QUANTITATIVE METHODS FOR DECISION-MAKING

QMDM – APR 2024 – L2 – Q6 – Rural Bank Investment Proposals NPV

The management of a Rural Bank must decide between two investment proposals using Net Discounted Value (NPV) calculations at a 14% discount rate, explain the term, compute NPVs, and advise on selection.

Question

The Management of a Rural Bank must decide between two proposals, on the basis of the following information:

Proposal	Investment Now	Net Cash Inflow at the End of	1991	1992	1993
A	GHS 80,000		GHS 95,400	GHS 39,400	GHS 12,000
B	GHS 100,000		GHS 35,000	GHS 58,000	GHS 80,000

Assume that on Projects of this type of the company can earn 14 percent per annum. (a) Explain briefly the term Net Discount Value in relation to the projects. (b) Calculate the Net Discounted Value of Proposal A. (c) Calculate the Net Discounted Value of Proposal B. (d) Using the values in (a) and (b), advise Management regarding the proposal that should be selected.

Answer

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Tags: Decision Making, Discounted Cash Flow, Investment Appraisal, Net Present Value, NPV, proposals, rural bank
Level: Level 2

QMDM – APR 2024 – L2 – Q5 – Normal Distribution in Insurance Policy Payments

Using normal distribution for policyholders' lifetimes to calculate probabilities of receiving payments at specific ages in an insurance policy.

Question

An Actuary in an insurance company formulates insurance policies that will be both profitable and marketable. For a particular policy, the lifetimes of the policyholders follow a normal distribution with a mean of 66.20 years and standard deviation of 4.4 years. One of the options with this policy is to receive a payment following the $65^{\mathrm{h}$ birthday and a payment every five years thereafter. Let $X$ be the age at death (in years) of a policyholder (a) Draw the graph of the distribution of $X$ showing clearly the key decision numbers i.e. 66.2 years, 4.4years, 65years, 70years, 75years. (b) Determine the (i) percentage of policyholders who will receive at least one payment using the option above. (ii) percentage of policyholders who will receive two or more payments. (iii) percentage of policyholders who will receive exactly two payments.

Answer

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Tags: chi-squared tests, hypothesis testing, insurance policies, lifetimes, Normal distribution, policyholders, Probability, Z-Score
Level: Level 2

QMDM – APR 2024 – L2 – Q4 – Exponential Smoothing in Time Series Forecasting for Mango Demand

Using monthly demand data for mangos over 15 months, explain exponential smoothing, compute and compare forecasts using alpha=0.1 and 0.4 with initial forecast of 500, describe plots of actual vs forecasts, and comment on suitability.

Question

Kiki, the commercial mango seller has collected demand figures for mangos over the last 15 months in the table below:

Month	Demand
1	470
2	510
3	460
4	490
5	520
6	460
7	1500
8	1450
9	1550
10	1500
11	1480
12	1520
13	1500
14	1490
15	1500

(a) Explain briefly the term “Exponential Smoothing” in Time Series Analysis of the data above. [3 Marks]
(b) Use an initial forecast of 500 to compare Exponential Smoothing Forecasts with Smoothing Constant Values a = 0.1 and a=0.4.
(c) Plot the actual values of the time series and superimpose the forecast for the Smoothing Constant Values a= 0.1 and a=0.4 on the graph of the actual values.
(d) Comment on the suitability of the forecast from the Smoothing Constant Values a= 0.1 and a=0.4.

Answer

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Tags: alpha values, demand data, Exponential Smoothing, Forecasting, plot description, smoothing constant, suitability comment, Time Series Analysis
Level: Level 2

Topic: demonstrate how time-series analysis can be used in business forecasting
Series: APR 2024

QMDM – APR 2024 – L2 – Q3 – Spearman’s Rank Correlation in Employee Aptitude and Interview Ranking

Using data on aptitude scores and interview rankings for 10 employees at a community bank, state when Spearman's rank correlation is suitable, calculate a suitable correlation measure, and comment on the result.

