Download CHAPTER 15 FIRM VALUATION: COST OF CAPITAL AND ... and more Study notes Finance in PDF only on Docsity!
CHAPTER 15
FIRM VALUATION: COST OF CAPITAL AND APV APPROACHES
In the last two chapters, we examined two approaches to valuing the equity in the firm -- the dividend discount model and the FCFE valuation model. This chapter develops another approach to valuation where the entire firm is valued, by either discounting the cumulated cashflows to all claim holders in the firm by the weighted average cost of capital (the cost of capital approach) or by adding the marginal impact of debt on value to the unlevered firm value (adjusted present value approach). In the process of looking at firm valuation, we also look at how leverage may or may not affect firm value. We note that in the presence of default risk, taxes and agency costs, increasing leverage can sometimes increase firm value and sometimes decrease it. In fact, we argue that the optimal financing mix for a firm is the one that maximizes firm value.
The Free Cashflow to the Firm The free cashflow to the firm is the sum of the cashflows to all claim holders in the firm, including stockholders, bondholders and preferred stockholders. There are two ways of measuring the free cashflow to the firm (FCFF). One is to add up the cashflows to the claim holders, which would include cash flows to equity (defined either as free cash flow to equity or dividends), cashflows to lenders (which would include principal payments, interest expenses and new debt issues) and cash flows to preferred stockholders (usually preferred dividends). FCFF = Free Cashflow to Equity
- Interest Expense (1 - tax rate) + Principal Repayments - New Debt Issues
- Preferred Dividends Note, however, that we are reversing the process that we used to get to free cash flow to equity, where we subtracted out payments to lenders and preferred stockholders to estimate the cash flow left for stockholders. A simpler way of getting to free cash flow to the firm is to estimate the cash flows prior to any of these claims. Thus, we could begin
with the earnings before interest and taxes, net out taxes and reinvestment needs and arrive at an estimate of the free cash flow to the firm. FCFF = EBIT (1 - tax rate) + Depreciation - Capital Expenditure - ∆ Working Capital Since this cash flow is prior to debt payments, it is often referred to as an unlevered cash flow. Note that this free cash flow to the firm does not incorporate any of the tax benefits due to interest payments. This is by design, because the use of the after-tax cost of debt in the cost of capital already considers this benefit and including it in the cash flows would double count it.
FCFF and other cashflow measures The differences between FCFF and FCFE arise primarily from cashflows associated with debt -- interest payments, principal repayments, new debt issues and other non-equity claims such as preferred dividends. For firms at their desired debt level, which finance their capital expenditures and working capital needs with this mix of debt and equity. As for the use of debt issues to finance principal repayments, the free cashflow to the firm will exceed the free cashflow to equity. One measure that is widely used in valuation is the earnings before interest, taxes, depreciation and amortization (EBITDA). The free cashflow to the firm is a closely related concept but it takes into account the potential tax liability from the earnings as well as capital expenditures and working capital requirements. Three measures of earnings are also often used to derive cash flows. The earnings before interest and taxes (EBIT) or operating income comes directly from a firm’s income statements. Adjustments to EBIT yield the net operating profit or loss after taxes (NOPLAT) or the net operating income (NOI). The net operating income is defined to be the income from operations, prior to taxes and non-operating expenses. Each of these measures is used in valuation models and each can be related to the free cashflow to the firm. Each, however, makes some assumptions about the relationship between depreciation and capital expenditures that are made explicit in the Table 15.1. Table 15.1: Free Cash Flows to the Firm: Comparison to other measures
Cashflow used Definition Use in valuation
life but no growth.
