The William Companies (WMB) owns and operates natural gas pipelines that deliver 12% of the natural gas consumed in the United States. WMB is concerned that a major hurricane could disrupt its Gulfstream pipeline, which runs 691 miles through the Gulf of Mexico. In the event of a disruption, the firm anticipates a loss of profits of $65 million. Suppose the likelihood of a disruption is 3% per year, and the beta associated with such a loss is –0.25. If the risk-free interest rate is 5% and the expected return of the market is 10%, what is the actuarially fair insurance premium?

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Answer 1

Textbook Question

Chapter 30, Problem 1P

The William Companies (WMB) owns and operates natural gas pipelines that deliver 12% of the natural gas consumed in the United States. WMB is concerned that a major hurricane could disrupt its Gulfstream pipeline, which runs 691 miles through the Gulf of Mexico. In the event of a disruption, the firm anticipates a loss of profits of $65 million. Suppose the likelihood of a disruption is 3% per year, and the beta associated with such a loss is –0.25. If the risk-free interest rate is 5% and the expected return of the market is 10%, what is the actuarially fair insurance premium?

Expert Solution & Answer

Summary Introduction

To determine: Insurance premium.

Introduction:

To manage risk, a firm pays a yearly payment called insurance premium, instead of purchasing the insurance to pay off the losses.

Answer to Problem 1P

The insurance premium is $1.88 million.

Explanation of Solution

Given information:

Loss of profit is $65 million, disruption is 3%, beta is -0.25, risk-free interest rate is 5%, and the expected return is 10%.

The formula to calculate the insurance premium:

Insurance premium=P(Loss)×E(Payment in the Event of Loss)l + rL

Here,

P refers to the probability.

E refers to the expected payment of loss.

rL refers to the appropriate cost of capital.

The formula to calculate the cost of capital:

Cost of capital=Risk-free interest rate−Beta(Expected return−Risk-free interest rate)

Compute the appropriate cost of capital:

Cost of capital=Risk-free interest rate−Beta(Expected return−Risk-free interest rate)=0.05−0.25(0.10−0.05)=0.05−0.0125=0.0375

Hence, the cost of capital is 0.0375.

Compute the insurance premium:

Insurance premium=P(Loss)×E(Payment in the Event of Loss)l + rL=0.03×$65,000,0001+0.0375=$1.88 million

Hence, the insurance premium is $1.88 million.

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Answer 2

Textbook Question

Chapter 30, Problem 1P

The William Companies (WMB) owns and operates natural gas pipelines that deliver 12% of the natural gas consumed in the United States. WMB is concerned that a major hurricane could disrupt its Gulfstream pipeline, which runs 691 miles through the Gulf of Mexico. In the event of a disruption, the firm anticipates a loss of profits of $65 million. Suppose the likelihood of a disruption is 3% per year, and the beta associated with such a loss is –0.25. If the risk-free interest rate is 5% and the expected return of the market is 10%, what is the actuarially fair insurance premium?

Expert Solution & Answer

Summary Introduction

To determine: Insurance premium.

Introduction:

To manage risk, a firm pays a yearly payment called insurance premium, instead of purchasing the insurance to pay off the losses.

Answer to Problem 1P

The insurance premium is $1.88 million.

Explanation of Solution

Given information:

Loss of profit is $65 million, disruption is 3%, beta is -0.25, risk-free interest rate is 5%, and the expected return is 10%.

The formula to calculate the insurance premium:

Insurance premium=P(Loss)×E(Payment in the Event of Loss)l + rL

Here,

P refers to the probability.

E refers to the expected payment of loss.

rL refers to the appropriate cost of capital.

The formula to calculate the cost of capital:

Cost of capital=Risk-free interest rate−Beta(Expected return−Risk-free interest rate)

Compute the appropriate cost of capital:

Cost of capital=Risk-free interest rate−Beta(Expected return−Risk-free interest rate)=0.05−0.25(0.10−0.05)=0.05−0.0125=0.0375

Hence, the cost of capital is 0.0375.

