Question

# Consider a project with free cash flow in one year of \$140,738 or \$162,796​, with either...

Consider a project with free cash flow in one year of

\$140,738

or

\$162,796​,

with either outcome being equally likely. The initial investment required for the project is

\$80,000​,

and the​ project's cost of capital is

18%.

The​ risk-free interest rate is

11%.

​(Assume no taxes or distress​ costs.)

a. What is the NPV of this​ project?

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 initial market value of the unlevered​ equity?  c. Suppose the initial

\$80,000

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​ M&M?

a. What is the NPV of this​ project?

The NPV is

​\$48616.10

​(Round to the nearest​ dollar.)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 initial market value of the unlevered​ equity?  The initial market value of the unlevered equity is

​\$128616.10

​(Round to the nearest​ dollar.)c. Suppose the initial

\$80,000

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​ M&M?

The cash flows of the levered equity and the initial market value of the levered equity according to​ M&M is:  ​(Round to the nearest​ dollar.)

 Date 0 Date 1 Initial Value \$80,000 ​\$ ​\$ ​\$ ​\$ ​\$

Fill in the table

Solution:

Cash flow = ?

Required rate of return=18%

Risk free interest rate=11%

N=TIME period

Initial investment=\$80000

ExPECTED cash flow of project in one year =1/2(cash flow strong economy+weak economy)

=1/2(140738+162796)

=1/2*303534

=\$151767

A)Present value=cash flow/(1+r)n-Initial investment

=151767/(1+0.18)-80000

=128616.10-80000

=\$48616.10

B)Initial market value of the unlevered equity=pre tax earning(1-tax rate)/required rate of return

=151767(1-0)/1.18

=151767/1.18=\$128616.10

C)

 IN \$ DATE0 DATE1 INITIAL VALUE INTEREST CASH FLOW STRONG ECONOMY CASH FLOW WEAK ECONOMY DEBT 80000 88000*11% =8800 88800 88800 LEVERAGED EQUITY 48616.10 48616*18% =8750.8 73996 51938

cash flow available to debt holder=80000(1.11)=88800

cash flow available to equity=140738-88800=51938

=162796-88800=73996

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