Growth in FCFE versus Growth in FCFF Will equity cashflows and firm cashflows grow at the same rate? Consider the starting point for the two cash flows. Equity cash flows are based upon net income or earnings per share – measures of equity income. Firm cash flows are based upon operating income – i.e. income prior to debt payments. As a general rule, you would expect growth in operating income to be lower than growth in net income, because financial leverage can augment the latter. To see why, let us go back to the fundamental growth equations we laid out in Chapter 11. Expected growth in net income = Equity Reinvestment rate * Return on Equity Expected growth in operating income = Reinvestment Rate * Return on Capital We also defined the return on equity in terms of the return on capital: Return on Equity =
Return onCapital EqutiyDebt (Return oncapital-After-taxcostofdebt)
When a firm borrows money and invests in projects that earn more than the after-tax cost of debt, the return on equity will be higher than the return on capital. This, in turn, will translate into a higher growth rate in equity income at least in the short term. In stable growth, though, the growth rates in equity income and operating income have to converge. To see why, assume that you have a firm whose revenues and operating income and growing at 5% a year forever. If you assume that the same firm’s net income grows at 6% a year forever, the net income will catch up with operating income at some point in time in the future and exceed revenues at a later point in time. In stable growth, therefore, even if return on equity exceeds the return on capital, the expected growth will
be the same in all measures of income.
Firm Valuation: The Cost of Capital Approach
(^1) The equity reinvestment rate and firm reinvestment rate will adjust to ensure that this happens. The equity reinvestment rate will be a lower number than the firm reinvestment rate in stable growth for any levered firm.
The value of the firm is obtained by discounting the free cashflow to the firm at the weighted average cost of capital. Embedded in this value are the tax benefits of debt (in the use of the after-tax cost of debt in the cost of capital) and expected additional risk associated with debt (in the form of higher costs of equity and debt at higher debt ratios). Just as with the dividend discount model and the FCFE model, the version of the model used will depend upon assumptions made about future growth.
Stable Growth Firm As with the dividend discount and FCFE models, a firm that is growing at a rate that it can sustain in perpetuity – a stable growth rate – can be valued using a stable growth model.
The Model A firm with free cashflows to the firm growing at a stable growth rate can be valued using the following equation:
Value of firm = n
1 WACC- g
FCFF
where, FCFF1 = Expected FCFF next year WACC = Weighted average cost of capital gn = Growth rate in the FCFF (forever)
The Caveats There are two conditions that need to be met in using this model. First, the growth rate used in the model has to be less than or equal to the growth rate in the economy – nominal growth if the cost of capital is in nominal terms, or real growth if the cost of capital is a real cost of capital. Second, the characteristics of the firm have to be consistent with assumptions of stable growth. In particular, the reinvestment rate used to estimate free cash flows to the firm should be consistent with the stable growth rate. The best way of enforcing this consistency is to derive the reinvestment rate from the stable growth rate.
Rs 3432.1 million rupees and book value of debt of Rs. 1377.2 million at the end of 1998. The firm’s return on capital can be estimated as follows:
Return on capital
( )
( ) (^9). 20 %
- 1 1377. 2
Book valueofdebt Book valueofEquity
EBIT 1 - t
= +− =
The firm is in stable businesses and expects to grow only 5% a year.3 Assuming that it maintains its current return on capital, the reinvestment rate for the firm will be:
Reinvestment rate = (^) ROCg^ =9.20%5% =54.34%
The firm’s expected free cash flow to the firm next year can be estimated as follows: Expected EBIT (1-t) next year = 632.2 (1-0.30) (1.05) = 464.
- Expected Reinvestment next year = EBIT(1-t) (Reinvestment rate) = 464.7 (0.5435) = 252. Expected Free Cash flow to the firm = 212. To estimate the cost of capital, we use a bottom-up beta (adjusted to 1.17 to reflect TI’s additional leverage), a nominal rupee riskfree rate of 10.50% and a risk premium of 9.23% (4% for the mature market premium and 5.23% for country risk in India). The cost of equity can then be estimated as follows: Cost of Equity = 10.5% + 1.17 (9.23%) = 21.30% The cost of debt for Tube Investments is 12%, which in conjunction with their market debt to capital ratio of 44.19% - the market value of equity at the time of the valuation was Rs.2282 million and the market value of debt was Rs. 1807.3 million - yields a cost of capital of 15.60%:
Cost of capital (^ )^ (^ ) (21.30% )(0.5581 ) (12% )( 1 - 0.3)(0.4419 ) 15.60%
D E
After-taxCostofDebt D D E CostofEquity E = + =
With the perpetual growth of 5%, the expected free cash flow to the firm shown above (Rs 212.2 million) and the cost of capital of 15.60%, we obtain a value for the firm of:
(^3) Note that while this resembles growth rates we have used for other firms, it is a low growth rate given that this valuation is in Indian rupees. As a simple check, note that the riskfree rate that we use is 10.50%.
