This problem set question is going through a variety of pricing changes related to a one$-$period bond with a certain payoff. The equation for pricing such a bond is:

P$=$X$/$ I$+$ R

Where X is the amount the bond pays and R is the discount rate.

a$)$ At $10$am$,$ the discount rate, R$,$ is $10\%$ and the bond pays $$100,$ X$,$ at maturity. What is the price of the bond at $10$am$?$

b$)$ What is the expected return holding the bond to maturity? Do you need to worry about the difference between expected and realized returns? Use the basic return formula, so it will be:

X$-$P

Return to maturity$=$p

c$)$ At $11$am$,$ the discount rate changes to $25\%.$ What is the price of the bond at $11$am$?$ What is the realized return from $10$ am until $11$am$?$ What is the change in the expected return holding to maturity $($R$)$ from $10$am until $11$am$?$ Are realized and expected returns positively or negatively correlated? Is the news from $10$am until $11$ am return news or cash flow news?

d$)$ At $12$pm we learn that the bond will actually pay $$50.$ The interest rate stays at $25\%.$ What is the price of the bond at $12$pm$?$ What is the realized return from $11$ am until $12$pm$?$ What is the change in the expected return $($R$)$ from $11$ am until $12$pm$?$ Are realized and expected returns positively or negatively correlated? Is the news from $11$ am until $12$pm return news or cash flow news?

e$)$ What is the return on holding the bond from $10$am until $12$pm$?$ Did return news or cash flow news have a bigger impact on these returns?

$)$ Use the present value relation to talk about return news and cash flows news for equities. Would you expect to find similar patterns in pricing based on return news and cash flow news for such a stock? Why or why not?