Chapter 5 Valuation and the Use of Free Cash Flows

Education Course Notes [Session 3 & 4]

LEARNING OBJECTIVES

1. Apply asset based, income based and cash flow based models to value equity. 2. Apply appropriate models, including term structure of interest rates, the yield curve and credit spreads to value corporate debt. 3. Forecast an organization’s free cash flow and its free cash flow to equity. 4. Advise on the value of a firm using its free cash flow and free cash flow to equity under alternative horizon and growth assumptions.

Discounted Cash Flow Techniques

Yield Curve & Forecasting Free Cash Flow Valuations of Valuation by Assessing Default Bond Price Free Cash Flow to Equity Equity Free Cash Flow Risk Using Option Pricing Model

Definition of Meaning Asset-based Using Free Cash Free Cash Flow Methods Flow

Forecasting Direct Method Income based Terminal Free Cash Flow Methods Values

Indirect Method Dividend Valuation Model

Prepared by Patrick Lui P. 143 Copyright @ Kaplan Financial 2016 Education Course Notes [Session 3 & 4]

1. Yield Curve and Bond Price

1.1 In all your previous learning, the risk free rate has been given as a single figure, based on the return required on government bonds. 1.2 However, in reality the return required will usually be higher for longer dated government bonds, to compensate investors for the additional uncertainty created by the longer time period. 1.3 Therefore, you might be given a “spot yield curve” for government bonds, instead of a “single risk free rate”. Then to calculate the yield curve for an individual company’s bonds, add the given credit spread to the relevant government bond yield.

Example 1 – Spot yield curve for government bonds A government has three bonds in issue that all have a par value of $100 and are redeemable in one year, two years and three years respectively. Since the bonds are all government bonds, let’s assume that they are of the same risk class. Let’s also assume that coupons are payable on an annual basis.

Bond A, which is redeemable in a year’s time, has a coupon rate of 7% and is trading at $103.

Bond B, which is redeemable in two years, has a coupon rate of 6% and is trading at $102.

Bond C, which is redeemable in three years, has a coupon rate of 5% and is trading at $98.

To determine the spot yield curve, each bond’s cash flows are discounted in turn to determine the annual spot rates for the three years, as follows:

$107 Bond A: $103  (1r1)

So r1 = 3.88%

$6 $106 Bond B: $102   2 1.0388 (1 r2 )

So r2 = 4.96%

$5 $5 $105 Bond C: $98   2  3 1.0388 1.0496 (1 r3 )

So r3 = 5.80%

The annual spot yield curve is therefore:

Year % 1 3.88 2 4.96 3 5.80

Example 2 – Individual yield curve The spot yield curve for government bonds is: Year % 1 3.50 2 3.65 3 3.80

The following table of credit spreads (in basis points) is presented by Standard and Poor’s:

Rating 1 year 2 year 3 year AAA 14 25 38 AA 29 41 55 A 46 60 76

Required:

Estimate the individual yield curve for Stone Co, an A rated company.

Solution: The individual yield curve for Stone Co is found by adding the government spot yield curve figures to the credit spreads for an A rated company:

Year Spot yield (%) Credit spread (%) Individual yield curve (%) 1 3.50 0.46 3.96 2 3.65 0.60 4.25 3 3.80 0.76 4.56

This shows that (for example) the yield on a 2 year Stone Co bond will be 4.25%.

Example 3 – Bond price and YTM ABC Co wants to issue a five year redeemable bond with an annual coupon of 4%. The bond is redeemable at par ($100). Tax can be ignored.

The annual spot yield curve for this risk class of bond in the financial press is given as

Year % 1 3.3 2 3.8 3 4.2 4 4.8 5 5.5

Required: (a) The expected price at which the bond can be issued. (b) The yield to maturity of the bond.

