Use the following formula to answer problems on $$shareholder returns, where is the share price at time t$,$ and is the dividend paid at time t$.$ Shareholder$$Return $=$ D$2/$P$1+$P$2-$P$1/$P$1$

$4\mathrm{.}1$ Emaline Returns. If the share price of Emaline, a New Orleans$-$based shipping firm, rises from $$12$ to $$15$ over a one$-$year period, what is the rate of return to the shareholder given each of the following: The company paid no dividends. The company paid a dividend of $$1$ per share. The company paid the dividend and the total return to the shareholder is separated into the dividend yield and the capital gain.

$4\mathrm{.}2$ Vaniteux$$s Returns $($A$).$ Spencer Grant is a New York$-$based investor. He has been closely following his investment in $100$ shares of Vaniteux, a French firm that went public in February $2010.$ When he purchased his $100$ shares at $17\mathrm{.}25$ per share, the euro was trading at $$1\mathrm{.}360/.$ Currently, the share is trading at $28\mathrm{.}33$ per share, and the dollar has fallen to $$1\mathrm{.}4170/.$ If Spencer sells his shares today, what percentage change in the share price would he receive? What is the percentage change in the value of the euro versus the dollar over this same period? What would be the total return Spencer would earn on his shares if he sold them at these rates?

$4\mathrm{.}3$ Vaniteux$$s Returns $($B$).$ Spencer Grant chooses not to sell his shares at the time described in Problem $4\mathrm{.}2.$ He waits, expecting the share price to rise further after the announcement of quarterly earnings. His expectations are correct, and the share price rises to $31\mathrm{.}14$ per share after the announcement. He now wishes to recalculate his returns. The current spot exchange rate is $$1\mathrm{.}3110/.4\mathrm{.}4$ Vaniteux$$s Returns $($C$).$ Using the same prices and exchange rates as in Problem $4\mathrm{.}3,$ Vaniteux $($B$),$ what would be the total return on the Vaniteux investment by Laurent Vuagnoux, a Paris$-$based investor?

$4\mathrm{.}5$ Microsoft$$s Dividend. In January $2003,$ Microsoft announced that it would begin paying a dividend of $$0\mathrm{.}16$ per share. Given the following share prices for Microsoft stock in the recent past, how would a constant dividend of $$0\mathrm{.}16$ per share per year have changed the company$$s return to its shareholders over this period? First Closing First Closing Trading Day Share Price Trading Day Share Price $1998($Jan $2)$ $$131\mathrm{.}132001($Jan $2)$ $$43\mathrm{.}381999($Jan $4)$ $$141\mathrm{.}002002($Jan $2)$ $$67\mathrm{.}042000($Jan $3)$ $$116\mathrm{.}562003($Jan $2)$ $$53\mathrm{.}724\mathrm{.}6$ Carty$$s Choices. Brian Carty, a prominent investor, is evaluating investment alternatives. If he believes an individual equity will rise in price from $$59$ to $$71$ in the coming one$-$year period, and the share is expected to pay a dividend of $$1\mathrm{.}75$ per share, and he expects at least a $15\%$ rate of return on an investment of this type, should he invest in this particular equity?