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Ameritrade

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HBS 9-201-046 Cost of Capital at Ameritrade

1. Qual é a sua estimativa de Rf para utilizar no cálculo do custo de capital da Ameritrade? Fundamente a escolha.
A taxa Rf é estimada através de títulos do tesouro nacional, normalmente compatíveis com o tamanho do projeto que se deseja financiar. Visto que não há menção do tamanho do projeto (duração em anos), iremos utilizar a taxa de títulos do tesouro nacional de 10 anos. Estes títulos, diferente dos títulos de curto prazo, não são tão voláteis, englobam taxas semelhantes às taxas utilizadas por títulos de longo prazo de uma empresa, como a taxa de inflação, e um período de 10 anos representa, de maneira aproximada, a duração de um projeto empresarial. Assim, estimamos que a taxa risk-free é 6,34%, como no exhibit 3

2. Qual é a sua estimativa de MRP para utilizar no cálculo do custo de capital da Ameritrade? Fundamente a escolha.
Para descobrir o Market Risk Premium é a taxa de retorno, de um determinado período, a mais que os bonds de longo prazo, deste determinado período, oferecem. De maneira mais exemplificada, se as empresas oferecem bonds a taxas de 6% e ao mesmo tempo oferecem uma taxa de retorno para suas ações de 10%, teremos que o investidor tem um prêmio de mercado de 4% caso decida comprar ações. Isto porque nenhum investidor, avesso à risco, assumiria mais risco sem ter uma compensação, em termos de retorno, por isto.

No caso, podemos observar que o Exhibit 3 mostra as taxas médias de Bonds de longo prazo, 5,5% e o valor médio de retorno de ações de grandes empresas, 12,7%. Desta maneira, podemos assumir que o MRP é igual a 7,2%. Como o período selecionado é de 1992-96, como o valor dos betas encontrados posteriormente, podemos assumir que utilizar esta taxa para achar o retorno exigido da Ameritrade é uma estimativa razoável.

3. Como as ações da Ameritrade têm sido negociadas por um período relativamente curto, não é aconselhável usar esses dados de retorno para calcular seu beta. O Exhibit 4 contém várias empresas que podem ser utilizadas como comparáveis. Quais você recomenda utilizar como referência?

As ações da Ameritrade estão negociadas em apenas 6 meses (março 97 – agosto 97), o que representa um período muito curto para estimar seu beta. Dessa forma, dentre as empresas apresentadas no Exhibit 4 utilizamos as empresas Charles Schwab Corp., Quick & Reilley Group e a Waterhouse Investor Services como referência para se calcular o beta da Ameritrade. Apesar de ter sido avaliada como uma empresa de Internet por analistas da ABN-AMRO, comparamos a Ameritrade como sendo uma brokerage firm (empresa de corretagem). Diante disso, comparamos a Ameritrade com empresas classificadas do mesmo setor, visto que mais de 90% de suas receitas provém de comissões de corretagem (brokerage commissions) e de contas de clientes (brokerage accounts of customers).
Além disso, para se calcular o beta de cada empresa é necessário saber tanto a quantidade de ações, quanto o preço delas no mercado. Diante disso, o caso nos fornece a quantidade de ações e o preço apenas das empresas do setor de comissão de corretagem e, por isso, tivemos também como referência essa empresas. Vale ressaltar que a empresa E*Trade também apresentou dados de um curto período de tempo e, dessa forma não foi incluída nos cálculos. Por fim, após descobrir o beta de cada uma das empresas utilizadas como referência (Charles Schwab, Quick & Reilley e Waterhouse), foi tirado uma média, a fim de se ter uma ideia e/ou um intervalo para encontrar o beta da Ameritrade.

