$1.$ Interpreting Beta and Portfolio Betas

The table below shows the Betas for four firms.

Firm A Firm B Firm C Firm D

Beta $0\mathrm{.}791\mathrm{.}051\mathrm{.}360\mathrm{.}85$

$1.$ Does Firm A$$s stock have more or less systematic risk than the typical stock?

$2.$ Is Firm B$$s stock more or less volatile than the overall market?

$3.$ If market returns increase by $1\%,$ how much would Firm A$$s returns change by$?$

$4.$ If market returns increase by $1\%,$ how much would Firm B$$s returns change by$?$

$5.$ If market returns increase by $1\%,$ how much would Firm C$$s returns change by$?$

$6.$ If market returns increase by $1\%,$ how much would Firm D$$s returns change by$?$

$7.$ What is the portfolio Beta if a portfolio contains $1$ share each of Firm A$,$ B$,$ C$,$ and D$$s stocks? Assume the price of each stock is the same.

$8.$ Is the portfolio in $(7.)$ more or less volatile than the overall market?

$9.$ What is the portfolio Beta if a portfolio contains $10$ shares of Firm A$$s stock, $5$ shares of Firm B$$s stock, $5$ shares of Firm C$$s stock, and $20$ shares of Firm D$$s stock? Assume the price o each stock is the same.

$10.$ Is the portfolio in $(9.)$ more or less volatile than the overall market?

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$2.$ CAPM and Required Returns

The table below shows the Betas for four firms.

Firm A Firm B Firm C Firm D

Beta $0\mathrm{.}791\mathrm{.}051\mathrm{.}360\mathrm{.}85$

$1.$ If the return on the market is $20\%$ and the risk$-$free rate of return is $5\%,$ what is the risk premium?

$2.$ If the return on the market is $20\%$ and the risk$-$free rate of return is $5\%,$ what is the required return on Firm A$$s stock?

$3.$ If the return on the market is $20\%$ and the risk$-$free rate of return is $5\%,$ what is the required return on Firm B$$s stock?

$4.$ If the return on the market is $15\%$ and the risk$-$free rate of return is $3\%,$ what is the risk premium?

$5.$ If the return on the market is $15\%$ and the risk$-$free rate of return is $3\%,$ what is the required return on Firm C$$s stock?

$6.$ If the return on the market is $15\%$ and the risk$-$free rate of return is $3\%,$ what is the required return on Firm D$$s stock?

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$3.$ Bonds

The table below shows PV factors for interest rates of $2\%,5\%,$ and $8\%.$

Year $1$ Year $2$ Year $3$

PV Factor $(2\%)0\mathrm{.}98040\mathrm{.}96120\mathrm{.}9423$

PV Factor $(5\%)0\mathrm{.}95240\mathrm{.}90700\mathrm{.}8638$

PV Factor $(8\%)0\mathrm{.}92590\mathrm{.}85730\mathrm{.}7938$

$1.$ If a $$1,000$ par value bond has a coupon interest rate of $5\%,$ what is the annual interest payment?

$2.$ What is the value of a bond with a $$1,000$ par value and a $5\%$ coupon interest rate with $3$ years until maturity if investors require a $5\%$ rate of return on similar bonds?

$3.$ What is the value of a bond with a $$1,000$ par value and a $5\%$ coupon interest rate with $3$ years until maturity if investors require a $2\%$ rate of return on similar bonds?

$4.$ What is the value of a bond with a $$1,000$ par value and a $5\%$ coupon interest rate with $3$ years until maturity if investors require an $8\%$ rate of return on similar bonds?

$5.$ Is the bond at a discount or premium when the required rate of return on similar bonds is $2\%?$

$6.$ Is the bond at a discount or premium when the required rate of return on similar bonds is $8\%?$

$7.$ What required rate of return will cause the bond to be at par $($i$.$e$.,$ the bond value is $$1,000)?$

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$4.$ Preferred Stock

$1.$ A firm$$s preferred stock pays an annual dividend of $$3\mathrm{.}60.$ What is the value of the stock if an investor$$s required rate of return is $10\%$

$2.$ A firm$$s preferred stock currently trades at a price of $$33$ and pays an annual dividend of $$3\mathrm{.}60.$ What is the expected rate of return on the stock?

$3.$ Does the expected rate of return increase or decrease if the stock price increases to $$36?$ Assume the annual dividend remains constant at $$3\mathrm{.}60.$

$4.$ Does the expected rate of return increase or decrease if the annual dividend increases to $$4\mathrm{.}00?$ Assume the stock price remains constant at $$33.$

$5.$ Common Stock

A firm$$s common stock paid a dividend of $$3\mathrm{.}50$ at the end of last year and has a dividend growth rate of $5\%.$

$1.$ What dividend will the firm pay at the end of this year?

$2.$ What is the value of the stock if an investor$$s required rate of return is $20\%?$

$3.$ What is the expected rate of return on this stock if it currently trades at a price of $$24\mathrm{.}50?$

$4.$ Does the expected rate of return increase or decrease if the stock price increases to $$27\mathrm{.}50?$ Assume the dividend is the same as in $(1.)$ and the dividend growth rate remains constant at $5\%.$