Solution:

(a) Expected bond price

Year Cash flow ($) Discount at Present value ($) 1 4 1 / 1.033 3.87 2 4 1 / 1.0382 3.71 3 4 1 / 1.0423 3.54 4 4 1 / 1.0484 3.32 5 104 1 / 1.0555 79.57 94.01

(b) An IRR style calculation is needed to calculate the YTM

Year Cash flow DF PV DF PV ($) 5% ($) 8% ($) 0 Market value (94.01) 1.000 (94.01) 1.000 (94.01) 1 – 5 Interest 4 4.329 17.32 3.993 15.97

5 Capital payment 100 0.784 78.40 0.681 68.10 1.71 (9.94)

1.71 YTM = 5%   (8%  5%)  5.44% 1.71 9.94

2. Forecasting a Firm’s Free Cash Flow

2.1 Definition of free cash flow

2.1.1 The free cash flow is the cash flow derived from the operations of a company after subtracting working capital, investment and taxes and represents the funds available for distribution to the capital contributors, i.e. shareholders and debt holders. 2.1.2 The idea is to provide a measure of what is available to the owners of a firm, after providing for capital expenditures to maintain existing assets and to create new assets for future growth and is measured as follows:

Free cash flow = EBIT – Tax on EBIT + Non cash charges (e.g. depreciation) – Capital expenditure – Net working capital increases + Net working capital decreases + Salvage value received

Example 4 – Free cash flow ABC Inc needs to invest $9,000 to increase productive capacity and also to increase its working capital by $1,000. Earnings before taxes are $90,000 and it sets off against tax $6,000 of depreciation. Profits are taxed at 40%. What is the free cash flow? Solution: $ EBIT 90,000 Less: Taxes (40%) (36,000) Operating income after taxes 54,000 Add: Depreciation (non cash item) 6,000 Less: Capital expenditures (9,000) Less: Changes to working capital (1,000)

Free cash flow 50,000

2.2 Forecasting free cash flows

2.2.1 Free cash flows can be forecast in similar ways to such other items as expenses, sales and capital expenditure. We must consider the likely behaviour of each of the elements that make up the free cash flow figure – such as movements in future tax rates, potential spending on capital projects and the associated working capital requirements.

A. Constant growth

2.2.2 One approach to forecasting free cash flows is to assume that they will grow at a constant rate. The calculation of free cash flows is therefore quite straightforward.

FCFt = FCFt-1 × (1 + g)

Where:

FCFt = the free cash flow at time t

FCFt-1 = the free cash flow in the previous period g = growth rate

If you wish to forecast the total free cash flow over a number of periods where the growth rate is assumed to be constant the following formula can be used.

n FCF = FCF0 × (1 + g)

Where: FCF = the total forecast cash flow

FCF0 = the free cash flow at the beginning of the forecast period n = the number of years for which the free cash flow is being forecast

B. Differing growth rates

2.2.3 When the elements of free cash flow are expected to grow at different rates each

element must be forecast separately using the appropriate rate. Free cash flow can then be estimated using the revised figures for each year.

Example 5 – Differing growth rates ABC Inc is trying to forecast its free cash flow for the next three years. Current free cash flow is as follows.

Expected annual increase % $ EBIT 4 500,000 Tax 30% of EBIT 150,000 Depreciation 5 85,000 Capital expenditure 2 150,000 Working capital requirements 3 60,000

By what percentage will free cash flow have increased between now and the end of year 3?

Solution:

Year 0 Year 3 $ $ EBIT (500,000 × 1.043) 500,000 562,432 Tax (150,000) (168,730) Depreciation (85,000 × 1.053) 85,000 98,398 Capital expenditure (150,000 × 1.023) (150,000) (159,181) Working capital (60,000 × 1.033) (60,000) (65,564) Free cash flow 225,000 267,355

267,355  225,000 Percentage increase =  18.8% 225,000

3. Free Cash Flow to Equity

3.1 Meaning of free cash flow to equity

3.1.1 The free cash flow derived in the previous section is the amount of money that is available for distribution to the capital contributors. If the project is financed by equity only, then these funds could be potentially distributed to the shareholders of the company. 3.1.2 However, if the company is financing the project by issuing debt, then the shareholders are entitled to the residual cash flow left over after meeting interest and principal payments. This residual cash flow is called free cash to equity (FCFE).

