Fountain Corporation's economists estimate that a good business environment and a bad business environment are equally likely for the coming year. The managers of the company must choose between two mutually exclusive projects. Assume that the project the company chooses will be the firm's only activity and that the firm will close one year from today. The company is obligated to make a $5,400 payment to bondholders at the end of the year. The projects have the same systematic risk but different volatilities. Consider the following information pertaining to the two projects: Economy Probability .50 .50 Bad Good Low-Volatility Project Payoff $5,400 6,550 High-Volatility Project Payoff $ 4,800 7,150 a. What is the expected value of the company if the low-volatility project is undertaken? The high-volatility project? (Do not round intermediate calculations and round your answers to the nearest whole number, e.g., 32.) b. What is the expected value of the company's equity if the low-volatility project is undertaken? The high-volatility project? (Do not round intermediate calculations and round your answers to the nearest whole number, e.g., 32.) c. Which project would the company's stockholders prefer if they are risk neutral? d. Suppose bondholders are fully aware that stockholders might choose to maximize equity value rather than total company value and opt for the high-volatility project. To minimize this agency cost, the company's bondholders decide to use a bond covenant to stipulate that the bondholders can demand a higher payment if the company chooses to take on the high-volatility project. What payment to bondholders would make stockholders indifferent between the two projects? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
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Chapter1: Investments: Background And Issues
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**Fountain Corporation's Project Evaluation**

Fountain Corporation’s economists predict an equal chance of either a good or bad business environment next year. The company must choose between two mutually exclusive projects, as this will be the sole activity for the firm, which is projected to close in one year. A mandatory payment of $5,400 to bondholders is due at year's end. Both projects share the same systematic risk but differ in volatility.

**Project Details:**

| Economy | Probability | Low-Volatility Project Payoff | High-Volatility Project Payoff |
|---------|-------------|-------------------------------|--------------------------------|
| Bad     | 0.50        | $5,400                        | $4,800                         |
| Good    | 0.50        | $6,550                        | $7,150                         |

**Questions:**

a. **Expected Value of the Company**
   - Calculate the expected value if the low-volatility project is chosen.
   - Calculate the expected value if the high-volatility project is chosen.
   - *Note: Do not round intermediate calculations. Round answers to the nearest whole number.*

b. **Expected Value of the Company's Equity**
   - Determine the expected value of equity with the low-volatility project.
   - Determine the expected value of equity with the high-volatility project.
   - *Note: Do not round intermediate calculations. Round answers to the nearest whole number.*

c. **Stockholder Preference**
   - Consider which project stockholders would prefer if they are risk-neutral.

d. **Bondholder Payment**
   - Assume bondholders realize stockholders may favor maximizing equity value, leading to the high-volatility project preference. Bondholders utilize a bond covenant mandating increased payments if this higher-risk project is chosen.
   - Calculate the bondholder payment that would equalize stockholder preference between projects.
   - *Note: Do not round intermediate calculations. Round answers to the nearest whole number.*

This exercise involves expected value calculation and risk assessment, providing insights into decision-making under uncertain economic conditions.
Transcribed Image Text:**Fountain Corporation's Project Evaluation** Fountain Corporation’s economists predict an equal chance of either a good or bad business environment next year. The company must choose between two mutually exclusive projects, as this will be the sole activity for the firm, which is projected to close in one year. A mandatory payment of $5,400 to bondholders is due at year's end. Both projects share the same systematic risk but differ in volatility. **Project Details:** | Economy | Probability | Low-Volatility Project Payoff | High-Volatility Project Payoff | |---------|-------------|-------------------------------|--------------------------------| | Bad | 0.50 | $5,400 | $4,800 | | Good | 0.50 | $6,550 | $7,150 | **Questions:** a. **Expected Value of the Company** - Calculate the expected value if the low-volatility project is chosen. - Calculate the expected value if the high-volatility project is chosen. - *Note: Do not round intermediate calculations. Round answers to the nearest whole number.* b. **Expected Value of the Company's Equity** - Determine the expected value of equity with the low-volatility project. - Determine the expected value of equity with the high-volatility project. - *Note: Do not round intermediate calculations. Round answers to the nearest whole number.* c. **Stockholder Preference** - Consider which project stockholders would prefer if they are risk-neutral. d. **Bondholder Payment** - Assume bondholders realize stockholders may favor maximizing equity value, leading to the high-volatility project preference. Bondholders utilize a bond covenant mandating increased payments if this higher-risk project is chosen. - Calculate the bondholder payment that would equalize stockholder preference between projects. - *Note: Do not round intermediate calculations. Round answers to the nearest whole number.* This exercise involves expected value calculation and risk assessment, providing insights into decision-making under uncertain economic conditions.
**Table of Financial Outcomes**

This table outlines different financial outcomes related to company value, equity value, stockholder preferences, and payments, considering both low-volatility and high-volatility projects.

1. **Expected Company Value with Low-Volatility Project**  
   - Description: The probable valuation of a company investing in a project with minimal risk and fluctuation.
   
2. **Expected Company Value with High-Volatility Project**  
   - Description: The probable valuation of a company investing in a project with higher risk and potential fluctuations.
   
3. **Expected Equity Value with Low-Volatility Project**  
   - Description: The anticipated valuation of shareholders' equity in a low-risk project.
   
4. **Expected Equity Value with High-Volatility Project**  
   - Description: The anticipated valuation of shareholders' equity in a high-risk project.
   
5. **The Company’s Stockholders Prefer if they are Risk Neutral**  
   - Description: Preferences of the company's stockholders if their decisions are unaffected by risk.
   
6. **Payment to Stockholders**  
   - Description: The distribution of financial returns or dividends to stockholders.

Each row includes a blank box, indicating fields or levels that need to be filled in, likely representing numerical values, assessments, or conclusions based on further analysis or application.
Transcribed Image Text:**Table of Financial Outcomes** This table outlines different financial outcomes related to company value, equity value, stockholder preferences, and payments, considering both low-volatility and high-volatility projects. 1. **Expected Company Value with Low-Volatility Project** - Description: The probable valuation of a company investing in a project with minimal risk and fluctuation. 2. **Expected Company Value with High-Volatility Project** - Description: The probable valuation of a company investing in a project with higher risk and potential fluctuations. 3. **Expected Equity Value with Low-Volatility Project** - Description: The anticipated valuation of shareholders' equity in a low-risk project. 4. **Expected Equity Value with High-Volatility Project** - Description: The anticipated valuation of shareholders' equity in a high-risk project. 5. **The Company’s Stockholders Prefer if they are Risk Neutral** - Description: Preferences of the company's stockholders if their decisions are unaffected by risk. 6. **Payment to Stockholders** - Description: The distribution of financial returns or dividends to stockholders. Each row includes a blank box, indicating fields or levels that need to be filled in, likely representing numerical values, assessments, or conclusions based on further analysis or application.
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