4. Com base nos preços de ação e dados de retorno dos Exhibits 5 e 6 e nas informações de estrutura de capital do Exhibit 4, calcule os betas dos ativos para as empresas que você considera comparáveis.
Calculamos os betas das seguintes empresa Charles Schwab Corp., Quick & Reilley Group e a Waterhouse Investor Services. A seguir iremos descrever o que fizemos para calcular os betas de cada empresa, sendo a planilha utilizada por nós no Anexo I deste trabalho * Charles Schwab
Após calcular o retorno esperado da ação (Rs) e o desvio padrão (sigma s), calculamos tanto o retorno médio do período (0,0334), quanto o desvio padrão também do período (0,1151).
Em seguida, tiramos a média do índice de mercado VW NYSE, AMEX and NASDAQ (0,01), a fim de descobrir a variância do mercado (0,000613) para, em seguida, descobrir a covariância entre o valor médio da ação e a variância do mercado, ou seja, (valor da ação - valor médio do preço)* (valor do índice de mercado – média do índice de mercado). A somatória do resultado do período dividido pelo número de meses desse período, menos 1, (60 – 1 = 59) será equivalente a covariância entre ação e mercado. Por fim, fazemos a covariância entre ação e mercado e dividimos pela variância do mercado, o que nos resulta no Beta = 2,2970.
Vale ressaltar que a Charles Schwab possui um histórico de divida considerável, possuindo uma média (1992-1996) de 0,087 de dívida sobre o equity (debt/equity) . Diante disso, nesse caso deve-se tirar as dívidas da empresa e considerar apenas o risco do negócio, na medida em que nem toda empresa possui um endividamento como a Charles Schwab. Dessa forma, deve-se primeiro tirar as dívidas da empresa e considerar que ela está somente sob efeito de impostos (40%) e em seguida calcular o risco do negócio, ao invés do risco geral dela e, por fim, poder comparar com a Ameritrade.
Dessa forma o Beta da Charles Schwab será igual:
=2,2970 / (1+(1-0,4)*0,87)
Beta = 2,1831 * Quick & Reilley Group
Como a empresa apresentava uma média de divida igual a zero, os cálculos seguiram o padrão normal.
Calculamos o retorno esperado da ação (Rs) e o desvio padrão (sigma s), calculamos tanto o retorno médio do período, quanto o desvio padrão também do período.
Em seguida, tiramos a média do índice de mercado VW NYSE, AMEX and NASDAQ (0,01), a fim de descobrir a variância do mercado (0,000613) para, em seguida, descobrir a covariância entre o valor médio da ação e a variância do mercado, ou seja, (valor da ação - valor médio do preço)* (valor do índice de mercado – média do índice de mercado). A somatória do resultado do período dividido pelo número de meses desse período, menos 1, (60 – 1 = 59), será equivalente a covariância entre ação e mercado. Por fim, fazemos a covariância entre ação e mercado e dividimos pela variância do mercado, o que nos resulta:
Beta = 2,2042.

* Waterhouse Investor Services
Já a Waterhouse, assim como a Charles Schwab, apresentou uma média (1992-1996) de dívida considerável (0,61) em relação ao equity da empresa.
Dessa forma, feito o cálculo padrão para o Beta da empresa, deve-se tirar a dívida para focar somente no risco do negócio.
Primeiramente o cálculo padrão do Beta. Calculamos o retorno esperado da ação (Rs) e o desvio padrão (sigma s), e depois calculamos tanto o retorno médio do período, quanto o desvio padrão também do período.
Em seguida, tiramos a média do índice de mercado VW NYSE, AMEX & NASDAQ (0,01), a fim de descobrir a variância do mercado (0,0005842) para, em seguida, descobrir a covariância entre o valor médio da ação e a variância do mercado, ou seja, (valor da ação - valor médio do preço)* (valor do índice de mercado – média do índice de mercado). A somatória do resultado do período dividido pelo número de meses desse período, menos 1, (57 – 1 = 56) será equivalente a covariância entre ação e mercado. Por fim, fazemos a covariância entre ação e mercado e dividimos pela variância do mercado, o que nos resulta no Beta = 3,190.
Dessa forma o Beta da Waterhouse será igual:
=3,190 / (1+(1-0,4)*0,6129)
Beta = 2,3322
*sendo: 0,4 = imposto 0,6129 = debt/equity