3.2 Direct method of calculation

3.2.1 Free cash flow to equity can be measured as follows:

Free cash flow to equity = Net income (EBIT – net interest – tax paid) + Depreciation – Total net investment (change in capital investment + change in working capital) + Net debt issued (new borrowings less any repayment

Example 6 – Free cash flow to equity by direct method The following information is available for ABC Co:

Capital expenditure $20m Corporate tax rate 35% Debt repayment $23m Depreciation charges $10m $m Sales 650.00 Less: Cost of goods sold (438.00) Gross profit 212.00 Operating expenses (107.50) EBIT 104.50 Less: Interest expense (8.00) Earnings before tax 96.50 Less: Taxes (33.77) Net income 62.73

What is the FCFE?

Solution:

$m Net income 62.73 Add: Depreciation 10.00 Less: Capital expenditures (20.00) Less: Debt repayment (23.00) Free cash flow to equity 29.73

B. Indirect method of calculation

3.2.2 Using the indirect method, FCFE is calculated as follows:

Free cash flow to equity = Free cash flow (using formula in section 2.1 above) – (net interest + net debt paid) + Tax benefit from debt (net interest × tax rate)

Example 7 – Free cash flow to equity by indirect method Same information as Example 6

What is the FCFE using indirect method?

Solution:

$m EBIT 104.50 Less: Tax (35%) (36.57) 67.93 Add: Depreciation expense 10.00 Less: Capital expenditure (20.00) Free cash flow 57.93 Less: (net interest + net debt paid) (8 + 23) (31.00) Add: Tax benefit from debt (8 × 35%) 2.80

FCFE 29.73

4. Valuations of Equity

4.1 Asset-based valuations

4.1.1 Choice of valuation bases – the difficulty in an asset valuation method is establishing the asset values to use. Values ought to be realistic. The figure attached to an individual asset may vary considerably depending on whether it is valued on a going concern or a break-up basis. (a) Historic basis – unlikely to give a realistic value as it is dependent upon the business’s depreciation and amortization policy. (b) Replacement basis – if the assets are to be used on an on-going basis. (c) Realisable basis – if the assets are to be sold, or the business as a whole broken up. This won’t be relevant if a minority shareholder is selling his stake, as the assets will continue in the business’s use.

4.2 Income/earnings based methods

4.2.1 Income-based methods of valuation are of particular use when valuing a majority shareholding.

(a) Price Earnings (P/E) ratio method

4.2.2 P/E Ratio Method This is a common method of valuing a controlling interest in a company, where the owner can decide on dividend and retentions policy. The P/E ratio relates earning per share to a share’s value.

Formula: P/E = Market price per share / Earnings per share (EPS)

This can then be used to value shares in unquoted companies as: Market value (or market capitalization) of company = total earnings × P/E ratio Value per share = EPS × P/E ratio Using an adjusted P/E multiple from a similar quoted company (or industry average).

Example 8 – P/E method Catcher wishes to make a takeover bid for the shares of an unquoted company, Julyfly. The earnings of Julyfly. The earnings of Julyfly over the past five years have been as follows.

2006 $50,000 2009 $71,000 2007 $72,000 2010 $75,000 2008 $68,000

The average P/E ratio of quoted companies in the industry in which Julyfly operates is 10. Quoted companies which are similar in many respects to Julyfly are: (a) Bumblebee, which has a P/E ratio of 15, but is a company with very good growth prospects. (b) Wasp, which has had a poor profit record for several years, and has a P/E ratio of 7.

