sixty percent and the remainder in ordinary shares. Forecasts have shown the following possibilities in as far as scenarios and their chances of occurring as well as annual returns are concerned.

Required

1. Determine the annual expected return for each scenario for this portfolio.         
2. If the target of the company is to get at least $16 800/ annum from funds invested, does this portfolio presents such prospect overally? Support your answer with workings         
3. Compute the risk of each investment in the portfolio if it were to stand alone and which one has greater risk. Use the standard deviation.
4. Calculate the covariance of returns for the above investment and interpret.
5. Determine the correlation coefficient of investment returns in the portfolio and comment on their potential to reduce diversifiable risk.
6. Determine the portfolio risk as measured by standard deviation and comment on whether the portfolio has been constructed using correct investments.         
7. If the objective of the portfolio manager is not to have expected returns fluctuating by more than $1 500/annum. Can it be concluded that this portfolio is ideal for the company and why?

Question 1
M & M (Pvt) Ltd, a small entity in the mining industry is involved in operations that result
in the company having stocks of cash resource. The company has thus decided to
create a portfolio of investments comprising of agriculture notes, a debt instrument, and
ordinary shares of a company that is into telecommunications. The intended investment
in Agriculture Notes is sixty percent and the remainder in ordinary shares. Forecasts
have shown the following possibilities in as far as scenarios and their chances of
occurring as well as annual returns are concerned.
Scenarios Probability Return on Agric
Notes ($)
Return on Ordinary
Shares ($)
Booming
Economy
0.3 25 000 10 000
Normal
Economy
04 20 000 11 000
Depressed
Economy
0.2 18 000 22 000
Recession 0.1 10 000 28 000
Required
a) Determine the annual expected return for each scenario for this portfolio. (8
marks)
b) If the target of the company is to get at least $16 800/ annum from funds
invested, does this portfolio presents such prospect overally? Support your
answer with workings
c) Compute the risk of each investment in the portfolio if it were to stand alone and
which one has greater risk. Use the standard deviation.
d) Calculate the covariance of returns for the above investment and interpret. (7
marks)
e) Determine the correlation coefficient of investment returns in the portfolio and
comment on their potential to reduce diversifiable risk.
f) Determine the portfolio risk as measured by standard deviation and comment on
whether the portfolio has been constructed using correct investments. (5
marks)
g) If the objective of the portfolio manager is not to have expected returns
fluctuating by more than $1 500/annum. Can it be concluded that this portfolio is
ideal for the company and why?

One of the potential problems with supplementing endangered wild populations with captive bred individuals is that captive bred organisms often have reduced fitness compared to their wild counterparts. Reasons for this are varied, but work suggests it is a combination of reduced genetic variation in captive bred populations (small population sizes and assortative mating leading to reduced genetic variation) as well as reduced fitness due to individuals adapting to a captive environment as opposed to a wild environment. Fundy Atlantic salmon (Salmo salar) are an endangered salmon species whose numbers have declined to a point that scientists started to supplement their wild numbers with captive bred individuals. The question you will answer here is: is supplementing wild salmon populations with captive-bred individuals beneficial if the captive bred individuals have lower fitness than the wild population?

The average number of eggs laid by females in the wild population is about 2,500/female. The captive bred individuals typically exhibit about 30% lower fecundity than wild individuals (some estimates are up to 40% lower, but we will use 30% for purposes of this assignment).

1. If the heritability of fecundity is 0.1, what do you predict the fecundity of the new population will be (assume you add just as many new individuals as were already in the wild population)? (2 points)

2. Now consider if the heritability of fecundity was higher, let’s say 0.3 Now what do you predict the fecundity of the new population will be (using all the original numbers, not after one generation of selection)? (2 points)

3. If fecundity exhibits high heritability, what do you predict will happen to population numbers in this population over time if captive bred individuals are added every year (2 point)?

Lucky Restaurant makes and sells a variety of soups. It also makes and sells whole-grain bread. It anticipates the following financial performance for its bread business during the month of May.

Lucky's management expects its selling price, variable cost per unit, and total fixed cost to remain the same for next year.