5. Finalmente, calcule o WACC que a Ameritrade deve utilizar para analisar a atratividade dos investimentos propostos.
Primeiramente, é necessário estimar as taxas alvos (target capital strutcture) da empresa. Portanto, começaremos por estimar o valor de mercado das ações da empresa. Como é possível perceber pelo Balanço Patrimonial da empresa, Exhibit 2, a Ameritrade não possui ações preferências, o que diminui o WACC para RsWs + WdRd(1-t). Então, multiplicamos a quantidade de ações em 1997 pelo valor das ações em Março de 1997, chegando no valor de mercado das ações igual à 215.138.891. Como não existe distinção entre passivo circulante e passivo não-circulante, utilizamos o valor completo das dívidas da empresa para o cálculo das taxas alvo, 371.017.168. Assim, achamos que os valores de 63,17% para as dívidas da empresa e 36,83% para as ações da empresa.
O próximo passo é estimar o beta da Ameritrade e o retornos exigido pelos acionistas:
Como é possível perceber acima, o Beta da Ameritrade foi estimado pela média dos betas livres do risco das dívidas da empresas (unlevered Beta). A partir dai, utilizamos a média dos betas como o beta da Ameritrade e, assim, calculamos um retorno exigido de 22,47% pelos acionistas.
Por último, é necessário o retorno exigido por terceiros, que financiam a dívida da empresa. Como não existe nenhuma informação referente somente a Ameritrade sobre o custo da dívida da empresa, utilizamos o valor de bonds de longo prazo, apresentadas no Exhibit 3. Mas, observando o valor alto do beta 2,24 em relação ao mercado, 1, consideramos que a empresa apresenta mais risco do que a média do mercado e, portanto, “corrigimos” a taxa de retorno exigida no período considerado para aproximarmos a Ameritrade do que consideramos a realidade. Assim, ao invés de 5,5%, achamos que a empresa, por ser mais arriscada do que as outras apresentadas no exhibit 6, em termos de beta, apresenta uma taxa que deve ser entre 0,5 e 1,5 desvios-padrões para cima. Assim, assumimos a taxa deveria ser 5,5% mais 1 desvio-padrão, chegando na taxa de bonds de longo prazo de 14,7%. Como a taxa tem um “tax shield”, desconsiderando o imposto (40%), encontramos uma taxa de para as dívidas da empresa de 8,82%.
Assim, estimamos que o WACC da Ameritrade é igual a 14,3%, como demonstrado abaixo.

Anexo I

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...Cost of Capital at Ameritrade: 1. What factors should Ameritrade management consider when evaluating the proposed advertising program and technology upgrades? Why? When deciding whether or not to invest in the proposed advertising program and technology upgrades, Ameritrade should consider the following four key factors: 1. Cost of Capital: It is important that Ameritrade understand the risk associated with this project’s cost of capital. Ameritrade should look at the cost of capital to determine if the expected return on this project will be equal to or greater than investing this capital elsewhere. 2. Net present value of the cash flow: After looking at the cost of capital, Ameritrade will want to look at the cash flows for the project and determine the net present value of the cash flows. This will help Ameritrade understand if this is where they want to invest their money, but understanding how much they will receive annually from this project. 3. Accurate discount rate: Ameritrade will want to know if this project can deliver more than the discount rate. It is important to choose an accurate discount rate since an overstatement or understatement could lead to the wrong investment decision because of using an incorrect benchmark. 4. Debt to Equity ratio: Ameritrade should look at their debt to equity ratio compared to other companies in their industry. Since Ameritrade could potentially compare against two different industries, they will want to...

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