5 30011 Discount Rates Problem Set S2 20 PDF

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FNCE30011 Essentials of Corporate Valuation PROBLEM SET 5 Estimating Discount Rates For DCF Valuations

QUESTION 1 This question looks at the relationship between equity betas and unlevered equity betas within the perpetuity setting originally considered by Modigliani and Miller. Consider a firm which is expected to generate unlevered free cash flow of ฀฀฀฀฀฀ ฀฀ at the end of each period in perpetuity. The firm is financed by equity and perpetual bonds and has a (constant) leverage ratio of ฀฀. The cost of equity is ฀฀฀฀ , the unlevered cost of equity is ฀฀฀฀ , the cost of debt is ฀฀฀฀ and the corporate tax rate is ฀฀. If we assume the interest tax shields have the same risk as the firm’s debt (as MM did), then we know from problem set 3 that the standard WACC can also be written as: ฀฀฀ ฀ = ฀฀฀฀ (1 − ฀฀฀฀) (a)

Show that the unlevered cost of equity can be written as: 1 − ฀฀ ฀฀(1 − ฀฀) � ฀฀฀฀ ฀฀฀ ฀ = � � ฀฀฀ ฀ + � 1 − ฀฀฀฀ 1 − ฀฀฀฀ Hint: Equate the two ways to express the standard WACC and work through the algebra.

Assume we use the CAPM to estimate the cost of equity, the unlevered cost of equity and the cost of debt (that is, the expected return on equity, the expected return on unlevered equity and the expected return on debt)

(b)

Show that the relationship between the equity beta ฀฀฀฀ of the firm and the unlevered equity beta ฀฀฀฀ of the firm is … 1 − ฀฀ ฀฀(1 − ฀฀) � ฀฀฀฀ ฀฀฀ ฀ = � � ฀฀฀ ฀ + � 1 − ฀฀฀฀ 1 − ฀฀฀฀

where ฀฀฀ ฀ =

฀฀฀฀฀฀(฀฀฀฀ ,฀฀฀฀ ) 2 ฀฀฀฀

฀฀฀ ฀ =

฀฀฀฀฀฀(฀฀฀฀ ,฀฀฀฀ ) 2 ฀฀฀฀

฀฀฀ ฀ =

฀฀฀฀฀฀(฀฀฀฀ ,฀฀฀฀) 2 ฀฀฀฀

Assume the debt beta of the firm is ฀฀฀ ฀ = 0. (c)

Show that the expression in part (b) simplifies to … ฀฀ ฀฀฀ ฀ = �1 + (1 − ฀฀) � ฀฀฀฀ ฀฀

(d)

Reconsider part (c) assuming there are no corporate taxes. Does it make sense to use this formula for levering/de-levering purposes ?

QUESTION 2 This question takes another look at the Independent Expert Report prepared by Grant Samuel in relation to KKR’s takeover of MYOB in early 2019. Grant Samuel determined the enterprise value of MYOB to be $2,300 - $2,600 million based on “evidence drawn from capitalisation of earnings analysis (including multiples of EBITDA, EBIT and free cash flow from operations), supported by indicative discounted cash flow (“DCF”) scenario analysis and evidence from the process by which, following the announcement of the KKR Proposal, MYOB and its advisers sought counterproposals from third parties to acquire MYOB” 1 They further state that “in the absence of any detailed published forecasts by MYOB of its future performance, Grant Samuel has undertaken an indicative and high level DCF scenario analysis. … [and has] adopted three indicative scenarios, as described in more detail below. The scenarios do not constitute forecasts or projections and have been adopted only for the purpose of assessing the theoretical values associated with specified scenarios and their assumptions regarding future operating performances” 2 The results of their DCF analysis is set out below …

1 2

MYOB Group Limited, Scheme Booklet, 13 March 2019, page 118 MYOB Group Limited, Scheme Booklet, 13 March 2019, page 135

2

…

Source: MYOB Group Limited, Scheme Booklet, 13 March 2019, page 137

(a)

Use the information in the footnote to confirm the discount rates used by Grant Samuel in their DCF scenario analysis.

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QUESTION 3 This question examines the effect of credit risk on bond prices and yields Consider the following one-year zero-coupon bonds: Issuer Credit Rating Face Value Maturity Current Price

Treasury AAA $1,000.00 1 year $952.38

Corporate A $1,000.00 1 year $924.53

Corporate B– $1,000.00 1 year $772.73

Assume:   

the Treasury bond is default-free there is a 10% chance that the investment grade corporate bond will default, in which case investors would receive only 80% of the face value at maturity there is a 25% chance that the speculative grade corporate bond will default, in which case investors would receive only 40% of the face value at maturity

For each bond … (a)

What are the promised cash flows on the bond ?

(b)

What is the yield on the bond ?

(c)

What are the expected cash flows on the bond ? Compare your answers to those in part (a) and comment. Hint: consider the cash flows assuming default and assuming no default

(d)

What is the expected return on the bond ? Compare your answers to those in part (b) and comment.

(e)

What is the credit spread on the bond ?

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QUESTION 4 This question looks at how the CAPM and Fama-French models can be used to estimate the expected return on a stock. You wish to estimate the expected return on Apple Inc. over the next year using both the CAPM and the Fama-French model. Based on an examination of historic data and analysts’ forecasts you decide to use a risk-free rate of 2% per annum, a market risk premium of 6% per annum, a size premium of 2% per annum and a value premium of 5% per annum. You also decide to run an OLS regression to estimate the CAPM and Fama-French betas using five years of monthly returns data Your beta estimates are as follows … CAPM • Market beta

1.1773

Fama-French Model • Market beta 1.3106 • Size beta – 0.5347 • Value beta – 0.7675

(a)

Recall the CAPM beta of the market portfolio is equal to 1. What does your estimate of the CAPM beta tells us about Apple ?

(b)

Use the CAPM to estimate the expected return on Apple.

(c)

In the Fama-French model, SMB reflects the risk premium on small stocks (compared to big stocks) and HML reflects the risk premium on value stocks (compared to growth stocks). What does your estimate of the Fama-French size and value betas tells us about Apple ? (We will discuss value and growth stocks in a later class)

(d)

Use the Fama-French model to estimate the expected return on Apple.

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QUESTION 5

This question is optional

This question illustrates how to estimate betas for the CAPM and the Fama-French model. Refer to the data-file: “5-30011-Data-For-Problem-Set-Q5.csv” which you can download from the class website. The file contains monthly raw returns on Apple Inc stock for the period January 2001 to May 2017, monthly returns on the risk-free asset for the period January 1927 to May 2017 and monthly excess returns on the MRP, SMB and HML portfolios for the period January 1927 to May 2017. (The data for the risk-free asset, MRP, SMB and HML was downloaded from Ken French’s website). Assume today is 1 June 2017. You wish to estimate the expected return on Apple Inc. over the next year using both the CAPM and the Fama-French model and decide to calculate your beta estimates using the last five years of monthly excess returns data from 6/2012 to 5/2017. Use an OLS regression (in Excel or some other software) … (a)

Estimate the CAPM (market) beta for Apple over the sample period. Hint: You first need to calculate the time series of monthly excess returns on the stock, which for each month is equal to the raw return on the stock less the return on the risk-free asset.

(b)

Estimate the Fama-French market beta, size beta and value beta for Apple over the sample period.

(c)

How important is the choice to use a 5 year sample period ?

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