Chapter $7$ AND Chapter $9$ Problems $(22$ points$)($where applicable, use the time value of money template$)$:

a$.$ Assume a $$1000$ face value bond has a coupon rate of $8\mathrm{.}5\%,$ pays interest annually, and has an $8-$year life.

i$.$ If investors are willing to accept a $9\mathrm{.}25\%$ rate of return on bonds of similar quality, what is the $($present$)$ value of this bond and is it selling at a premium or discount?

ii$.$ What would be value of this same bond if investors are instead willing to accept an $8\mathrm{.}25\%$ rate, and is it selling a premium or discount?

b$.$ The Garcia Company's bonds have a face value of $$1000,$ will mature in $10$ years, and carry a coupon rate of $6\%.$ Assume that interest payments are made semiannually.

i$.$ Determine the price of the bond today if the investor required rate of return is $7\mathrm{.}2\%.$

ii$.$ Determine the price of the bond today if the investor required rate of return is $5\mathrm{.}8\%.$

c$.$ The Fridge$-$Air Company's preferred stock pays a dividirad of $$5\mathrm{.}50$ per share annually. If the required rate of return on comparable quality preferred stocks is $14\%,$ calculate the value of Fridge$-$Air's preferred stock today.

d$.$ The Lo Company earned $$2\mathrm{.}60$ per share and paid a dividend of $$1\mathrm{.}50$ per share in the year just ended. Earnings and dividends per share are expected to grow at a rate of $6\%$ per year in the future. Determine the value of the stock $($using the Gordon growth model of valuation$)$:

i$.$ If the required rate of return is $12\%$

ii$.$ If the required rate of return is $15\%$

iii. How are the stock prices different as calculated in parts $($i$)$ and $($ii$)$ above?

e$.$ Mercier Corporation's stock is selling for $$95.$ It has just paid a dividend of $$5$ per share. The expected growth rate in dividends is $6\%.$

i$.$ What is the required rate of return on this stock?

ii$.$ If the growth rate is $8\%$ annually $($instead of $6\%),$ what will the stock price be$?$

iii. Given your answers to parts $($i$)$ and $($ii$)$ above, how important are investors' expectations on future dividend growth to the current stock price and why?