Question

Mumuadu Community Bank Ltd’s Personnel Department now has records on ten (10) recent employees that give an aptitude score and an interview ranking, as displayed below:

Employee	Aptitude Score	Interview Ranking
A	38	10
B	59	5
C	68	8
D	40	7
E	14	9
F	33	1
G	87	2
H	71	3
I	62	3
J	81	6

(a) State the situation under which the Spearman’s Rank Correlation Coefficient is a suitable measure of correlation.
(b) Determine a suitable measure of correlation
(c) Comment on your correlation value in (b) above

Answer

Find Related Questions by Tags, levels, etc.

Tags: aptitude score, bank personnel, Correlation Coefficient, interview ranking, non-parametric, ordinal data, Spearman’s Rank Correlation
Level: Level 2

QMFD – APR 2024 – L2 – Q2 – Measures of Central Tendency and Skewness in Student Spending

Analyze spending data from 18 students on textbooks by sketching mean-median-mode relationships for different distribution shapes, calculating central tendency measures, and commenting on the actual data distribution.

Question

The Dean of Students of a premier private university in Ghana has been given the responses of 18 students to a question on how much money (in GHS) they have spent on textbooks in the last semester:

0 0 19.99 32.98 19.99 19.99 48.20 32.98 0 19.99 0 32.98 19.99 0 24.50 0 32.98 24.50

(a) Sketch graphs (not drawn to scale) which will show the relationship between the mean, median and mode, and the shape of the distribution when the data above is

(i) Negative Skew

(ii) Positive Skew

(iii) Symmetric

(b) Determine, the

(i) Mean

(ii) Median

(iii) Mode

(c) Using your answer in (a) and (b) above, give a detailed comment on the distribution of the responses of the 18 students, to the Dean.

Answer

Find Related Questions by Tags, levels, etc.

Tags: Data Distribution, Mean, Median, Mode, negative skew, positive skew, Skewness, student expenditure, summary statistics, symmetric distribution
Level: Level 2

QMFD – APR 2024 – L2 – Q1 – Linear Programming in Delivery Optimization

Formulate and solve a linear programming problem using graphical method to minimize running costs for two lorries delivering minimum quantities of two products with capacity and usage constraints.

Question

Dokument Courier Services has two Vans which it uses for deliveries. The first (X) can carry 10 of Product A or 4 of Product B. The second (Y) can carry 3 of A or 5 of Product B. Minimum deliveries are 200 of A and 150 of B. In order to maintain roadworthiness, each lorry must be used for a minimum of two journeys per week. Suppose the running costs are GHS20000.00 per journey for Lorry X and GHS 15000.0 per journey for Lorry Y. find the number of deliveries made by each lorry to minimize costs. If the aim of the manager of Dokument is to minimize costs. (a) Identify the decision variables. (b) Formulate the problem into a linear programming problem (LPM). (c) Display the LPM on a graph and shade the critical region.

(d) Use the graphical approach to solving the LPM

Answer

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Tags: critical region, Decision Variables, formulation, graph, graphical method, Linear Programming, Minimization
Level: Level 2

Topic: Linear Programming, Mathematical relationships in business problems
Series: APR 2024

QMDM – APR 2024 – L2 – Q6 – Rural Bank Investment Proposals NPV

The management of a Rural Bank must decide between two investment proposals using Net Discounted Value (NPV) calculations at a 14% discount rate, explain the term, compute NPVs, and advise on selection.

Question

The Management of a Rural Bank must decide between two proposals, on the basis of the following information:

Proposal	Investment Now	Net Cash Inflow at the End of	1991	1992	1993
A	GHS 80,000		GHS 95,400	GHS 39,400	GHS 12,000
B	GHS 100,000		GHS 35,000	GHS 58,000	GHS 80,000

Answer

Find Related Questions by Tags, levels, etc.

Tags: Decision Making, Discounted Cash Flow, Investment Appraisal, Net Present Value, NPV, proposals, rural bank
Level: Level 2

QMDM – APR 2024 – L2 – Q5 – Normal Distribution in Insurance Policy Payments

Using normal distribution for policyholders' lifetimes to calculate probabilities of receiving payments at specific ages in an insurance policy.