Value of the operating assets of firm = (^) 0.156212.2-0.05^ =Rs^2002 million
Adding back cash and marketable securities with a value of Rs 1365.3 million and subtracting out the debt outstanding of Rs 1807.3 million yields a value for the equity of Rs 1560 million and a value per share of Rs. 63.36 (based upon the 24.62 million shares outstanding). The stock was trading at Rs 92.70 at the time of this valuation. An interesting aspect of this valuation is that the return on capital used to compute the reinvestment rate is significantly lower than the cost of capital. In other words, we are locking in this firm into investing in negative excess return projects forever. If we assume that the firm will find a way to earn its cost of capital of 15.6% on investments, the reinvestment rate would be much lower.
Reinvestment rateROC=Cost of capital = (^) ROCg^ =0.1560.05 =32.05%
Value of operating assets =(464.7^ )^ 0.1560^1 - 0.3205- 0.05 = Rs. 2979 million
- Value of cash and marketable securities = Rs 1365 million
- Debt = Rs 1807 million Value of equity = Rs 2537 million
Value per share = (^) 24.62^2537 = Rs 103.04 per share
Market Value Weights, Cost of Capital and Circular Reasoning To value a firm, you first need to estimate a cost of capital. Every textbook is categorical that the weights in the cost of capital calculation be market value weights. The problem, however, is that the cost of capital is then used to estimate new values for debt and equity that might not match the values used in the original calculation. One defense that can be offered for this inconsistency is that if you went out and bought all of the debt and equity in a publicly traded firm, you would pay current market value and not your estimated value and your cost of capital reflects this. To those who are bothered by this inconsistency, there is a way out. You could do a conventional valuation using market value weights for debt and equity, but then use the estimated values of debt and equity from the valuation to re-estimate the cost of
If the firm reaches steady state after n years and starts growing at a stable growth rate gn
after that, the value of the firm can be written as:
Value of Firm = (^) (1+FCFF WACC)t t t = 1
t = n ∑ +^ [FCFF(1n++^1 / (WACCWACC)n^ −^ gn^ )]
Best suited for: Firms that have very high leverage or are in the process of changing their leverage are best valued using the FCFF approach. The calculation of FCFE is much more difficult in these cases because of the volatility induced by debt payments (or new issues) and the value of equity, which is a small slice of the total value of the firm, is more sensitive to assumptions about growth and risk. It is worth noting, though, that in theory, the two approaches should yield the same value for the equity. Getting them to agree in practice is an entirely different challenge and we will return to examine it later in this chapter.
Best suited for: There are three problems that we see with the free cash flow to the firm model. The first is that the free cash flows to equity are a much more intuitive measure of cash flows than cash flows to the firm. When asked to estimate cash flows, most of us look at cash flows after debt payments (free cash flows to equity), because we tend to think like business owners and consider interest payments and the repayment of debt as cash outflows. Furthermore, the free cash flow to equity is a real cash flow that can be traced and analyzed in a firm. The free cash flow to the firm is the answer to a hypothetical question: What would this firm’s cash flow be, if it had no debt (and associated payments)? The second is that its focus on pre-debt cash flows can sometimes blind us to real problems with survival. To illustrate, assume that a firm has free cash flows to the firm of $100 million but because of its large debt load makes the free cash flows to equity equal to -$50 million. This firm will have to raise $50 million in new equity to survive and, if it cannot, all cash flows beyond this point are put in jeopardy. Using free cash flows to equity would have alerted you to this problem, but free cash flows to the firm are unlikely to reflect this.
