**QUESTION ONE**

Platinum Real Estate Consulting Group, owner of a number of properties dotted around Lusaka is faced with a choice of:

- A large-scale investment (A) to improve its flats. This could produce a substantial pay-off in terms of increased revenue net of costs but will require an investment of K1, 400,000. After extensive market research it is considered that there is a 40% chance that a pay-off of K2, 500,000 will be obtained, but there is a 60% chance that it will be only K800, 000.
- A smaller scale project (B) to re-decorate its premises. At K500, 000 this is less costly but will produce a lower pay-off. Research data suggests a 30% chance of a gain of K1, 000,000 but a 70% chance of it being only K500, 000.
- Continuing the present operation without change (C). It will cost nothing, but neither will it produce any pay-off. Clients will be unhappy and it will become harder and harder to rent the flats out when they become free.

**REQUIRED:**

- Draw the decision tree representing the options open to Platinum Real Estate Consulting Group
**.** - Calculate the expected values.
- Calculate the net expected value.
- How will a decision tree help the taking of the decision?

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**QUESTION TWO**

An investor has the choice to accept a guaranteed K9 million cash inflow or an option with the following expectations:

- A 30% chance of receiving K7.5 million
- A 45% chance of receiving K15.5 million
- A 25% chance of receiving K4 million

Assume the risk-adjusted rate of return used to discount this option is 13.75% and the risk-free rate is 3.25%.

- What is certainty equivalent and why is it important in financial risk management.
- Calculate the expected cash flow of this investment.
- Calculate the certainty equivalent cash flow.
- If the investor prefers to avoid risk, what guaranteed option should accept?

**QUESTION THREE**

- You are concerned about the possibility of experiencing on Coronavirus (COVID-19) during the next year. The probability of a COVID-19 outbreak is 0.5%. Your local insurer offers to pay you K300, 000 if a registered member of your family contracted COVID-19. The insurance policy costs K1, 500.00. If the inflation rate is forecast to be 10% during the next year, is the price of insurance policy fair.
- A coin is biased so that it has a 60% chance of landing on heads. If it is thrown three times, find the probability of getting
- Three heads
- 2 heads and a tail
- At least one head

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