Question

Answer

Find Related Questions by Tags, levels, etc.

Tags: chi-squared tests, hypothesis testing, insurance policies, lifetimes, Normal distribution, policyholders, Probability, Z-Score
Level: Level 2

QMDM – APR 2024 – L2 – Q4 – Exponential Smoothing in Time Series Forecasting for Mango Demand

Using monthly demand data for mangos over 15 months, explain exponential smoothing, compute and compare forecasts using alpha=0.1 and 0.4 with initial forecast of 500, describe plots of actual vs forecasts, and comment on suitability.

Question

Kiki, the commercial mango seller has collected demand figures for mangos over the last 15 months in the table below:

Month	Demand
1	470
2	510
3	460
4	490
5	520
6	460
7	1500
8	1450
9	1550
10	1500
11	1480
12	1520
13	1500
14	1490
15	1500

Answer

Find Related Questions by Tags, levels, etc.

Tags: alpha values, demand data, Exponential Smoothing, Forecasting, plot description, smoothing constant, suitability comment, Time Series Analysis
Level: Level 2

Topic: demonstrate how time-series analysis can be used in business forecasting
Series: APR 2024

QMDM – APR 2024 – L2 – Q3 – Spearman’s Rank Correlation in Employee Aptitude and Interview Ranking

Using data on aptitude scores and interview rankings for 10 employees at a community bank, state when Spearman's rank correlation is suitable, calculate a suitable correlation measure, and comment on the result.

Question

Mumuadu Community Bank Ltd’s Personnel Department now has records on ten (10) recent employees that give an aptitude score and an interview ranking, as displayed below:

Employee	Aptitude Score	Interview Ranking
A	38	10
B	59	5
C	68	8
D	40	7
E	14	9
F	33	1
G	87	2
H	71	3
I	62	3
J	81	6

Answer

Find Related Questions by Tags, levels, etc.

Tags: aptitude score, bank personnel, Correlation Coefficient, interview ranking, non-parametric, ordinal data, Spearman’s Rank Correlation
Level: Level 2

QMFD – APR 2024 – L2 – Q2 – Measures of Central Tendency and Skewness in Student Spending

Analyze spending data from 18 students on textbooks by sketching mean-median-mode relationships for different distribution shapes, calculating central tendency measures, and commenting on the actual data distribution.

Question

The Dean of Students of a premier private university in Ghana has been given the responses of 18 students to a question on how much money (in GHS) they have spent on textbooks in the last semester:

0 0 19.99 32.98 19.99 19.99 48.20 32.98 0 19.99 0 32.98 19.99 0 24.50 0 32.98 24.50

(a) Sketch graphs (not drawn to scale) which will show the relationship between the mean, median and mode, and the shape of the distribution when the data above is

(i) Negative Skew

(ii) Positive Skew

(iii) Symmetric

(b) Determine, the

(i) Mean

(ii) Median

(iii) Mode

(c) Using your answer in (a) and (b) above, give a detailed comment on the distribution of the responses of the 18 students, to the Dean.

Answer

Find Related Questions by Tags, levels, etc.

Tags: Data Distribution, Mean, Median, Mode, negative skew, positive skew, Skewness, student expenditure, summary statistics, symmetric distribution
Level: Level 2

QMFD – APR 2024 – L2 – Q1 – Linear Programming in Delivery Optimization

Formulate and solve a linear programming problem using graphical method to minimize running costs for two lorries delivering minimum quantities of two products with capacity and usage constraints.

Question

(d) Use the graphical approach to solving the LPM

Answer

Find Related Questions by Tags, levels, etc.

Tags: critical region, Decision Variables, formulation, graph, graphical method, Linear Programming, Minimization
Level: Level 2

Topic: Linear Programming, Mathematical relationships in business problems
Series: APR 2024

Subject: QUANTITATIVE METHODS FOR DECISION-MAKING

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QMDM – APR 2024 – L2 – Q6 – Rural Bank Investment Proposals NPV

The management of a Rural Bank must decide between two investment proposals using Net Discounted Value (NPV) calculations at a 14% discount rate, explain the term, compute NPVs, and advise on selection.

