Beta

The beta value 𝛽 represents the systematic risk of an asset in comparison to the market portfolio. The beta measures the sensitivity of an asset’s movement in relation to the market, and furthermore explains whether a stock moves in the same direction as the rest of the market.

Table 5.8: Own creation

The standard procedure for estimating the beta in the CAPM involves running a regression of stocks returns against market returns as the slope of the regression corresponds to the beta and measures the risk added on by that investment to the index used to capture the market portfolio. This information is absent in the case with Lego as a private company, and according to Damodaran, there are three other ways to estimate beta for private companies (Damodaran, C).

Accounting beta refers to the regression of changes in a private company’s accounting earnings against changes in earnings for an equity index such as the S&P 500 to estimate accounting beta. Using operating earnings would yield an unlevered beta, whereas using net income would yield a levered beta. This approach is limited as private firms, Lego included, only measure earnings once a year which leads to regressions with few observations and limited statistical power (ibid).

Fundamental beta relates the beta of comparable publicly traded firms to observable variables such as earnings growth, debt ratios and variance in earnings. The approach is simple but is only as good as the underlying regression (ibid).

Bottom-up beta can be estimated by running a regression of stock returns from comparable companies in the industry against a market return (ibid). This approach will be applied to estimate the beta for Lego is based on the betas of peer companies, Mattel and Hasbro.

If beta is Then it

0 Indicates that an investment is equal to a risk-free investment.

0 < β < 1 Indicates that an investment has lower risk than the market. It is less volatile.

1 Indicates that an investment has the same risk as the market.

> 1 Indicates that an investment has higher than the market. It is more volatile.

< 0 Indicates that an investment is invers correlated to the market.

105

There is no common standard for the choice of estimation period or choice of return intervals for conducting a regression analysis. Academic literature offers different recommendations for estimating beta, whereas, in practice, data providers also use different estimation periods and return intervals.

Early empirical tests of the capital asset pricing model suggest using five years of monthly data to obtain estimates of beta (Jensen et al., 1979 and Fama & MachBeth, 1973) whereas subsequent test of optimal measurement periods found four-year and six-year estimation periods to be most optimal (Alexander

& Chervany, 1980). Daves et al. (2000) conclude that an estimation period of two to three years is more appropriate to use when estimating beta with weekly returns, as weekly returns provide a smaller standard error or greatest precision of the beta estimate than when using weekly or monthly returns.

Choosing a long time period for estimating beta has the advantage of having more observations in the regression, but this can be offset by the fact it can result in a higher likelihood that there will be a significant change in beta which will result in a biased beta. Changes in corporate strategy can lead to changes in risk why using a long estimation period would underestimate the changes in risk (Koller et al., 2010: 252). Shorter return intervals increase the number of observations in the regression, but these can be problematic when a stock is rarely traded. An illiquid stock will have many reported returns equal to zero as it has not traded, which can affect the beta estimated. Using longer-dated returns will lessen this effect (ibid). Based on above-mentioned reasons, it is assessed that conducting a two-year, weekly and five-year, monthly regression analysis for Mattel and Hasbro is appropriate.

As the true market portfolio is unobservable, a proxy representing the market portfolio is necessary (Koller et al., 2010: 253). The most well-diversified indexes are highly correlated, why the choice of the index will have a small effect on the estimated beta. The S&P 500 Index is the most commonly used proxy for U.S. stocks why this is used for the regression analysis. The regression analysis is to be found in appendix 16.

The beta values conducted reflect beta value for equity, i.e. a levered beta, why they must be adjusted for financial leverage, by using the following equation:

𝛽_{𝑢𝑛𝑙𝑒𝑣𝑒𝑟𝑒𝑑} = 𝛽_{𝑙𝑒𝑣𝑒𝑟𝑒𝑑} (1 + (1 − 𝑇) ∗ ( 𝑑𝑒𝑏𝑡

𝑒𝑞𝑢𝑖𝑡𝑦)

The unlevered betas for Mattel and Hasbro are shown in the table below.

106 Table 5.9: Own creation

The beta for Lego is determined based on an arithmetic average of the beta values for Mattel and Hasbro, as shown in the table above.

The future net debt to equity ratio for Lego is estimated to be 0, as it is expected that the company will have no debt, due to the supposed target capital structure. The levered beta for Lego is therefore expected to be equal to the estimated unlevered beta. This beta is estimated to be 0.9064.

Calculating the cost of equity

Based on the estimated values for the risk-free rate, the market risk premium, and the beta, the cost of equity can be determined.

The WACC can due to above mentioned and estimated factors be calculated as:

𝐸(𝑟_𝑖) = 1.21 + (0.9064 ∗ 5.84) 𝐸(𝑟_𝑖) = 6.51%

The cost of equity is estimated to be 6.51 %. As previously mentioned, the capital structure of Lego is assessed to be 100 % equity financed why the cost of equity constitutes the WACC for Lego.

Firm Beta levered NIBL Share price (USD) Number of shares (mn) Equity (mn) Net Debt/Equity Tax rate Beta unlevered

Mattel 1.3281 2864 13.7 346.9 4742 60.39% 21% 0.8991

Hasbro 0.8979 -312 103.5 137.0 14183 -2.20% 21% 0.9137

Average numbers 1.113 0.9064

Lego calculation 0.9064 0 22% 0.9064

Part 6

Valuation

108

6 Valuation

This part of the thesis will make use of previous analysis, forecast and estimations, to compute a fair value of the LEGO Group as of March 31, 2020.

This part will examine the two selected present value approaches, Discounted Cash Flow model and the Economic Value-Added model where after a sensitivity analysis is conducted. Lastly, the relative valuation approach is assessed.