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**Unformatted text preview: **Chapter 18
In-Class Practice Problems on FCF and FCFE Valuation 1) Consider a ﬁrm with year 0 free cash ﬂows (FCF) of $106.77 million. Assume that
these free cash ﬂows are a growing perpetuity, growing at a constant growth rate of
4% per year, forever. Assume that year 0 ended yesterday, and the year 1 free cash
ﬂow is exactly one year away. Other information for the ﬁrm is as follows: Cost of
Debt, R3 = 9%; Cost of Equity, R5 = 21%; Tax Rate = 35%; and the ﬁrm uses
33% debt and 67% equity in its capital structure. ____.————-— a) What is the appropriate discount rate at which the free cash ﬂows of the ﬁrm should
be discounted to compute this ﬁrm’s value? b) What is the value of the ﬁrm? Solution for question 1 a) The appropriate discount rate to discount PCP and obtain ﬁrm value is the WACC. WACC = RS(SI(B+S))) + RB (Bl(B+S))(1—TC) WACC 21*0.67 + 9*0.33*(1— 0.35)
= 16%
b) Value of the Firm is the discounted PV of the FCFs, discounted at WACC. 0 106.77*(1.04) 106.77*(1.04)2 106.77*(1.04)3 I ------------------ ——| ------------------ --1 ------------------ --l ------------------ --| ------- we
PV=? 1 2 3 4 [53(qabgu): debt
491 (516159)”3 7 €010”th V 106.77*(1.04) / (0.16 — 0.04) $925.34 million. 2) Consider a ﬁrm with free cash ﬂows to equity (FCFE) of $167.10 million, $212.73
million, and $92.05 million each year for years 1, 2, and 3, reSpectively. Assume
that the ﬁrst free cash ﬂow to equity of $167.10 million is exactly one year away
from today. Assume also that after year 3 the FCFE of the ﬁrm grows at a constant
rate of 7% each year forever. Other information for the ﬁrm is as follows: Cost of Debt, R3 = 10%; Cost of Equity, R5 = 18%; Tax Rate = 35%; and the firm uses
25% debt and 75% equity in its capital structure. a) What is the appropriate discount rate at which to discount the free cash ﬂows to equityoftheﬁrm? '___—_——' QS:QJ([email protected])% (\-TC)
b) Whatis the shareholder value of the firm? _
Rs: 1% * 13 (Qm ‘92) Solution for Question 2 a) The appropriate discount rate to discount FCFE and obtain shareholder value is R3,
the cost of equity. RS = 18% (given in the problem). 167.10 212.73 92.05 92.05*(1.07)
b) I ------------------ --l ------------------ --| ------------------ --| ------------------ --l ------- "'9
PV:? 1 2 3 4
s .—. 167101018)1 + 212.73/(118)2 + 92.0510.le
+ [(92.05)*(1.07)/(0.18 — 0.07)]!(1.18)3
s = 141.61 + 152.78 + 56.02 + 544.97 $895.38 million. a 3:. 757. UP \{L 3) Consider a ﬁrm with the following cash flows as of year 0: Sales $800 million
Cost of goods sold I 60% of Sales COhS * 1‘ QBOIOOO 1°00
Selling, General, & Admn. Expenses 10% of Sales 1 (50 m
Depreciation 10% of Sales 80 m
Capital Expenditures 10% of Sales 30 m
Net Working Capital 2% of Sales (incurred for the ﬁrst
time in year 0). lb r“
Tax Rate 35%
{01.18 0 30113 [L $351111 3%
250m 9500mow Chou“) qwuem‘ : C119 The Sales of the company is expected to grow at a 15% rate over the next year, and
at a constant rate of 3% annually thereafter (i.e., Sales for year 1 would be 15%
more than the previous year’s Sales, while Sales for years 2 and after would be 3%
more than the previous year’s Sales). Compute the Free Cash Flows (FCF) to the ﬁrm at the end of years 1 through 3. Solution for question 3
./’ Tax Rate 35.00% \ Year 1 Growth Rate in Sales 15.00% ‘4‘ ) Terminal (Year 2+) growth rate of "r 15 Q7.)
Sales 3.00% (309 “(Aqu Year 0 Year 1 "-Year 2 Year 3
1, m Sales 800.00 920.00 947.60 976.03
- Cost of Goods Sold (60%) -— 480.00 552.00 _ 568.56 585.62
- Selling & Admin. Expenses (10%) " 80.00 92.00 -' 94.76 97.60
— Depreciation Expenses (10%) 4 80.00 92.00 94.76 97.60 f :\\ = EBIT 9: 160.00 184.00 189.52 195.21 EBIT*(1—Tax Rate) 104.00 119.60 € 123.19 126.88
+ Depreciation J< 80.00 92.00 194.76 97.60
- Capital Expenditures (10%) ‘04 80.00 92.00 94.76 97.60 Net Working Capital (2%) " lb 16.00 18.40 18.95 19.52
— Increase in NWC ,. 16.00 2.40 I 0.55 0.57
= Free Cash Flow 88.00 117.20 122.64 126.32 @5590
\u \\ '
*\ “Q \ 3&3“ 1
D ‘ J
. . XL r6.»
’le Q“ 4) Consider a firm with the following cash ﬂows as of year 0: Sales $600 million
Cost of goods sold 50% of Sales
Selling, General, & Admn. Expenses 10% of Sales
Depreciation 10% of Sales
Interest Expenses $100 million each year, forever,
except year 2 when it’s $107 million - enema; “Wed ~
Capltal Expendltures 10% of Sales m L m Sécmsed m
Net Working Capital None
Tax Rate 35% The Sales of the company is expected to grow at a 20% annual rate over the next
year, and at a constant rate of 2% annually thereafter (that is, Sales for year 1 will
be 20% more than the year 0’s Sales, while Sales for years 2 and after would be 2%
more than the previous year’s Sales). Further, the company plans some additional borrowing of $60 million in year 1, and would repay this in year 2. After year 2 there are no more additions or subtractions
to the ﬁrm’s debt level. The ﬁrm’s total year 2 interest expense will be 107 million, while it will be $100
million in all other years. What are the Free Cash Flows to Equity (FCFE) to the ﬁrm in years 1, 2, and 3? Solution for question 4 Tax Rate 35.00% ON
Year 1 Growth Rate in Sales 20.00% 6" N; I, 4?
Terminal (Year 2 on) growth rate in 01 Sales 2.00% <—- 9 “Ir £000 Yearo Year 1 Year-2 Year3 5’ r,__/ Net Sales 600.00 720.00 734.40 749.09
- Cost of Goods Sold (50%) _ 300.00 360.00 367.20 374.54
- Selling & Admin. Expenses (10%) 1 60.00 72.00 73.44 74.91
- Depreciation Expenses (10%) — 60.00 72.00 73.44 74.91
= EBIT = 180.00 216.00 220.32 224.73
- Interest Expenses - 100.00 (1004.00; 100.00
= Taxable Income ~: 80.00 116.00 113.32 124.73
- Taxes «7571'? ’— 28.00 40.60 39.66 43.65
= Net Income 3 52.00 75.40 73.66 81.07
+Deprecciation .3, 60.00 72.00 73.44 74.91
- Capex (10%) ~ 60.00 72.00 73.44 74.91
- Increase in NWC __ 0 ~— 0 0 0
+ Increase in debt Ar 0 i 60 '60 0
= FCFE : 52 z: 135 : 14 81 u U
.11— __ ...

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- Spring '14
- VenkatSubramaniam