$11$

Problem $9-23($Algo$)$ Present value $[$L$09-3]$

Jack Hammer invests in a stock that will pay dividends of $$3\mathrm{.}05$ at the end of the first year; $$3\mathrm{.}40$ at the end of the second year; and $$3\mathrm{.}75$ at the end of the third year. Also, he believes that at the end of the third year he will be able to sell the stock for $$55.$

What is the present value of all future benefits if a discount rate of $12$ percent is applied? Use Appendix B for an approximate answer, but calculate your final answer using the formula and financial calculator methods.

Note: Do not round intermediate calculations. Round your final answers to $2$ decimal places.

$\backslash$table$[[$Dividend$,$Present Value$],[3\mathrm{.}05,],[3\mathrm{.}40,],[3\mathrm{.}75,],[55\mathrm{.}00,7],[$Total$,0\mathrm{.}00]]$

Step $2$

present value $=$ future value $\frac{?}{(1+\text{d}\text{i}\text{s}\text{c}\text{o}\text{u}\text{n}\text{t}\text{r}\text{a}\text{t}\text{e}{)}^{{?}^{{?}^{?}}}}$ number of years till cash flow

Present value $=(D\frac{1}{(1+i{)}^1})+(D\frac{2}{(1+i{)}^2})+(D\frac{3}{(1+i{)}^3})+(P\frac{3}{(1+i{)}^3})$

$=(\frac{\text{\$}3\mathrm{.}05}{(1+12\%{)}^1})+(\frac{\text{\$}3\mathrm{.}40}{(1+12\%{)}^2})+(\frac{\text{\$}3\mathrm{.}75}{(1+12\%{)}^3})+(\frac{\text{\$}55}{(1+12\%{)}^3})$

$=47\mathrm{.}25$

The present value of all future benefits if a discount rate of $12$ percent is applied is $$47\mathrm{.}25$

Answer

The present value of all future benefits if a discount rate of $12$ percent is applied is $$47\mathrm{.}25$