# Estratégia Financeira

Part 4 - ch.12 Estimating the Cost of Capital

Henrique C. Martins

10-03-2024

## Chapter Outline

12.1 The Equity Cost of Capital

12.2 The Market Portfolio

12.3 Beta Estimation

12.4 The Debt Cost of Capital

12.5 A Project’s Cost of Capital

12.6 Project Risk Characteristics and Financing

12.7 Final Thoughts on Using the CAPM

# 12.1 The Equity Cost of Capital

## 12.1 The Equity Cost of Capital

The CAPM Equation for the Cost of Capital (using the Security Market Line).

The cost of capital of any investment opportunity equals the expected return of available investments with the same beta.

$R_i = R_f + \beta \times (E[R_m] - R_f)$

## 12.1 The Equity Cost of Capital

Problem

Suppose you estimate that Disney’s stock (DIS) has a volatility of 20% and a beta of 1.29. A similar process for Chipotle (CMG) yields a volatility of 30% and a beta of 0.55.

Which stock carries more total risk? Which has more market risk?

Disney has more Systematic risk.

Chipotle has more total risk.

## 12.1 The Equity Cost of Capital

Problem

Suppose you estimate that Disney’s stock (DIS) has a volatility of 20% and a beta of 1.29. A similar process for Chipotle (CMG) yields a volatility of 30% and a beta of 0.55.

If the risk-free interest rate is 3% and you estimate the market’s expected return to be 8%, calculate the equity cost of capital for DIS and CMG. Which company has a higher cost of equity capital?

$R_{DIS}=3\%+1.29 \times (8\%−3\%) = 3\% + 6.45\% =9.45\%$

$R_{GMG}=3\%+0.55 \times(8\%−3\%)=3\%+2.75\%=5.75\%$

Because market risk cannot be diversified, it is market risk that determines the cost of capital; thus DIS has a higher cost of equity capital than CMG, even though it is less volatile.

## 12.1 The Equity Cost of Capital

Suppose you estimate that Walmart’s stock has a volatility of 16.1% and a beta of 0.20. A similar process for Johnson & Johnson yields a volatility of 13.7% and a beta of 0.54. Which stock carries more total risk? Which has more market risk?

Walmart stock has more total risk.

Johnson & Johnson has a higher beta, so it has more market risk

## 12.1 The Equity Cost of Capital

Suppose you estimate that Walmart’s stock has a volatility of 16.1% and a beta of 0.20. A similar process for Johnson & Johnson yields a volatility of 13.7% and a beta of 0.54. Which stock carries more total risk? Which has more market risk?

If the risk-free interest rate is 4% and you estimate the market’s expected return to be 12%, calculate the equity cost of capital for Walmart and Johnson & Johnson. Which company has a higher cost of equity capital?

$r_{JNJ}=4\%+0.54×(12\%−4\%)=4\%+4.32\%=8.32\%$

$r_{WMT}=4\%+0.20×(12\%−4\%)=4\%+1.6\%=5.6\%$

Because market risk cannot be diversified, it is market risk that determines the cost of capital; thus, Johnson & Johnson has a higher cost of equity capital than Walmart, even though it is less volatile.

# 12.2 The Market Portfolio

## 12.2 The Market Portfolio

To use the CAPM, we need to understand what the market portfolio is.

Because the market portfolio is the total supply of securities, the proportions of each security should correspond to the proportion of the total market that each security represents.

Thus, the market portfolio contains more of the largest stocks and less of the smallest stocks.

Market capitalization (of one firm):

• The total market value of a firm’s outstanding shares

$MV_i = (nr\;of\;shares\;outstanding) \times (price\;per\;share) = N_i \times P_i$

## 12.2 The Market Portfolio

We then calculate the portfolio weights of each security: that is a Value-Weighted Portfolio

• A portfolio in which each security is held in proportion to its market capitalization

$x_i = \frac{MV_i}{Total\; MV}= \frac{MV_i}{\sum{MV}}$

## 12.2 The Market Portfolio

Passive portfolio

• trade not often

Active portfolio

• trade often

## 12.2 The Market Portfolio

Examples of indexes:

• SP500: A value-weighted portfolio of the 500 largest U.S. stocks
• Dow Jones Industrial Average (DJIA): A price-weighted portfolio of 30 large industrial stocks (holds an equal number of shares of each stock).
• Ibov : Around 90 BR stocks. Follows an algorithm focusing on liquidity.

ETFs (Exchange-traded funds): A portfolio that follows an index, like the SP500.

SP500 and Ibov are not considered as the market portfolio, they are proxies for the market portfolios. I.e., reasonable approximations.

R
stocks <-c('SPY', 'IVV','VOO', 'SPLG' , '^GSPC')
start <-'2010-01-01'
end   <-Sys.Date()
data <- yf_get(tickers = stocks,
first_date = start,
last_date = end)
data<-data[complete.cases(data),]
stock1 <- subset(data, ticker == stocks[1])
stock2 <- subset(data, ticker == stocks[2])
stock3 <- subset(data, ticker == stocks[3])
stock4 <- subset(data, ticker == stocks[4])
stock5 <- subset(data, ticker == stocks[5])
stock1$price_close2 <- stock1$price_close  / stock1$price_close[1] * 100 stock2$price_close2 <- stock2$price_close / stock2$price_close[1] * 100
stock3$price_close2 <- stock3$price_close  / stock3$price_close[1] * 100 stock4$price_close2 <- stock4$price_close / stock4$price_close[1] * 100
stock5$price_close2 <- stock5$price_close  / stock5\$price_close[1] * 100
data2 <- rbind(stock1, stock2, stock3, stock4, stock5)
p<-ggplot(data2, aes(ref_date , price_close2, color=ticker))+
geom_line() +
labs(x = "",
y='Closing prices',
title="SP500 against 4 ETFs, Initial price = 100",
subtitle = "Begin 01/01/2010") +   theme_solarized()
ggplotly(p)