Chapter 14, Problem 1P

Consider a project with free cash flows in one year of $130,000 or $180,000, with each outcome being equally likely. The initial investment required for the project is $100,000, and the project’s cost of capital is 20%. The risk-free interest rate is 10%.

1. a. What is the NPV of this project?
2. b. Suppose that to raise the funds for the initial investment, the project is sold to investors as an all-equity firm. The equity holders will receive the cash flows of the project in one year. How much money can be raised in this way-that is, what is the in initial market value of the unlevered equity?
3. c. Suppose the initial $100,000 is instead raised by borrowing at the risk-free interest rate. What are the cash flows of the levered equity, and what is its initial value according to MM?

Summary Introduction

To determine: The net present value (NPV) of the project.

Introduction:

Net present value (NPV)

The net present value (NPV) is the distinction between the present value of cash inflow and the present value of cash outflow for a particular period of time. NPV is used to analyze the profits of a particular investment or project. The difference between the present value of cash outflow and the present value of cash inflow is termed as the net present value.

Answer to Problem 1P

The NPV of the project is $29,167.

Explanation of Solution

Calculation of the NPV of the project:

First, calculate the average cash flow of year 1.

$\begin{array}{c}\text{Average}\text{cash}\text{flow}\text{=}\frac{\text{Sum}\text{of}\text{given}\text{free}\text{cash}{\text{flow}}_1}{2}\\ =\frac{\$130,000+\$180,000}{2}\\ =\$155,000\end{array}$

Therefore, the average cash flow of year 1 is $155,000.

Now, calculate the NPV of the project.

$\begin{array}{c}\text{NPV}=-\text{Initial}\text{cash}\text{flow}+\frac{\text{Average}\text{cash}{\text{flow}}_{\text{1}}}{\left(1+\text{Cost}\text{of}\text{capital}\right)}\\ =-\$100,000+\frac{\$155,000}{\left(1+20\%\right)}\\ =-\$100,000+\$129,166.67\\ =\$29,166.67\end{array}$

Therefore, the NPV of the project $29,166.67.

Summary Introduction

To determine: The initial market value of the unlevered equity.

Introduction:

Unlevered equity defined as a stock of a company that is considered in financing business operations with all equity and no debt, unlevered equity do not have debt as it is a debt source of financing.

Answer to Problem 1P

The initial market value of the unlevered equity is $129,167.67.

Explanation of Solution

Calculation of the initial market value of the unlevered equity:

$\begin{array}{c}\text{Unlevered equity}=\frac{\text{Average}\text{cash}{\text{flow}}_{\text{1}}}{\left(1+\text{Cost}\text{of}\text{capital}\right)}\\ =\frac{\$155,000}{\left(1+20.00\%\right)}\\ =\$129,167.67\end{array}$

Therefore, the initial market value of the unlevered equity is $129,167.67.

Summary Introduction

To determine: The cash flows of the levered equity and the initial value according to Modigliani-Miller (MM).

Introduction:

Modigliani-Miller:

The changes of the distribution of cash flows between equity and debt, without altering the total cash flows of the firm is known as Modigliani- Miller. It is denoted by MM.

Answer to Problem 1P

The cash flows of the levered equity in a strong economy is $70,000 and in a weak economy is $30,000.

Explanation of Solution

Calculation of the equity value in a strong economy:

If the economy is strong, then the cash for year 1 is $180,000 and borrowing is raised at the risk-free interest rate of $100,000; therefore, borrowing is $10,000 and debt payment is $100,000.

$\begin{array}{c}\text{Equity value in a strong economy}\text{=}\left[\text{Cash}\text{flow}\text{in a strong economy}-\left(\text{Debt}+\text{Borrwing}\right)\right]\\ \text{= \$180,000}-\left(\$100,000+\$10,000\right)\\ =\$180,000-\$110,000\\ =\$70,000\end{array}$

Therefore, equity value in a strong economy is $70,000.

Calculation of the equity value in a weak economy:

If the economy is weak, then the cash for year 1 is $130,000 and borrowing is raised at the risk-free interest rate of $100,000; therefore, borrowing is $10,000 and debt payment is $100,000.

$\begin{array}{c}\text{Equity value in a weak economy}\text{=}\text{Cash}\text{flow}\text{in a weak economy}-\text{Debt}-\text{Borrwing}\\ \text{= \$130,000}-\$100,000-\$10,000\\ =\$20,000\end{array}$

Therefore, equity value in strong economy is $20,000.

Calculation of the initial value according to Modigliani-Miller (MM)

$\begin{array}{c}\text{Initial value}=\text{Initial market value of the unlevered equity}-\text{Initial investment}\\ =\$129,167-\$100,000\\ =\$29,167\end{array}$

Therefore, the initial value according to Modigliani-Miller (MM) is $29,167.67.