The final problem is that the use of a debt ratio in the cost of capital to incorporate the effect of leverage requires us to make implicit assumptions that might not be feasible or reasonable. For instance, assuming that the market value debt ratio is 30% will require a growing firm to issue large amounts of debt in future years to reach that ratio. In the process, the book debt ratio might reach stratospheric proportions and trigger covenants or other negative consequences. In fact, we count the expected tax benefits from future debt issues implicitly into the value of equity today.
Illustration 15.2: Valuing The Gap: Dealing with Operating Leases The Gap is one of the largest specialty retailers in the world and sells its products at Gap, GapKids, babyGap, Banana Republic and Old Navy stores. While it has operations around the world, it gets the bulk of its revenues from the United States. Rationale for using Model
- Why two-stage? While the Gap is one of the largest and most successful specialty retailers in the world, its dependence on the mature U.S. market for growth restricts its capacity to maintain high growth in the future. We will assume a high growth period of 5 years and then put the firm into stable growth.
- Why FCFF? The Gap has a significant operating lease commitments and the firm has increased its leverage aggressively over the last few years. Background Information In 2000, the Gap reported operating income $1,445 million on revenues of $13,673 million. The firm also reported capital expenditures of $1,859 million and depreciation of $590 million for the year, and its non-cash working capital increased by $323 million during the year. The operating lease expenses for the year were $705. million and Table 15.2 reports the lease commitments for future years. Table 15.2: Lease Commitments for future years: The Gap Year Commitment 1 $774. 2 $749. 3 $696. 4 $635.
Adjusted after-tax operating income = Adjusted Operating Income (1- tax rate) = 1851 (1-0.35) = $1,203 million Dividing this value by the book value of debt (including capitalized operating leases) and the book value of equity at the end of the previous year yields an adjusted return on capital of 13.61% in 2000 for the firm.
ROC 2000
( )
660412032233 13.^61 %
BVofDebt BVofEquity
EBIT 1 - t 1999 1999
2000
= + =
We will assume that the firm will be able to maintain this return on capital in perpetuity. Valuation We will begin with a cost of equity estimate for the Gap, using a bottom-up beta of 1.20 (based upon the betas of specialty retailers) for the high growth period, a riskfree rate of 5.4% and a mature market premium of 4%. In stable growth, we will lower the beta to 1.00, keeping the riskfree rate and risk premium unchanged. Cost of equityHigh Growth = 5.4% + 1.2 (4%) = 10.2% Cost of equityStable Growth = 5.4% + 1.0 (4%) = 9.4% To estimate the cost of capital during the high growth and stable growth phases, we will assume that the pre-tax cost of debt will remain at 7.2% in perpetuity and that the current market debt ratio of 20.58% will remain the debt ratio. Cost of capitalHigh Growth = 10.2%(0.7942)+ 7.2% (1-0.35)(0.2058) = 9.06% Cost of capitalStable Growth = 9.4%(0.7942)+ 7.2% (1-0.35)(0.2058) = 8.43% To estimate the expected growth in operating earnings during the high growth period, we will assume that the firm will continue to earn 13.61% as its return on capital and that its
reinvestment rate will equal its average reinvestment rate over the last 4 years. Average reinvestment rate over last 4 years = 93.53% Expected Growth rate = Reinvestment rate * Return on Capital = 0.9353*0.1361 = 12.73%
(^5) The Gap has had volatile capital expenditures and working capital changes. This is our attempt to average out this volatility.
