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Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977

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BuyFindarrow_forward

Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977
Textbook Problem

EXPECTED RETURNS Suppose you won the lottery and had two options: (1) receiving $0.5 million or (2) taking a gamble in which, at the flip of a coin, you receive $1 million if a head comes up but receive zero if a tail comes up.

  1. a. What is the expected value of the gamble?
  2. b. Would you take the sure $0.5 million or the gamble?
  3. c. If you chose the sure $0.5 million, would that indicate that you are a risk averter or a risk seeker?
  4. d. Suppose the payoff was actually $0.5 million that was the only choice. You now face the choice of investing it in a U.S. Treasury bond that will return $537,500 at the end of a year or a common stock that has a 50-50 chance of being worthless or worth $1,150,000 at the end of the year.

l. The expected profit on the T-bond investment is $37,500. What is the expected dollar profit on the stock investment?

2. The expected rate of return on the T-bond investment is 7.5%. What is the expected rate of return on the stock investment?

3. Would you invest in the bond or the stock? Why?

4. Exactly how large would the expected profit (or the expected rate of return) have to be on the stock investment to make you invest in the stock, given the 7.5% return on the bond?

5. How might your decision be affected if, rather than buying one stock for $0.5 million, you could construct a portfolio consisting of 100 stocks with $5,000 invested in each? Each of these stocks has the same return characteristics as the one stock that is, a 50-50 chance of being worth zero or $11,300 at year-end. Would the correlation between returns on these stocks matter? Explain.

a.

Summary Introduction

To determine: The expected value of the gamble.

Portfolio:

The portfolio refers to a group of financial assets like bonds, stocks, and equivalents of cash. The portfolio is held by the investors and financial users. A portfolio is constructed in accordance with the risk tolerance and the objectives of the company.

The expected value:

The expected value refers to the weighted average of the estimated outcomes in different scenarios that are put together.

Explanation

Given,

The two options are (1) obtaining $0.5 million and (2) Playing a gamble in which the amount if the head comes is $1 million and the amount if tail comes is $0 million.

The probability of a head is 0.5 and the probability of a tail is 0.5.

Calculation of the expected value of the gamble:

The formula to calculate the expected value of the gamble is,

Expectedvalueofthegamble=(Amountifheadcomes×Probabilityofcominghead+Amountiftailcomes×<

b.

Summary Introduction

To determine: The decision to be taken.

c.

Summary Introduction

To determine: The indication of whether a person is a risk averter or a risk seeker.

d.1.

Summary Introduction

To determine:

1. The expected dollar profit on the stock investment.

2. The expected rate of return on the stock investment.

3. The reason for investing in the bond or the stock.

4. The expected profit on the stock investment.

5. The effect on the decision if rather than buying one stock a portfolio is constructed and the correlation between the stocks.

2.

Summary Introduction

To determine:

1. The expected dollar profit on the stock investment.

2. The expected rate of return on the stock investment.

3. The reason for investing in the bond or the stock.

4. The expected profit on the stock investment.

5. The effect on the decision if rather than buying one stock a portfolio is constructed and the correlation between the stocks.

3.

Summary Introduction

To determine:

1. The expected dollar profit on the stock investment.

2. The expected rate of return on the stock investment.

3. The reason for investing in the bond or the stock.

4. The expected profit on the stock investment.

5. The effect on the decision if rather than buying one stock a portfolio is constructed and the correlation between the stocks.

4.

Summary Introduction

To determine:

1. The expected dollar profit on the stock investment.

2. The expected rate of return on the stock investment.

3. The reason for investing in the bond or the stock.

4. The expected profit on the stock investment.

5. The effect on the decision if rather than buying one stock a portfolio is constructed and the correlation between the stocks.

5.

Summary Introduction

To determine:

1. The expected dollar profit on the stock investment.

2. The expected rate of return on the stock investment.

3. The reason for investing in the bond or the stock.

4. The expected profit on the stock investment.

5. The effect on the decision if rather than buying one stock a portfolio is constructed and the correlation between the stocks.

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