Question
In: Finance
The following are the projected cash flows to the firm over the next five years: Year...
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?
Solutions
Expert Solution
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%
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