QMDM – APR 2024 – L2 – Q5 – Normal Distribution in Insurance Policy Payments

Using normal distribution for policyholders' lifetimes to calculate probabilities of receiving payments at specific ages in an insurance policy.

QMDM – APR 2024 – L2 – Q4 – Exponential Smoothing in Time Series Forecasting for Mango Demand

Using monthly demand data for mangos over 15 months, explain exponential smoothing, compute and compare forecasts using alpha=0.1 and 0.4 with initial forecast of 500, describe plots of actual vs forecasts, and comment on suitability.

QMDM – APR 2024 – L2 – Q3 – Spearman’s Rank Correlation in Employee Aptitude and Interview Ranking

Using data on aptitude scores and interview rankings for 10 employees at a community bank, state when Spearman's rank correlation is suitable, calculate a suitable correlation measure, and comment on the result.

QMFD – APR 2024 – L2 – Q2 – Measures of Central Tendency and Skewness in Student Spending

Analyze spending data from 18 students on textbooks by sketching mean-median-mode relationships for different distribution shapes, calculating central tendency measures, and commenting on the actual data distribution.

QMFD – APR 2024 – L2 – Q1 – Linear Programming in Delivery Optimization

Formulate and solve a linear programming problem using graphical method to minimize running costs for two lorries delivering minimum quantities of two products with capacity and usage constraints.

QMDM – APR 2024 – L2 – Q6 – Rural Bank Investment Proposals NPV

The management of a Rural Bank must decide between two investment proposals using Net Discounted Value (NPV) calculations at a 14% discount rate, explain the term, compute NPVs, and advise on selection.

QMDM – APR 2024 – L2 – Q5 – Normal Distribution in Insurance Policy Payments

Using normal distribution for policyholders' lifetimes to calculate probabilities of receiving payments at specific ages in an insurance policy.

QMDM – APR 2024 – L2 – Q4 – Exponential Smoothing in Time Series Forecasting for Mango Demand

Using monthly demand data for mangos over 15 months, explain exponential smoothing, compute and compare forecasts using alpha=0.1 and 0.4 with initial forecast of 500, describe plots of actual vs forecasts, and comment on suitability.

QMDM – APR 2024 – L2 – Q3 – Spearman’s Rank Correlation in Employee Aptitude and Interview Ranking

Using data on aptitude scores and interview rankings for 10 employees at a community bank, state when Spearman's rank correlation is suitable, calculate a suitable correlation measure, and comment on the result.

QMFD – APR 2024 – L2 – Q2 – Measures of Central Tendency and Skewness in Student Spending

Analyze spending data from 18 students on textbooks by sketching mean-median-mode relationships for different distribution shapes, calculating central tendency measures, and commenting on the actual data distribution.

QMFD – APR 2024 – L2 – Q1 – Linear Programming in Delivery Optimization

Formulate and solve a linear programming problem using graphical method to minimize running costs for two lorries delivering minimum quantities of two products with capacity and usage constraints.

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QMDM – APR 2024 – L2 – Q6 – Rural Bank Investment Proposals NPV

The management of a Rural Bank must decide between two investment proposals using Net Discounted Value (NPV) calculations at a 14% discount rate, explain the term, compute NPVs, and advise on selection.

You're reporting an error for "QMDM – APR 2024 – L2 – Q6 – Rural Bank Investment Proposals NPV"

QMDM – APR 2024 – L2 – Q5 – Normal Distribution in Insurance Policy Payments

Using normal distribution for policyholders' lifetimes to calculate probabilities of receiving payments at specific ages in an insurance policy.