Compute the insurance premium:

Insurance premium=P(Loss)×E(Payment in the Event of Loss)l + rL=0.03×$65,000,0001+0.0375=$1.88 million

Hence, the insurance premium is $1.88 million.

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Answer 3

Textbook Question

Chapter 30, Problem 1P

The William Companies (WMB) owns and operates natural gas pipelines that deliver 12% of the natural gas consumed in the United States. WMB is concerned that a major hurricane could disrupt its Gulfstream pipeline, which runs 691 miles through the Gulf of Mexico. In the event of a disruption, the firm anticipates a loss of profits of $65 million. Suppose the likelihood of a disruption is 3% per year, and the beta associated with such a loss is –0.25. If the risk-free interest rate is 5% and the expected return of the market is 10%, what is the actuarially fair insurance premium?

Expert Solution & Answer

Summary Introduction

To determine: Insurance premium.

Introduction:

To manage risk, a firm pays a yearly payment called insurance premium, instead of purchasing the insurance to pay off the losses.

Answer to Problem 1P

The insurance premium is $1.88 million.

Explanation of Solution

Given information:

Loss of profit is $65 million, disruption is 3%, beta is -0.25, risk-free interest rate is 5%, and the expected return is 10%.

The formula to calculate the insurance premium:

Insurance premium=P(Loss)×E(Payment in the Event of Loss)l + rL

Here,

P refers to the probability.

E refers to the expected payment of loss.

rL refers to the appropriate cost of capital.

The formula to calculate the cost of capital:

Cost of capital=Risk-free interest rate−Beta(Expected return−Risk-free interest rate)

Compute the appropriate cost of capital:

Cost of capital=Risk-free interest rate−Beta(Expected return−Risk-free interest rate)=0.05−0.25(0.10−0.05)=0.05−0.0125=0.0375

Hence, the cost of capital is 0.0375.

Compute the insurance premium:

Insurance premium=P(Loss)×E(Payment in the Event of Loss)l + rL=0.03×$65,000,0001+0.0375=$1.88 million

Hence, the insurance premium is $1.88 million.

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Answer 4

Textbook Question

Chapter 30, Problem 1P

The William Companies (WMB) owns and operates natural gas pipelines that deliver 12% of the natural gas consumed in the United States. WMB is concerned that a major hurricane could disrupt its Gulfstream pipeline, which runs 691 miles through the Gulf of Mexico. In the event of a disruption, the firm anticipates a loss of profits of $65 million. Suppose the likelihood of a disruption is 3% per year, and the beta associated with such a loss is –0.25. If the risk-free interest rate is 5% and the expected return of the market is 10%, what is the actuarially fair insurance premium?

Expert Solution & Answer

Summary Introduction

To determine: Insurance premium.

Introduction:

To manage risk, a firm pays a yearly payment called insurance premium, instead of purchasing the insurance to pay off the losses.

Answer to Problem 1P

The insurance premium is $1.88 million.

Explanation of Solution

Given information:

Loss of profit is $65 million, disruption is 3%, beta is -0.25, risk-free interest rate is 5%, and the expected return is 10%.

The formula to calculate the insurance premium:

Insurance premium=P(Loss)×E(Payment in the Event of Loss)l + rL

Here,

P refers to the probability.

E refers to the expected payment of loss.

rL refers to the appropriate cost of capital.

The formula to calculate the cost of capital:

Cost of capital=Risk-free interest rate−Beta(Expected return−Risk-free interest rate)

Compute the appropriate cost of capital:

Cost of capital=Risk-free interest rate−Beta(Expected return−Risk-free interest rate)=0.05−0.25(0.10−0.05)=0.05−0.0125=0.0375

Hence, the cost of capital is 0.0375.