What would be a suitable range of valuations for the shares of Julyfly?

Solution:

(a) Earnings. Average earnings over the last five years have been $67,200, and over the last four years $71,500. There might appear to be some growth prospects, but estimates of future earnings are uncertain.

A low estimate of earnings in 2011 would be, perhaps, $71,500.

A high estimate of earnings might be $75,000 or more. This solution will use the most recent earnings figure of $75,000 as the high estimate. (b) P/E ratio. A P/E ratio of 15 (Bumblebee’s) would be much too high for Julyfly, because the growth of Julyfly earnings is not as certain, and Julyfly is an unquoted company.

On the other hand, Julyfly’s expectations of earnings are probably better than those of Wasp. A suitable P/E ratio might be based on the industry’s average, 10; but since Julyfly is an unquoted company and therefore more risky, a lower P/E ratio might be more appropriate: perhaps 60% to 70% of 10 = 6 or 7, or conceivably even as low as 50% of 10 = 5

The valuation of Julyfly’s shares might therefore range between:

High P/E ratio and high earnings: 7 × $75,000 = $525,000; and Low P/E ratio and low earnings: 5 × $71,500 = $357,500.

4.2.3 The basic choice for a suitable P/E ratio will be that of a quoted company of comparable size in the same industry.

4.2.4 Problems with using P/E ratio (a) Finding a quoted company with a similar range of activities may be difficult. Quoted companies are often diversified. (b) A single year’s P/E ratio may not be a good basis, if earnings are volatile, or the quoted company’s share price is at an abnormal level, due for example to the expectation of a takeover bid. (c) If a P/E ratio trend is used, then historical data will be being used to value how the unquoted company will do in the future. (d) The quoted company may have a different capital structure to the unquoted company.

4.2.5 When one company is thinking about taking over another, it should look at the target company’s forecast earnings, not just its historical results. Forecasts of earnings growth should only be used if: (a) There are good reasons to believe that earnings growth will be achieved. (b) A reasonable estimate of growth can be made. (c) Forecasts supplied by the target company’s directors are made in good faith and using reasonable assumptions and fair accounting policies.

(b) Earning yield method

4.2.6 Earning Yield Method Another income based method is the earnings yield method.

Earnings yield = EPS x 100% Market price per share

This method is effectively a variation on the P/E method (the earnings yield being the reciprocal of the P/E ratio), using an appropriate earnings yield effectively as a

discount rate to value the earnings:

Market value = Earnings Earnings yield

Example 9 – Earning yield method Company A has earnings of $300,000. A similar listed company has an earnings yield of 12.5%.

Company B has earnings of $420,500. A similar listed company has a P/E ratio of 7.

Estimate the value of each company.

Solution:

1 Company A: $300,000  $2,400,000 0.125 Company B: $420,500 × 7 = $2,943,500

4.3 Dividend valuation model (DVM)

4.3.1 Dividend Valuation Model The dividend valuation model is based on the theory that an equilibrium price for any share on a stock market is: (a) The future expected stream of income from the security. (b) Discounted at a suitable cost of capital.

Equilibrium market price is thus a present value of a future expected income stream. The annual income stream for a share is the expected dividend every year in perpetuity.

The basic dividend-based formula for the market value of shares is expressed in the DVM (assume no growth) as follows:

D D D D Market value (ex div) P0   2  ...    (1 K e ) (1 K e ) (1 K e ) K e

If the dividend has constant growth, dividend growth model can be applied: 2  D0 (1 g) D0 (1 g) D0 (1 g) D0 (1 g) D1 P0   2  ...     (1 K e ) (1 K e ) (1 K e ) K e  g K e  g

Where: D0 = Current year’s dividend g = Growth rate in earnings and dividends

D0(1+g) = D1 = Expected dividend in one year’s time

Ke = Shareholders’ required rate of return

P0 = Market value excluding any dividend currently payable

Example 10 – Dividend valuation model A company paid a dividend of $250,000 this year. The current return to shareholders of companies in the same industry is 12%, although it is expected that an additional risk premium of 2% will be applicable to the company, being a smaller and unquoted company. Compute the expected valuation of the company, if:

(a) The current level of dividend is expected to continue into the foreseeable future, or (b) The dividend is expected to grow at a rate of 4% pa into the foreseeable future.