Table 15.4 summarizes the expected cash flows for the high growth period. Table 15.4: Estimated FCFF: The Gap
Year EBIT(1-t)
Reinvestment rate Reinvestment FCFF Present Value Current $1, 1 $1,356 93.53% $1,269 $88 $ 2 $1,529 93.53% $1,430 $99 $ 3 $1,732 93.53% $1,620 $112 $ 4 $1,952 93.53% $1,826 $126 $ 5 $2,190 93.53% $2,049 $142 $ Sum of present values of cash flows = $
Note that the cash flows during the high growth period are discounted back at 9.06%. To estimate the terminal value at the end of year 5, we assume that this cash flow will grow forever at 5%. The reinvestment rate can then be estimated and used to measure the free cash flow to the firm in year 6: Expected growth rate =5%
Reinvestment rate in stable growth = (^) Stableperiodg^ ROC=13.61%5% =36.73%
FCFF (^6) ==^2190 EBIT(^5 1 ( 1.^05 - t)()( 11 −+ 0 g. 3673 StablePeriod) = 1455 )(^1 - ReinvestmentRate)
The terminal value is:
Terminal value
- 05 $^42 ,^441 million
Costofcapitalinstablegrowth-Growthrate
FCFF 11
Discounting the terminal value to the present and adding it to the present value of the cash flows over the high growth period yields a value for the operating assets of the firm. Value of Operating assets = PV of cash flows during high growth + PV of terminal value
= $430^ +1.0906$42,441 5 =$27,933million
Current 845.00 1.00 845. -1 822.80 0.90 740.52 $82. -2 663.30 0.80 530.64 $66. -3 630.80 0.70 441.56 $63. -4 528.30 0.60 316.98 $52. -5 451.70 0.50 225.85 $45. -6 323.63 0.40 129.45 $32. -7 255.32 0.30 76.60 $25. -8 182.30 0.20 36.46 $18. -9 120.94 0.10 12.09 $12. -10 0.00 0.00 0.00 $0. Value of Research Asset = $3,355.15 $397.
The operating income is adjusted by adding back the current year’s R& D expense and subtracting out the amortization of the research asset. Adjusted operating income = Operating income + Current year’s R&D – Amortization of Research asset = $1,549+ $845 - $398 = $1996 million To get to the after-tax operating income, we also consider the tax benefits from expensing R&D (as opposed to just the amortization of the research asset). Adjusted after-tax operating income = Adjusted Operating Income (1- tax rate) + (Current year R&D – Amortization) Tax rate = 1996 (1-0.35) + (845-398) (0.35) = $1,454 million The current year’s R&D expense is added to the capital expenditures for the year, and the amortization to the depreciation. In conjunction with an increase in working capital of $146 million, we estimate an adjusted reinvestment rate for the firm of 56.27%. Adjusted Capital expenditures = 437+ 845 = $1,282 million Adjusted Depreciation = 212 + 398 = $610 million Adjusted Reinvestment rate
( ) (^1282145461014656). 27 %
AdjustedEBIT 1 - t
CapitalExpenditures-Depreciation WC
= − + =
To estimate the return on capital, we estimated the value of the research asset at the end of the previous year and added it to the book value of equity. The resultant return on capital for the firm is shown. Return on capital ( )
59321454323 23.^24 %
Adjustedbook valueofequity(includesresearchasset) Book valueofdebt
AdjustedEBIT 1 - t
= + =
Valuation To value Amgen, we will begin with the estimates for the 5-year high growth period. We use a bottom-up beta estimate of 1.35, a riskfree rate of 5.4% and a risk premium of 4% to estimate the cost of equity: Cost of equity = 5.4% + 1.35 (4%) = 10.80% We estimate a synthetic rating of AAA for the firm, and use it to come up with a pre-tax cost of borrowing of 6.15% by adding a default spread of 0.75% to the treasury bond rate of 5.4%. With a marginal tax rate of 35% and a debt ratio of 0.55%, the firm’s cost of capital closely tracks its cost of equity. Cost of capital = 13.08% (0.9945) + 6.15%(1-0.35)(0.0055) = 10.76% To estimate the expected growth rate during the high growth period, we will assume that the firm can maintain its current return on capital and reinvestment rate estimated in the section above. Expected Growth rate = Reinvestment rate * Return on capital = 0.5627*0.2324 = 13.08% Before we consider the transition period, we estimate the inputs for the stable growth period. First, we assume that the beta for Amgen will drop to 1, and that the firm will raise its debt ratio to 10%. Keeping the cost of debt unchanged, we estimate a cost of capital of Cost of equity = 5.4% + 1(4%) = 9.4%
Adding the present value of the terminal value to the present value of the free cash flows to the firm in the first 10 years, we get: Value of the operating assets of the firm
( )(^ )(^ )(^ )(^ )(^ )
$ 39 , 161 million
$8,327 million $81, 5 =
Adding the value of cash and marketable securities ($2,029 million) and subtracting out debt ($323 million) yields a value for the equity of $40,867 million. At the time of this valuation in May 2001, the equity was trading at a market value of $58,000 million.
