Question Tag: Expected Value

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PM – Nov 2021 – L2 – Q5 – Decision-Making Techniques

Calculate and compare the expected net present value of two projects under uncertainty.

Gaskiya Nigeria Limited is considering whether or not to invest in any of the two projects where the initial cash investment would be ₦13,000,000 for A and ₦14,000,000 for B. The projects would have a five-year life and the estimated annual cash flows are as follows:

Year Project A (N) Project A Outflows (N) Project B (N) Project B Outflows (N)
1 6,000,000 3,000,000 10,000,000 5,000,000
2 8,000,000 4,000,000 9,000,000 4,000,000
3 10,000,000 4,000,000 8,000,000 3,000,000
4 9,000,000 3,000,000 8,000,000 3,000,000
5 6,000,000 3,000,000 4,000,000 2,000,000

The company’s cost of capital is 10%. Several factors could impact the inflows:

  • Factor 1: 20% probability of government measures reducing inflows by 25%.
  • Factor 2: 30% probability of a competitor entering the market, reducing inflows by 10%.
  • Factor 3: 40% probability of stronger-than-expected demand, increasing inflows by 5%.

Required:
a. Calculate the expected net present value of the two projects. (13 Marks)
b. Which of the projects will be more profitable? (2 Marks)

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QTB – May 2017 – L1 – SB – Q6a – Statistics

Calculate the monthly cost of replacing diodes based on failure probability and determine if a student can buy a gown based on expected money.

i. The laptops that are purchased by a company have 742 diodes with a life span of five months. These diodes fail on a regular basis according to the following probability distribution:

Life (months) 1 2 3 4 5
Probability of failure 0.10 0.30 0.35 0.20 0.05

If the cost of replacing a diode is ₦100, calculate the monthly cost of replacing the diodes as they fail. (4 Marks)

ii. Tadet, a student in the Accountancy Department of a Polytechnic, has the following chances of receiving money from her relatives:

  • 45% chance of receiving ₦5,000 from her sister,
  • 33% chance of receiving ₦8,000 from her brother,
  • 16% chance of receiving ₦11,000 from her aunt,
  • 6% chance of receiving ₦15,000 from her uncle.

Determine if Tadet will be able to buy a gown worth ₦8,000 from the money she is expecting from her relatives. (6 Marks)

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QT – Nov 2018 – L1 – Q4b – Measures of Central Tendency

Analyze car ownership data by calculating expected value, standard deviation, and creating a relative percentage histogram.

BomBo, a market researcher at a major African Automobile Company (African Moon), classified households by car ownership. The relative frequencies of households for each category of ownership are shown below:

Number of Cars Per Household Relative Frequencies
0 0.10
1 0.30
2 0.40
3 0.12
4 0.06
5 0.02

Required:
(i) Calculate the expected value of the random variable. (4 marks)

(ii) Calculate the standard deviation of the random variable. (4 marks)

(iii) Draw a Relative Percentage Histogram for the data. (4 marks)

(iv) Using (i)-(iii), comment on the distribution of the data. (3 marks)

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PM – Nov 2021 – L2 – Q5 – Decision-Making Techniques

Calculate and compare the expected net present value of two projects under uncertainty.

Gaskiya Nigeria Limited is considering whether or not to invest in any of the two projects where the initial cash investment would be ₦13,000,000 for A and ₦14,000,000 for B. The projects would have a five-year life and the estimated annual cash flows are as follows:

Year Project A (N) Project A Outflows (N) Project B (N) Project B Outflows (N)
1 6,000,000 3,000,000 10,000,000 5,000,000
2 8,000,000 4,000,000 9,000,000 4,000,000
3 10,000,000 4,000,000 8,000,000 3,000,000
4 9,000,000 3,000,000 8,000,000 3,000,000
5 6,000,000 3,000,000 4,000,000 2,000,000

The company’s cost of capital is 10%. Several factors could impact the inflows:

  • Factor 1: 20% probability of government measures reducing inflows by 25%.
  • Factor 2: 30% probability of a competitor entering the market, reducing inflows by 10%.
  • Factor 3: 40% probability of stronger-than-expected demand, increasing inflows by 5%.

Required:
a. Calculate the expected net present value of the two projects. (13 Marks)
b. Which of the projects will be more profitable? (2 Marks)

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QTB – May 2017 – L1 – SB – Q6a – Statistics

Calculate the monthly cost of replacing diodes based on failure probability and determine if a student can buy a gown based on expected money.

i. The laptops that are purchased by a company have 742 diodes with a life span of five months. These diodes fail on a regular basis according to the following probability distribution:

Life (months) 1 2 3 4 5
Probability of failure 0.10 0.30 0.35 0.20 0.05

If the cost of replacing a diode is ₦100, calculate the monthly cost of replacing the diodes as they fail. (4 Marks)

ii. Tadet, a student in the Accountancy Department of a Polytechnic, has the following chances of receiving money from her relatives:

  • 45% chance of receiving ₦5,000 from her sister,
  • 33% chance of receiving ₦8,000 from her brother,
  • 16% chance of receiving ₦11,000 from her aunt,
  • 6% chance of receiving ₦15,000 from her uncle.

Determine if Tadet will be able to buy a gown worth ₦8,000 from the money she is expecting from her relatives. (6 Marks)

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QT – Nov 2018 – L1 – Q4b – Measures of Central Tendency

Analyze car ownership data by calculating expected value, standard deviation, and creating a relative percentage histogram.

BomBo, a market researcher at a major African Automobile Company (African Moon), classified households by car ownership. The relative frequencies of households for each category of ownership are shown below:

Number of Cars Per Household Relative Frequencies
0 0.10
1 0.30
2 0.40
3 0.12
4 0.06
5 0.02

Required:
(i) Calculate the expected value of the random variable. (4 marks)

(ii) Calculate the standard deviation of the random variable. (4 marks)

(iii) Draw a Relative Percentage Histogram for the data. (4 marks)

(iv) Using (i)-(iii), comment on the distribution of the data. (3 marks)

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