应该要如何计算?第一条Todayyouhaveboughtastockandyourrequiredrateofreturnis10%.Anannualdividendof$1.8persharewillbepaidnextyearanditisexpectedtoincreaseatanannualrateof5%indefinitely.Whatwillbetheamoun

Question

应该要如何计算?
第一条
Today you have bought a stock and your required rate of return is 10%.An annual dividend of $1.8 per share will be paid next year and it is expected to increase at an
annual rate of 5% indefinitely.What will be the amount of your capital gain if you
sell the stock out five year from now?What is the stock dividend yield now?
第二条
Heidi owns 400 shares of Boyd Enterprises stock,which is valued at $17 a share.
Boyd Enterprises just declared a 10% stock dividend.How many shares will Heidi
own and what will the price per share be after the dividend?

Answer 1

第一条：今天你买了一支股票,预期回报率为10%.明年将有1.8美元/股的年分红,并且年分红预计以5%的年利率无限增长.如果你第五年五年卖掉股票,你的资本利得将为多少?（如果持有股票到无限期）现在的股息率为多少?
如果第五年卖掉股票,当期的资本利得Capital Gain=1.8*(1.1^4)+1.8*(1.1^3)*(1.05)+1.8*(1.1^2)*(1.05^2)+1.8*(1.1)*(1.05^3)+1.8*(1.05^4)=(结果请自己计算),
如果持有股票到无限期,那么今年为第0期,第i年为第i期,则第i期可获得红利为1.8*[1.05^(i-1)],折算成第0期的现值为1.8*[1.05^(i-1)]/ (1.1^i),那么所有期的红利折算到第0期,总现值为PTV=∑1.8*[1.05^(i-1)]/(1.1^i),（i=1,2,3,…,+∞）=36美元/股,
那么现在股息率Dividend Yield=PTV/每股股票价格P
本题中的股价P未给出,因而算不出股息率的具体数值,只能算得即期的总股息PTV=36美元/股
第二条：Heidi拥有Boyd Enterprises股票400股,每股价值17美元.Boyd Enterprises刚刚发布要派发10%的股票红利.Heidi将拥有多少股?在分红后每股价格将为多少?
当现金分红后,
如果不除权,那么分红后他将持有股票数仍400股,价值6800元,加上680的分红,总价值7480元.
如果除权,那么分红后他将持有股票数仍为400股,只是股价变为原来的0.9倍而已,总价值不变仍为6800元.