You're reporting an error for "QMDM – APR 2024 – L2 – Q5 – Normal Distribution in Insurance Policy Payments"

QMDM – APR 2024 – L2 – Q4 – Exponential Smoothing in Time Series Forecasting for Mango Demand

Using monthly demand data for mangos over 15 months, explain exponential smoothing, compute and compare forecasts using alpha=0.1 and 0.4 with initial forecast of 500, describe plots of actual vs forecasts, and comment on suitability.

You're reporting an error for "QMDM – APR 2024 – L2 – Q4 – Exponential Smoothing in Time Series Forecasting for Mango Demand"

QMDM – APR 2024 – L2 – Q3 – Spearman’s Rank Correlation in Employee Aptitude and Interview Ranking

Using data on aptitude scores and interview rankings for 10 employees at a community bank, state when Spearman's rank correlation is suitable, calculate a suitable correlation measure, and comment on the result.

You're reporting an error for "QMDM – APR 2024 – L2 – Q3 – Spearman’s Rank Correlation in Employee Aptitude and Interview Ranking"

QMFD – APR 2024 – L2 – Q2 – Measures of Central Tendency and Skewness in Student Spending

Analyze spending data from 18 students on textbooks by sketching mean-median-mode relationships for different distribution shapes, calculating central tendency measures, and commenting on the actual data distribution.

You're reporting an error for "QMFD – APR 2024 – L2 – Q2 – Measures of Central Tendency and Skewness in Student Spending"

QMFD – APR 2024 – L2 – Q1 – Linear Programming in Delivery Optimization

Formulate and solve a linear programming problem using graphical method to minimize running costs for two lorries delivering minimum quantities of two products with capacity and usage constraints.

You're reporting an error for "QMFD – APR 2024 – L2 – Q1 – Linear Programming in Delivery Optimization"

QMDM – APR 2024 – L2 – Q6 – Rural Bank Investment Proposals NPV

The management of a Rural Bank must decide between two investment proposals using Net Discounted Value (NPV) calculations at a 14% discount rate, explain the term, compute NPVs, and advise on selection.

You're reporting an error for "QMDM – APR 2024 – L2 – Q6 – Rural Bank Investment Proposals NPV"

QMDM – APR 2024 – L2 – Q5 – Normal Distribution in Insurance Policy Payments

Using normal distribution for policyholders' lifetimes to calculate probabilities of receiving payments at specific ages in an insurance policy.

You're reporting an error for "QMDM – APR 2024 – L2 – Q5 – Normal Distribution in Insurance Policy Payments"

QMDM – APR 2024 – L2 – Q4 – Exponential Smoothing in Time Series Forecasting for Mango Demand

Using monthly demand data for mangos over 15 months, explain exponential smoothing, compute and compare forecasts using alpha=0.1 and 0.4 with initial forecast of 500, describe plots of actual vs forecasts, and comment on suitability.

You're reporting an error for "QMDM – APR 2024 – L2 – Q4 – Exponential Smoothing in Time Series Forecasting for Mango Demand"

QMDM – APR 2024 – L2 – Q3 – Spearman’s Rank Correlation in Employee Aptitude and Interview Ranking

Using data on aptitude scores and interview rankings for 10 employees at a community bank, state when Spearman's rank correlation is suitable, calculate a suitable correlation measure, and comment on the result.

You're reporting an error for "QMDM – APR 2024 – L2 – Q3 – Spearman’s Rank Correlation in Employee Aptitude and Interview Ranking"

QMFD – APR 2024 – L2 – Q2 – Measures of Central Tendency and Skewness in Student Spending

Analyze spending data from 18 students on textbooks by sketching mean-median-mode relationships for different distribution shapes, calculating central tendency measures, and commenting on the actual data distribution.

You're reporting an error for "QMFD – APR 2024 – L2 – Q2 – Measures of Central Tendency and Skewness in Student Spending"

QMFD – APR 2024 – L2 – Q1 – Linear Programming in Delivery Optimization

Formulate and solve a linear programming problem using graphical method to minimize running costs for two lorries delivering minimum quantities of two products with capacity and usage constraints.

You're reporting an error for "QMFD – APR 2024 – L2 – Q1 – Linear Programming in Delivery Optimization"

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