DCF Valuation
Table of Content
Time value of money 114
Cost of capital 127
Free Cash Flows (FCF) 137
Sensitivity Analysis 138
DCF-based valuation 139
Terminal Value 145
Equity Value from Firm Value 148
Advantages and Disadvantages of DCF 149
Let’s review the three main concepts used in DCF-based valuation
Time value of money – Cash flows
– Present value (PV) – Net present value (NPV) – Perpetuities
– Discount rate – Discount rate
Cost of Capital – Cost of Equity – CAPM
– Cost of Debt – WACC
Free Cash Flow (FCF)
– Free cash flow to firm (FCFF) – Free cash flow to equity (FCFE)
Which would you take?
– Rs. 2 Crore today?
– Rs. 3 Crore in exactly 5 years?
Assume again:
– Both payments are riskless i.e. it is 100% certain that you will be paid once you make a choice
Assume also that:
– Bank offers 10% interest on 5 year deposits
5 =
+ Crore
Value of Rs. 2 Crore in 5 years: 2*(1+10%)5 =3.22 Crore
Conclusion: Rs. 2 Crore today is greater than Rs. 3 Crore in exactly 5 years!
But how much is Rs. 3 Crore in 5 years worth today?
– Alternatively, how much money deposited at 10% today will equal Rs. 3 Crore in 5 years?
Calculation: Crore
The amount of Rs. 1.86 Crore is known as the Present Value of Rs. 3 Crore in 5 years Crore
86 .
= 1
X
A “cashflow” is time-dated money
– It consists of an amount (in some currency), a date (or a point in time), and a sign (positive or negative)
In order to compare different cashflows, we convert all future cashflows to their present values
Use:
PVt=0 = present value (at time zero) Ct=i = cashflow in the future (in ith year)
rt=i = interest rate for payments in ith year (annualized) – also called discount rate
A simplification of PV formula
– Assume r is same for all time intervals (years)
i
Example 1: One future cashflow
What is the present value of US $100,000 received in year 10 if the discount rate (for ten-year horizons) is 12%
Cash Flow Diagram:
$100,000
Present Value Calculation:
32 , 197 . 32
%) 12 1 (
000 , 100
0 10
=
= +
=
PV
tPV = ?? Year 5 Year 10
Example 2: Effect of discount rate
What would you rather have:
– $10,000 today or $12,000 in exactly 2 years
Scenario 1: Discount rate = 8%
– Present value to have $12,000 in 2 years is:
– Value of $10,0000 in 2 years is:
Example 2: Effect of discount rate
What would you rather have:
– $10,000 today or $12,000 in exactly 2 years
Scenario 2: Discount rate = 10%
– Present value to have $12,000 in 2 years is:
– Value of $10,0000 in 2 years is:
– In this case, take $10,000 today
0
Example 3: Multiple future cash flows
What is the present value of $50,000 received in year 5 and $100,000 received in year 10 if the discount rate is 12%
Net present value combines the initial investment (usually made at time zero) and the PV of expected future cash flows
A positive NPV is a key criteria for a sound investment
∑
=+
What is the NPV for the following set of cash flows (assume r = 8%) – C0 = -$100, C1 = $10, C2 = $10, C3= $110
A perpetual stream of equal cash flows received at equal time intervals is known as a perpetuity
Present value of a perpetuity
C
Example 1: What is the PV of $10 received in perpetuity, starting in one year? Assume discount rate of 10%
– PV = $10/0.1 = $100
r
= C
Sum of infinite geometric series
Example 2: What is the PV of $10 received in perpetuity, starting in 6 years? Assume discount rate of 10%
Value of perpetuity at Year 5:
PV today (t=0):
Example 3: What is the PV of a perpetual cash flow starting at $10 in Year 1 and growing at 5% each year subsequently? Assume discount rate of 10%
g)
g = Growth rate of cashflows r = discount rate
– For our case, PV = 10/(0.1-0.05) = $200
Discount rate used for NPV calculations is the rate of return on the best alternate investment with comparable risk
It is also called the hurdle rate or the opportunity cost of capital
It often comes from the return on a traded asset such as stocks, bonds, etc. with comparable risk.