Required:

Question 1:

Lucky received a special order for 4,000 loaves of bread. The loaves are identical to the loaves it currently produces. However, because the order is a special order, it will not need to pay the $0.20 per loaf commission to its sales force.  Compute the minimum price per loaf that it should charge for the special order.

Question 2:

Management is considering whether to outsource the production of bread for the months of June and July so that its baker can take a two-month vacation. It believes that outsourcing will not affect bread sales and that bread sales will be the normal 22,000 loaves per month for June and July.

Management has gathered the following information about outsourcing:

• Whole Earth Breads will sell the bread to Lucky for $2.00 per loaf
• If bread production is outsourced, Lucky will be able to save a total of $8,800 in fixed costs($4,400 in June and $4,400 in July)

Compute the most Lucky should be willing to pay per loaf to purchase the break from Whole Earth Breads.

Suppose the manufacturer of a certain drug claims the adverse event rate of the drug is 20% (ie. 20% of people who take the drug have an adverse event), but you think the adverse event rate is higher. (In fact, you think the adverse event rate is 30%.) So, you want to do a study to show the adverse event rate is higher than 20%. If the adverse event rate is really 30% and you obtain a sample of size 10 patients, what is the power of your study for testing Ho: p=0.2 vs Ha: p > 0.2 with a significance level of 0.05? To address this question, answer the following: a) State in words what "power" means in the context of this problem. b) Determine the minimum number of adverse events among 10 patients that would need to happen to reject your null hypothesis. In other words, determine the minimum number of adverse events so that the one-sided p-value is less than 0.05. c) Now, calculate the probability of observing the number of events from part b or more events under the assumption that the true rate is 30%. In other words, calculate the power (the probability of rejecting the null hypothesis if the adverse event rate is really 0.3). d) Now do steps b) and c) to determine the power if the rate were really 70%. e) (*1 point) Compare the power in c) and d). This comparison illustrates (choose the best answer): i) power is higher with alternatives closer to the null hypothesis. ii) power is higher with alternatives farther from the null hypothesis. iii) power is higher with a smaller Type I error rate. iv) power is higher with a larger Type I error rate.

Study Design and Sample Size

The study is a non- randomized controlled trial including eight intervention and six control schools. The study assessed knowledge, attitudes and behaviors of the students three times over a period of eighteen months: March 2009 (Baseline), March 2010 (TI) and September 2010 (t20. We based the sample size calculation on the study objective of assessing whether or not the intervention influenced the time trend in condom use and recent history of sexual intercourse. Sample size calculations were conducted with Wald tests for odds ratio resulting from regression models with two binary variables (intervention/ control and TO/T1 OR T0/T2) and their interaction. For logistic regression models, a minimum of 1,241 observations are required to detect an adjusted odds ratio of 2 or more with 80% power under conservative assumptions of 30 % baseline prevalence of the outcome variable and no changes over time in the control group. For linear regression models, a minimum of 348observations are required to detect a small standardized effect size (Cohen’s d) of 0.3 with 80% power at the 0.05 significance level. Further, we assumed a design effect of 2, due to possibly strong correlation of repeated measurements from the same participant (TO/TI/T2), resulting in a minimum of 2,482 observations required from 1,241 participants. Anticipating a 25% loss t follow –up. We increased the target sample size to 1,655 participants at TO. Eventually for the research, the target sample was increased from 1,655 to 1950.

Question

The investigators described their sample size calculations, which are relatively complex. Did the investigators achieve the desired sample size? Do you think that the study findings are made stronger or weaker by the size of the sample? Explain your answer.

Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $0.30 per gallon for regular gasoline and $0.50 per gallon for premium gasoline. Each gallon of regular gasoline contains 0.3 gallons of grade A crude oil and each gallon of premium gasoline contains 0.6 gallons of grade A crude oil. For the next production period, Southern has 18,000 gallons of grade A crude oil available. The refinery used to produce the gasolines has a production capacity of 50,000 gallons for the next production period. Southern Oil's distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons.

1. Formulate a linear programming model that can be used to determine the number of gallons of regular gasoline and the number of gallons of premium gasoline that should be produced in order to maximize total profit contribution. If required, round your answers to two decimal places.

1. What is the optimal solution?

1. What are the values and interpretations of the slack variables?

1. What are the binding constraints?