Question

I am considering a project with free cash flows in one year of $200,000, $250,000 or $350,000 with equal probability. The cost of the project is $200,000. The project’s cost of capital is 15% and the risk-free rate is 4%. What is the NPV of the project? If the project is financed by all equity, what is the initial market value of the unlevered equity? If the project is financed with 40% debt (at the risk-free rate), what is the expected return on the levered equity?

Answer 1

From the question we get the following information:

	Legend		Option-1	Option-2	Option-3
Year	n	0	1	1	1
Initial Investment (I)	I	$ 200,000
Free Cash Flow	FCF		$ 200,000	$ 250,000	$ 350,000
Cost of Capital	K	15%
Risk Free Rate	R	4%

.

1st Question:

Here we will calculate the NPV of the project:

	Legend			Option-1	Option-2	Option-3
Year	n		0	1	1	1
Initial Investment	I		$ 200,000
Free Cash Flow	FCF			$ 200,000	$ 250,000	$ 350,000
Cost of Capital	K		15%
Present Value of Future Cash Flows	PV	= FCF / ((1+K)^n)		$ 173,913	$ 217,391	$ 304,348
Net Present Value	NPV	= PV - I		$ (26,087)	$    17,391	$ 104,348

2nd Question:

If the project is financed by all equity, it is called to be financed by unlevered equity. In such cases:

Cost of Equity = Cost of Capital

= 15%

Initial Market value of the Unlevered Equity = Discounted value of Net Income

= Net Operating Income / Cost of Equity

= Free Cash Flow / Cost of Equity

Based on the above information and formula we will calculate the Initial Market value of the Unlevered Equity:

	Legend	Formula	Option-1	Option-2	Option-3
Free Cash Flow or Net Operating Income	FCF		$ 200,000	$ 250,000	$ 350,000
Cost of Equity	Ke		15%	15%	15%
Initial Market Value of the Unlevered Equity	E	= FCF / Ke	$1,333,333	$1,666,667	$2,333,333

3rd Question:

If the project is financed with 40% debt (at the risk-free rate), then

Financing done by Debt = Cost of the Project * 40%

= $200,000 * 40%

= $80,000

Interest Expense (i) = Total Amount of Debt * Interest Rate

In this case, Interest Rate = Risk Free Rate = 4%

Interest Expense (i) = Total Amount of Debt * Risk Free Rate

= $80,000 * 4%

= $3,200

Financing done by Equity = Cost of the Project - Financing done by Debt

= $200,000 - $80,000

= $120,000

Since the project is financed by both equity and debt, it's a levered project.

So, the Value of the Levered Project (V)

= Value of the Equity (E) + Value of the Debt (D)

Now, Value of the Equity (E)

= (Net Operating Income - Interest Expense) / Cost of Equity

= (Free Cash Flow - Interest Expense) / Cost of Equity

Now, Value of the Debt (D)

= Interest Expense / Cost of Debt

= Interest Expense / Risk Free Rate

Based on the above information and formula we will calculate Value of the Levered Project:

	Legend	Formula	Option-1	Option-2	Option-3
Cost of Project	C		$     200,000	$     200,000	$     200,000
Debt	d		$        80,000	$        80,000	$        80,000
Cost of Debt	Kd		4%	4%	4%
Interest Expense	i	= d * Kd	$          3,200	$          3,200	$          3,200
Value of the Debt	D	= i / Kd	$        80,000	$        80,000	$        80,000
Free Cash Flow or Net Operating Income	FCF		$     200,000	$     250,000	$     350,000
Cost of Equity	Ke		15%	15%	15%
Value of the Equity	E	= (FCF - i) / Ke	$ 1,312,000	$ 1,645,333	$ 2,312,000
Value of the Levered Project	V	= D + E	$ 1,392,000	$ 1,725,333	$ 2,392,000

Now,

Expected Return on the Levered Equity (LE)

= Net Operating Income - Interest Expense

Based on the above information and formula we will calculate Expected Return on the Levered Equity (LE):

	Legend	Formula	Option-1	Option-2	Option-3
Interest Expense	i		$          3,200	$          3,200	$          3,200
Free Cash Flow or Net Operating Income	FCF		$     200,000	$     250,000	$     350,000
Expected Return on the Levered Equity	LE	= FCF - i	$     196,800	$     246,800	$     346,800