Discount Rate for Risky Cash Flow

Consider a risk$-$free bond and a stock. The bond has no coupons and will deliver a face value of $$100$ in year

The stock has no dividends, and its price in year $1$ will be either $$200$ or $$0$ with a $50\%$ chance of each

outcome.

$($a$)$ The current price of the bond is $$98.$ What is the risk$-$free rate?

$($b$)$ What is the expected future price of stock in year $1?($Hint: To find the expected future price, we

multiply each price outcome by the corresponding probability and sum across different outcomes.$)$

$($c$)$ In the market, the stock currently sells for $$93\mathrm{.}5($recall that this is the average from our class survey$).$

What is the equity cost of capital $($required return on stock$)?$

$($d$)$ Why is the discount rate in $($c$)$ different from the risk$-$free rate in $($a$)?$