Solution:

Ke = 12% + 2% = 14%; D0 = $250,000; g = 4%

D0 $250,000 (a) P0    $1,785,714 K e 14%

D0 (1 g) $250,000 (1 4%) (b) P0    $2,600,000 K e  g 14%  4%

4.3.2 Assumptions of Dividend Models The dividend models are underpinned by a number of assumptions that you should bear in mind. (a) Investors act rationally and homogenously. The model fails to take into account the different expectations of shareholders, nor how much are motivated by dividends vs future capital appreciation on their shares.

(b) The D0 figure used does not vary significantly from the trend of dividends.

If D0 does appear to be a rogue figure, it may be better to use an adjusted trend figure, calculated on the basis of the past few years’ dividends.

(c) The estimates of future dividends and prices used, and also the cost of capital are reasonable. As with other methods, it may be difficult to make a confident estimate of the cost of capital. Dividend estimates may be made from historical trends that may not be a good guide for a future, or derived from uncertain forecasts about future earnings. (d) Investors’ attitudes to receiving different cash flows at different times can be modeled using discounted cash flow arithmetic. (e) Directors use dividends to signal the strength of the company’s position (however companies that pay zero dividends do not have zero share values). (f) Dividends either show no growth or constant growth. If the growth rate is calculated using g = b x r, then the model assumes that b and r are constant. (g) Other influences on share prices are ignored. (h) The company’s earnings will increase sufficiently to maintain dividend growth levels. (i) The discount rate used exceeds the dividend growth rate.

5. Valuation by Free Cash Flow

5.1 Valuation using free cash flows

5.1.1 The valuation using free cash flows is very similar to carrying out a NPV calculation. The value of the organization is simply the sum of the discounted free cash flows over the appropriate horizon. 5.1.2 If we assume that free cash flows remain constant (i.e. with no growth) over the appropriate horizon, then the value of the organization is the free cash flow divided by the cost of capital. 5.1.3 Alternatively, if the free cash flows are growing at a constant rate every year, the value can be calculated using the Gordon Model (also known as the Constant Growth Model).

FCF0  (1 g) PV0  ke  g Where: g = growth rate

ke = cost of capital

Example 11 ABC Inc currently has free cash flows of $5 million per year and a cost of capital of 12%. Calculate the value of ABC Inc if (a) The free cash flows are expected to remain constant (b) The free cash flows are expected to grow at a constant rate of 4% per annum

Solution:

$5m (a) Value of ABC Inc = = $41.67m 0.12 $5m 1.04 (b) Use the Gordon Model, value of ABC Inc = = $65m 0.12  0.04

5.2 Terminal values

5.2.1 The terminal value of a project is the value of all the cash flows occurring from period N + 1 onwards, i.e. beyond the normal prediction horizon of periods 1 to N. 5.2.2 Terminal value is subject to a greater uncertainty as they are beyond the horizon 1 to N where normal forecasts are acceptable. As such simplifying assumptions need to be made for any flows occurring after period N. 5.2.3 When we refer to a project, the terminal value is equivalent to the salvage value remaining at the end of the expected project horizon.

Example 12 You have completed the following forecast of free cash flows for an eight year period, capturing the normal business cycle of ABC Inc:

Year FCF ($) 1 1,860.0 2 1,887.6 3 1,917.6

4 1,951.2 5 1,987.2 6 2,016.0 7 2,043.6 8 2,070.0

Free cash flows are expected to grow at 3% beyond year 8. The cost of capital is assumed to be 12%. What is ABC Inc’s value?