Compute the insurance premium:

Insurance premium=P(Loss)×E(Payment in the Event of Loss)l + rL=0.03×$65,000,0001+0.0375=$1.88 million

Hence, the insurance premium is $1.88 million.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

Summary Introduction

To determine: Insurance premium.

Introduction:

To manage risk, a firm pays a yearly payment called insurance premium, instead of purchasing the insurance to pay off the losses.

Answer to Problem 1P

The insurance premium is $1.88 million.

Explanation of Solution

Given information:

Loss of profit is $65 million, disruption is 3%, beta is -0.25, risk-free interest rate is 5%, and the expected return is 10%.

The formula to calculate the insurance premium:

Insurance premium=P(Loss)×E(Payment in the Event of Loss)l + rL

Here,

P refers to the probability.

E refers to the expected payment of loss.

rL refers to the appropriate cost of capital.

The formula to calculate the cost of capital:

Cost of capital=Risk-free interest rate−Beta(Expected return−Risk-free interest rate)

Compute the appropriate cost of capital:

Cost of capital=Risk-free interest rate−Beta(Expected return−Risk-free interest rate)=0.05−0.25(0.10−0.05)=0.05−0.0125=0.0375

Hence, the cost of capital is 0.0375.

Compute the insurance premium:

Insurance premium=P(Loss)×E(Payment in the Event of Loss)l + rL=0.03×$65,000,0001+0.0375=$1.88 million

Hence, the insurance premium is $1.88 million.

Answer 8

Expert Solution & Answer

Summary Introduction

To determine: Insurance premium.

Introduction:

To manage risk, a firm pays a yearly payment called insurance premium, instead of purchasing the insurance to pay off the losses.

Answer to Problem 1P

The insurance premium is $1.88 million.

Explanation of Solution

Given information:

Loss of profit is $65 million, disruption is 3%, beta is -0.25, risk-free interest rate is 5%, and the expected return is 10%.

The formula to calculate the insurance premium:

Insurance premium=P(Loss)×E(Payment in the Event of Loss)l + rL

Here,

P refers to the probability.

E refers to the expected payment of loss.

rL refers to the appropriate cost of capital.

The formula to calculate the cost of capital:

Cost of capital=Risk-free interest rate−Beta(Expected return−Risk-free interest rate)

Compute the appropriate cost of capital:

Cost of capital=Risk-free interest rate−Beta(Expected return−Risk-free interest rate)=0.05−0.25(0.10−0.05)=0.05−0.0125=0.0375

Hence, the cost of capital is 0.0375.

Compute the insurance premium:

Insurance premium=P(Loss)×E(Payment in the Event of Loss)l + rL=0.03×$65,000,0001+0.0375=$1.88 million

Hence, the insurance premium is $1.88 million.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Summary Introduction

To determine: Insurance premium.

Introduction:

To manage risk, a firm pays a yearly payment called insurance premium, instead of purchasing the insurance to pay off the losses.

Answer 12

Answer to Problem 1P

The insurance premium is $1.88 million.

Answer 13

Explanation of Solution

Given information:

Loss of profit is $65 million, disruption is 3%, beta is -0.25, risk-free interest rate is 5%, and the expected return is 10%.

The formula to calculate the insurance premium:

Insurance premium=P(Loss)×E(Payment in the Event of Loss)l + rL

Here,

P refers to the probability.

E refers to the expected payment of loss.

rL refers to the appropriate cost of capital.

The formula to calculate the cost of capital:

Cost of capital=Risk-free interest rate−Beta(Expected return−Risk-free interest rate)

Compute the appropriate cost of capital:

Cost of capital=Risk-free interest rate−Beta(Expected return−Risk-free interest rate)=0.05−0.25(0.10−0.05)=0.05−0.0125=0.0375

Hence, the cost of capital is 0.0375.

Compute the insurance premium:

Insurance premium=P(Loss)×E(Payment in the Event of Loss)l + rL=0.03×$65,000,0001+0.0375=$1.88 million

Hence, the insurance premium is $1.88 million.

Answer 14

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