Question

Consider a project with free cash flows in one year of

$143,408

in a weak market or

$172,483

in a strong​ market, with each outcome being equally likely. The initial investment required for the project is

$75,000​,

and the​ project's unlevered cost of capital is

10%.

The​ risk-free interest rate is

10%.

​(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

$75,000

is instead raised by borrowing at the​ risk-free interest rate. What are the cash flows of the levered equity in a weak market and a strong market at the end of year​ 1, and what is its initial market value of the levered equity according to​ MM?  Assume that the​ risk-free rate remains at its current level and ignore any arbitrage opportunity.

Answer 1

cash flows in one year of $143,408 in a weak market

Probability of Weak Market

Scenario	Probability	Cash Flow	Risk-Weighted Cash Flow
Strong	0.5	172,483	= 0.5* 172,483 = 86241.50
Weak	0.5	143,408	= 0.5*143,048 = 71,524.00
	Expected Cash Flow	= 86241.50 + 71,524.00 = 157,765.50

PV of Expected Cash Flow   = Expected Cash Flow   / ( 1 + cost of capital)

                                           = 157,765.50 / ( 1+10%) = 143,423.18

NPV of the Project = PV of Expected Cash Flow - Initial Cost = 143,423.18 - 75,000​ = 68,423.18

Ans a : NPV of this​ project = 68,423.18

Ans b: Value of Investor to all Equity Firm = NPV of the project = $ 68,423.18

Now

$75,000 is instead raised by borrowing.

So Interest on Loan Amount = Loan Amount * Risk Free Rate = 75,000 * 10% = 7,500

Expected Cash Flow = Expected Cash flow without Borrowing - Interest = 157,765.50 - 7,500 = 150,265.50

PV of Expected Cash Flow   = Expected Cash Flow   / ( 1 + cost of capital)

                                          = 150,265.50 / (1+10%)

                                           = 136,605.00

NPV of the Project = PV of Expected Cash Flow - Initial Cost = 136,605.00 - 75,000​ = 61605.00

Ans c: Value of Investor = 61,605.00