Solution:

1 2 3 4 5 6 7 8 9 onwards $ $ $ $ $ $ $ $ $ Cash flows 1,860.0 1,887.6 1,917.6 1,951.2 1,987.2 2,016.0 2,043.6 2,070.0 2,070 x 1.03 0.12 - 0.03 23,690.0 25,760.0 Discount at 12% 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 PV 1,661 1,504 1,365 1,241 1,127 1,022 924 10,407

Total value = 19,251

6. Assessing Default Risk Using Option Pricing Model

6.1 The role of option pricing models in the assessment of default risk is based on the limited liability property of equity investments. 6.2 Whereas shareholders can participate in an increase in the profits of a company, their losses are limited to the values of their holding 6.3 To see how this property is exploited, consider a firm with assets whose market value is denoted by V. Furthermore the firm is assumed to have a very simple capital structure where the acquisition of assets is funded by equity whose market value is denoted by E and by debt with market value D. The statement of financial position of this firm is given by:

Assets Liabilities V Equity E Debt D

The debt issued by the firm is a one year zero coupon bond with one year maturity

and face value F. The market value of debt is:

F D  1 y

Note that y is not the risk-free return but includes a risk premium over the risk- free rate to reflect the fact that bondholders are exposed to credit risk and they may not receive the promised payment F.

This can happen when on the date the debt matures, the value of the assets V1 are not

sufficient to pay the bondholders. The company will default on its debt if V1 < F in

which case bondholders will receive not F, but V1, suffering a loss of F – V.

Equity is a residual claim on the assets of the company and the value of equity on maturity date will be the difference between the value of the assets and the face value of debt. It will be positive if the value of the assets is higher than the outstanding debt and zero if the value of the assets is lower than the outstanding debt. In summary, the

value of the equity E1 will be:

E1 = V1 – F, if V1 > F

E1 = 0 if V1 ≦ F

The value of equity on maturity date is shown in the following figure. The value of

equity is positive when V1 > F and zero when V1 ≦ F. Because of the limited liability feature of equity, the lowest value it can reach is zero.

The value of the firm’s equity can therefore be estimated using a variation of the Black Scholes model for the valuation of a European call option.

rt C = Pa Nd1  Pe Nd2 e

 P  ln a   r  0.5s 2 t  P  d   e  1 s t

d2  d1  s t

The value of N(d1) shows how the value equity changes when the value of the assets change. This is the delta of the call option (delta is covered in more detail in later chapter).

The value of N(d2) is the probability that a call option will be in the money at expiration. In this case it is the probability that the value of the asset will exceed the

outstanding debt, i.e. V1 > F. The probability of default is therefore given by 1 – N(d2). This is show as the shaded part in the following figure.

The option pricing model provides useful insights on what determines the probability of default of a bond and it can therefore be used to asses the impact of its determinants on credit risk and the cost of debt capital. From the Black Scholes formula, it can be seen that the probability of default depends on three factor.  The debt/asset ratio, F/V  The volatility of the company asset (σ)  The maturity of debt (t)

Example 13 The market value of the assets is $100, and the face value of the 1-year debt is $70. The risk free rate is 5% and the volatility of asset value is 40%. Find the value of the default probability using the Black Scholes model.

Solution:

For this problem, we have V = 100 F = 70 r = 0.05 σ = 0.4

The Black Scholes model parameters are:

 V  ln   r  0.5 2 t  F  d1   t 100  ln   0.05  0.5 0.42  70 d     1.217 1 0.4

d 2  1.217  0.4  0.817

The delta of the option is:

N(d1) = N(1.217) = 0.5 + 0.3888 = 0.8888

N(d2) = N(0.817) = 0.5 + 0.2939 = 0.7939

From which, we have:

1 – N(d2) = 1 – 0.7939 = 0.2061

Thus the probability of default is 20.61%.