Illustration 15.4: Valuing Embraer: Dealing with Country Risk Embraer is a Brazilian aerospace firms that manufactures and sells both commercial and military aircraft. In this valuation, we will consider the implications of valuing the firm in the context of country risk and uncertainty about expected inflation. Rationale for using Model
- Why two-stage? Embraer has done exceptionally well in the last few years though it operates in a mature business with strong competition from giants such as Boeing and Airbus. We believe that it can sustain growth for a long period (10 years) and that there will be a transition to stable growth in the second half of this growth period.
- Why FCFF? The firm’s debt ratio has been volatile. While it does not use much debt to fund its operations currently, it does have the capacity to raise more debt now, especially in the United States.
- Why real cash flows? We had two choices when it came to valuation – to work with U.S. dollars or work in real cash flows. We avoided working with nominal real, largely because of the difficulties associated with getting a riskfree rate in that currency. Background Information In 2000, Embraer reported operating income of 810.32 million BR on revenues of 4560 million BR, and faced a marginal tax rate of 33% on its income. At the end of 2000, the firm had net debt (debt minus cash) of 215.5 million BR on which their net interest expenses for 2000 were 28.20 million BR. The firm’s non-cash working capital at the end
of 2000 amounted to 915 million BR, an increase of 609.7 million BR over the previous year’s amount. The firm’s capital expenditures were 233.5 million BR and depreciation was 127. million for the year, yielding a reinvestment rate of 131.83% for the year.
Reinvestment Rate 2000 = 233.5810.32^ - 127.5( 1 - 0.33+609.7) =131.83%
Normalizing the non-cash working capital component6 yields a change in non-cash working capital of 239.59 million BR and a normalized reinvestment rate.
Normalized Reinvestment Rate 2000 = 233.5810.32^ - 127.5( 1 - +0.33239.59) =63.65%
Based upon the capital invested of 1,470 million BR in the firm at the beginning of 2000, the return on capital at Embraer in 2000 was 36.94%.
Return on capital = 810.32 1470 (^1 - 0.33)^ =36.94%
Valuation We first have to estimate a country risk premium for Brazil. Drawing on the approach developed in Chapter 7, we estimate a country risk premium for Brazil of 10.24%. Country rating for Brazil = B Default spread on Brazilian Government C-bond (U.S. dollar denominated) = 5.37% To estimate the country equity risk premium, we estimated the standard deviation in weekly returns over the last 2 years in both the Bovespa (the Brazilian equity index) and the C-Bond. Standard deviation in the Bovespa = 32.6% Standard deviation in the C-Bond = 17.1%
Country risk premium
( )
( 5. 37 %) (^1732) .. 16 %% 10. 24 %
StandardDeviation DefaultSpread StandardDeviation C- Bond
Equity
^ =
(^6) The normalized change in non-cash working capital was computed as follows: Normalized change = (Non-cash WC 2000 /Revenues 2000 )*(Revenues 2000 -Revenues 1999 )