Risk-less cash flows are discounted using the current rate for US government bonds or bills as they are considered riskless
Corporate capital budgeting decisions are based on expected return on investment
– Investment examples include building a new plant, launching a new product, or acquiring another company
Cost of Capital is the required return necessary to make a capital investment worthwhile
Capital is provided as either debt or equity, hence Cost of capital includes Cost of Debt and Cost of Equity – Cost of Capital = Weighted average of Cost of Debt and Cost of Equity
The Cost of Capital determines the optimal way for the company to raise money (through a stock issue, borrowing, or a mix of the two)
The cost of equity is the rate of return that investors require to make an equity investment in a firm
There are two approaches to estimate the cost of equity – Dividend-growth model
– Risk and return model
Dividend growth model specifies the cost of equity to be the sum of the dividend yield and the expected growth in earnings
– Useful for mature companies that distribute most of the earnings to shareholders as dividends
Risk and return model, on the other hand, tries to answer two questions:
– How do you measure risk?
– How do you translate this risk measure into a risk premium?
We will use Risk and return model to compute Cost of Equity
CAPM or Capital Asset Pricing Model is a risk and return based model for computing expected return on equity (Cost of Equity to the firm)
According to CAPM, expected return of a security or a portfolio equals the return on a risk-free security plus a risk premium
– Re = Rf + b (Rm- Rf)
Rf: Rate of return for a risk-free security
Beta b: measure of equity risk relative to market portfolio
Beta b: measure of equity risk relative to market portfolio
Rm: Expected return on market portfolio (average risk investment)
Rm-Rf: Market risk premium
Example: Compute the expected return on IBM stock, given that risk-free rate is 4%, IBM beta is 1.4, and market risk premium is 5.5%
– Re [IBM] = 4% + 1.4*5.5% = 11.70%
– Implies that in the long-term, investors expect to earn 11.70% return on IBM stock
Rf: Riskfree rate
– Usually the short-term US Govt. T-bill rate or the long-term US Govt. Security rate, since they have no default risk
– The choice between short-term rate and long-term rate depends on the investment horizon
– Firm valuations are over a long-term horizon, so use long-term US Govt. Bond rate for firm valuation
Beta b: measure of equity risk relative to market portfolio – = 1 ... Average risk investment (same as Market Portfolio) – > 1 ... Above Average risk investment
– < 1 ... Below Average risk investment – = 0 ... Riskless investment
Computing Beta:
Approach 1: Regress the historical return on equity (Re) with historical market portfolio return (Rm) Regression output:: Re = a + b Rm
– Where a is the intercept and b, the slope of regression, is the beta of stock and measures the riskiness of the stock.
– This approach has several issues:
High standard error
High standard error
Beta is based on historical business and leverage of the firm, either or both of which may be different in the present
Approach 2: Bottom-up approach
– Find out the businesses that a firm operates in
– Find the unlevered betas of other firms in these businesses
– Take a weighted (by sales or operating income) average of these unlevered betas – Lever up using the firm’s debt/equity ratio
Let’s estimate Intel’s Cost of Equity – Intel equity beta: 1.36
– Current risk-free rate: 4.5% (long-term US Government Bond Rate) – Risk premium = 5.5% (Historical value)
– Expected return on equity using CAPM:
Re = 4.5% + 1.36*5.5% = 11.98%
– Hence, Intel needs to make at least 11.98% as return for their equity investors. This is the hurdle rate for projects, when investments are analyzed from an equity standpoint. In other words, Intel’s Cost of Equity is 11.98%
Cost of Debt is
– the market rate of interest at which the company can borrow today – corrected for the tax benefit it gets for interest payments
Cost of debt = Rd = Interest rate on debt (1 - tax rate)
Caution: Cost of debt is not the interest rate at which the company obtained the old debt that it has on its books
Use one of the following to estimate cost of debt
– If the firm has long-term bonds that are traded, use the current yield to maturity on firm’s bonds as the interest rate in cost of debt calculation
– If the firm is rated, use the rating and a typical default spread on bonds with that rating to estimate the interest rate
– If the firm has recently borrowed long-term from a bank, use the interest rate on the borrowing
– If the firm is not rated and no other information about recent bank loans is available, use interest coverage ratio (EBIT/Interest expense) of the firm to estimate a rating and use the default spread on bonds with that rating to estimate interest rate
– Quick (and dirty) computation of cost of debt: current interest expense/book value of total debt
NOTE: The cost of debt has to be estimated in the same currency as the cost of equity and the cash flows
Market Value of Equity (E) should include the following – Market Value of Shares outstanding
– Market Value of Warrants outstanding
– Market Value of Conversion Option in Convertible Bonds
Market Value of Debt is more difficult to estimate because few firms have only publicly traded debt. There are two solutions:
– Assume book value of debt is equal to market value – Assume book value of debt is equal to market value – Estimate the market value of debt from the book value?
