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00025B Stock valuation
Creation date：2024-05-24 17:21:18
Belonging category：金融Finance
Tag 00025B
Stock valuation

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CRICOS code 00025B

Stock valuation (2)

What is free cash flow?
• Cash flows into the company as it sells its products or provide services
• Cash flows out as it pays its cash operating expenses (e.g.. salaries and taxes, admin costs)
• Then the firm takes the leftover cash and makes short-term net investments in working capital
(e.g. inventory and receivables) and long-term net investments in property, plant and
equipment (PP&E).
• Remaining cash is free cash flow to the firm (FCFF) and available to pay out to the firm’s
investors
- Bondholders
- Shareholders
• The cash that is left after the firm has met all its obligations to other investors is free cash
flow to equity (FCFE).
Free cash flow model
2
CRICOS code 00025B
 Firm value = FCFF discounted at the WACC
 Equity value = FCFE discounted at the required return on equity
 Equity value = firm value – market value of debt
Why use free cash flow model?
• Many firms pay no, or low, cash dividends.
• Dividends are paid at the discretion of the board of directors, hence may be poorly aligned with
the firm’s long-run profitability.
• Free cash flows may be more related to long-run profitability of the firm as compared to
dividends.
Free cash flow model
3
CRICOS code 00025B
Calculate FCFF from net income
FCFF = NI + [Interest*(1 – tax rate)] + NCC – FCInv – WCInv
NCC: non cash charge
- Added back to net income because they represent expenses that reduced reported net
income but didn’t actually result in an outflow of cash.
- Depreciation and amortisation
FCInv: Fixed capital investment
- Investments in fixed capital do not appear on the income statement, they do represent cash
leaving from the firm.
- FCInv = capital expenditure – proceeds from sales of long-term assets
WCInv: working capital investment
- Investment in net working capital.
Free cash flow model
[Presentation Title] [Date] 4
CRICOS code 00025B
 Calculate FCFF from EBIT and EBITDA
 FCFF = EBIT(1-tax rate) + Dep – FCInv – WCInv
 FCFF = EBITDA(1-tax rate) + Dep*tax rate – FCInv – WCInv
 Calculate FCFE directly from FCFF
 FCFE = FCFF – [Interest*(1 – tax rate)] + net borrowing
 Net borrowing = new debt issues – debt repayments
 Free cash flow valuation model
 Single stage constant growth model
 Two, three or multi-stage model
Free cash flow model
5
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CRICOS code 00025B
Free cash flow model
6
where market value of equity and debt is applied
• Firm value is the present value of expected free cash flow to the firm (FCFF), discounted
at the weighted average cost of capital (WACC).
• Replacing FCFF and WACC using FCFE and required return on equity, respectively gives
the equity value.
• Equity value is firm value less the market value of debt.
• Under consistent assumptions about growth and capital structure, DDM and FCFF provide
exactly the same valuation.
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k
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CRICOS code 00025B
• Firm value assuming constant growth in the terminal state
Free cash flow to the firm model (2)
7
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CRICOS code 00025B
Example:
Zoe Ltd had a net profit margin of 25% on revenues of $30 million this year. Fixed capital
investment was $3million. Depreciation was also $3 million. Working capital investment is 7.5%
of total sales. Net income, fixed capital investment, depreciation, interest expense, and sales
are expected to increase at 10% per year for the next three years, after which, the growth will be
stable at 4% per year. Tax rate is 40% and the company has 1 million shares outstanding. The
company’s long term debt has market value of $30million. Interest rate is 10%. What is the firm
value and the firm’s equity value. Use FCFF model and assume WACC is 18% during the high-
growth stage and 13% during the stable stage.
Free cash flow
8
CRICOS code 00025B
Residual income
• The net income of a firm less a charge that measures stockholders’ opportunity cost of capital.
• Recognises the cost of equity capital in the measurement of income.
• Explicitly deducts all capital costs, unlike accounting net income which only deducts cost of
debt.
Et = expected EPS for year t
ke = required return on equity
Bt-1 = book value of equity in year t –1
Residual income model
9
11 )()(   tetett BkROEBkERI
CRICOS code 00025B
 Equity value is the book value of equity plus the present value of expected residual income.
 Residual income is the excess earnings above what would be earned if the book value of
equity earned a return just equal to the cost of equity capital.
 Book value of equity is typically well below market value of equity, so it is usual to expect
positive residual income.
Case category
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CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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