Question

The following are the projected cash flows to the firm over the next five years:

Year	Cash Flows to the Firm (Million)
1	$120
2	$145
3	$176
4	$199
5	$245

The firm has a cost of capital (WACC )of 12% and the cash flows are expected to grow at the rate of 4% in perpetuity?

a) What is the value of the firm today?

b) At what growth rate will the firm have a value of $3000 Million?

Answer 1

Value of firm = PV of Cfs from it.

PV of CFs from Year 6 at Year 5 = CF6 / [ Ke - g ]

= $ 245 * 1.04 / [ 12% - 4% ]

= 254.80 / 8 %

= $ 3185

Value of Firm Today = PV of CFs

Year	CF	PVF @12%	Disc CF
1	$    120.00	0.8929	$    107.14
2	$    145.00	0.7972	$    115.59
3	$    176.00	0.7118	$    125.27
4	$    199.00	0.6355	$    126.47
5	$    245.00	0.5674	$    139.02
5	$ 3,185.00	0.5674	$ 1,807.25
Value of Firm Today			$2,420.75

Part B:

Let X be the PV of CFs from Year 6

Year	CF	PVF @12%	Disc CF
1	$    120.00	0.8929	$                  107.14
2	$    145.00	0.7972	$                  115.59
3	$    176.00	0.7118	$                  125.27
4	$    199.00	0.6355	$                  126.47
5	$    245.00	0.5674	$                  139.02
5	X	0.5674	0.5674X
Value of Firm Today			613.50 + 0.5674X

613.50 + 0.5674 X = 3000

0.5674X = 3000 -613.50

= 2386.5

X = 2386.5 / 0.5674

= 4206.03

P5 = CF5(1+g) / [ Ke - g ]

4206.03 = 245(1+g) / [ 0.12 - g ]

4206.03 [ 0.12 - g ] = 245 + 245g

504.72 - 4206.03g = 245 + 245g

4451.03g = 259.72

g = 259.72 /4451.03

= 0.0584 i.e 5.84%

expected growth Rate is 5.84%