A firm’s Cost of Capital is calculated by taking a weighted average of the firm’s cost of equity and cost of debt.
WACC represents the investor’s opportunity cost for investing in a particular business instead of others with a similar risk.
Cost of capital so computed is called Weighted Average Cost of Capital or WACC
)
E = market value of the firm's equity D = market value of the firm's debt V = E + D
E/V = percentage of financing that is equity D/V = percentage of financing that is debt Tc = corporate tax rate
WACC is used as the discount rate for all cash flows with risk that is similar to that of the overall firm
c d
e
V
V
Example: Compute IBM’s WACC, given:
Re = cost of equity = 11.7%
Rd = cost of debt = 8%
E = market value of the firm's equity = $150 billion D = market value of the firm's debt = $50 billion Assume Tc = 35%
V = E+D = $200 billion
IBM’s Cost of Capital: 10.08%
)
Free Cash Flow to Firm (FCFF) is the cash flow that is generated by company’s operations and available to all the company’s capital providers (investors), including both debt and equity
Computed as operating income less expenses, taxes, and changes in net working capital and investments
Measures company's profitability after all expenses and reinvestments
FCFF is also equal to the sum of CFs paid to or received from all the capital providers (interest, dividends, new borrowing, debt repayments and so on)
FCFF = CF available to all investors = EBIT – taxes – increases in working capital +/- deferred taxes + D&A - Capex
Free Cash Flow to Equity (FCFE) is the portion of FCFF that is available to company’s equity investors.
This is a measure of how much cash can be paid to the equity shareholders of the company after all expenses, reinvestment and debt repayment
FCFE = CF available to equity investors only = Earnings after interest and taxes – increases in working capital +/-deferred taxes + D&A - Capex
Sensitivity Analysis aim at showing the value impact if changing individual key assumptions or the main value drivers. Following is an example of valuation sensitivity to assumptions regarding cost of capital and terminal growth.
Sensitivity Table
Few factors that are subject to sensitivities are:
– Revenue growth, price , Volume – EBIT, EBITDA, PE Margins – Capex, Cost of Capital
There are many lot many other potential sensitivity variables. However, the focus on those factors which have the greatest uncertainty or the greatest value impact.
Sensitivity Table
DCF-based valuation analysis discounts projected (expected) “cash flows” of a firm with an appropriate “discount rate” to determine firm’s value in present time
The fundamental choices for DCF-based valuation – Cash flows to Discount
Free Cash Flows to Equity (FCFE)
Free Cash Flows to Firm (FCFF) – Discount Rate
Cost of Equity
Cost of Capital (WACC) – Base Year Numbers
Current Earnings / Cash Flows
Normalized Earnings / Cash Flows
Firm / Equity Valuation Overview
There are two approaches to valuation: A firm can be valued from two different perspectives –
Firm valuation (Enterprise Value or Transaction Value) – represents the value of all capital invested in business EV = Equity Value + Net Debt
Equity valuation (Market Value or Offer Value) – Value attributable to owners of the company after paying debt.
Firm valuation vs. equity valuation
Firm valuation values the entire business including both debt and equity claims thereby giving value of the company to debt holders and shareholders.
Equity valuation values just the equity claim in business i.e. value of a company to shareholders Assets
Equity vs. Firm Valuation
Equity Valuation: value just the equity stake in the business
– Obtained by discounting expected cash-flows to equity (FCFE), i.e., the residual cash-flows after meeting all operating
expenses, tax obligations, interest and principal payments, and reinvestment needed for future growth
– Discount rate used is the Cost of Equity
∑
=Firm valuation: value the entire business, including, besides equity, the other claimholders in the firm
– Obtained by discounting expected cash-flows to the firm (FCFF), i.e., the residual cash-flows after meeting all operating
expenses, taxes, and reinvestments needed for future growth, but prior to debt payments
– Discount rate used is the weighted average cost of capital (WACC)