Question

I was just wondering how the present value of future cash flows and discount at 10% columns were calculated in this problem:

At the end of 2012, you forecast the following cash flows (in millions) for a firm with net debt of $759 million:

	2013	2014	2015
Cash flow from operations	$1,450	$1,576	$1,718
Cash investment	1,020	1,124	1,200

You forecast that free cash flow will grow at a rate of 4 percent per year after 2015. Use a required rate of return of 10 percent in answering the following two questions:

1. The firm’s enterprise value (in millions) at the end of 2012 is equal to:
2. The firm’s equity value (in millions) at the end of 2012 is equal to:

Free cash flow = Cash flow from operation - Capital expenditure
Calculation of free cash flow
		2013	2014	2015	Terminal value
Cash flow from operations		$1,450	$1,576	$1,718
Cash investment		$1,020	$1,124	$1,200
Free cash flow		$430	$452	$518	$539	(518*1.04)
Discount factor @10%		0.909091	0.826446	0.751315
Present value of free cash flow		$391	$374	$389
Sum of present value of free cash flow	$1,154
Present value of terminal value [(539/(0.10-0.04)]/(1.10^3)	$6,746
Enterprise Value	$7,900
Less: Value of debt	-759
Equity Value of firm	$7,141
Firm's enterpise value at the end of 2012 is equal to $7,900 million
Firm's equity value at the end of 2012 is equal to $7,141 million

Answer 1

Discount factor is calculated by above formula
1 / (1 + i)^n
(i) is discount rate = 10%
n = period like 1, 2, 3
So, Discount factor for 1st period = 1 / (1+0.10)^1 =					0.909091
for second period = 1 / (1 + 0.10)^2 =					0.826446
for third period = 1 / (1+0.10)^3 =					0.751315
Present value of free cash flow is calculated by multiplying discount factor value with future value.
year 2013 = 430 * 0.909091 =					391
Year 2014 = 452 * 0.826446 =					374
Year 2015 = 518 * 0.751315					389