$1$

$.$

$$You are making forecasts for two securities that promise perpetual, growing annual cash flows. For both securities

$,$

$$calculate the cash flow you can expect at the end of year

$7($

that is

$,$

$$seven years from now

$)$

$.$

a

$.$

$$Security A will pay $

$10$

$$next year

$($

year

$1)$

$,$

$$and the cash flows will grow at a rate of

$2$

$\%$

$$per year thereafter.

b

$.$

$$Security B paid $

$9$

$$last night, and the cash flows are expected to grow at a rate of

$2\mathrm{.}5$

$\%$

$$per year.

Answer Question

$1$

:

$)$

For Security

$-$

A:

Year

$-$

$1\text{'}$

s cash flows

$=$

$$$

$10\mathrm{.}0000[$

First cashflow

$]$

Year

$-$

$2\text{'}$

s cash flows

$=$

$$$

$10\mathrm{.}2000[$

$

$10$

$$x

$102$

$\%$

$=$

$$$

$10\mathrm{.}2]$

Year

$-$

$3\text{'}$

s cash flows

$=$

$$$

$10\mathrm{.}4040[$

$

$10\mathrm{.}2$

$$x

$102$

$\%$

$=$

$$$

$10\mathrm{.}404]$

Year

$-$

$4\text{'}$

s cash flows

$=$

$$$

$10\mathrm{.}6121[$

$

$10\mathrm{.}404$

$$x

$102$

$\%$

$=$

$$$

$10\mathrm{.}6121]$

Year

$-$

$5\text{'}$

s cash flows

$=$

$$$

$10\mathrm{.}8243[$

$

$10\mathrm{.}6121$

$$x

$102$

$\%$

$=$

$$$

$10\mathrm{.}8243]$

Year

$-$

$6\text{'}$

s cash flows

$=$

$$$

$11\mathrm{.}0408[$

$

$10\mathrm{.}8243$

$$x

$102$

$\%$

$=$

$$$

$11\mathrm{.}0408]$

Year

$-$

$7\text{'}$

s cash flows

$=$

$$$

$11\mathrm{.}26[$

$

$11\mathrm{.}0408$

$$x

$102$

$\%$

$=$

$$$

$11\mathrm{.}26]$

For Security

$-$

B:

Year

$-$

$0\text{'}$

s cash flows

$=$

$$$

$9\mathrm{.}0000[$

First cashflow

$]$

Year

$-$

$1\text{'}$

s cash flows

$=$

$$$

$9\mathrm{.}2250[$

$

$9$

$$x

$102\mathrm{.}5$

$\%$

$=$

$$$

$9\mathrm{.}225]$

Year

$-$

$2\text{'}$

s cash flows

$=$

$$$

$9\mathrm{.}4556[$

$

$9\mathrm{.}225$

$$x

$102\mathrm{.}5$

$\%$

$=$

$$$

$9\mathrm{.}4556]$

Year

$-$

$3\text{'}$

s cash flows

$=$

$$$

$9\mathrm{.}6920[$

$

$9\mathrm{.}4556$

$$x

$102\mathrm{.}5$

$\%$

$=$

$$$

$9\mathrm{.}692]$

Year

$-$

$4\text{'}$

s cash flows

$=$

$$$

$9\mathrm{.}9343[$

$

$9\mathrm{.}692$

$$x

$102\mathrm{.}5$

$\%$

$=$

$$$

$9\mathrm{.}9343]$

Year

$-$

$5\text{'}$

s cash flows

$=$

$$$

$10\mathrm{.}1827[$

$

$9\mathrm{.}9343$

$$x

$102\mathrm{.}5$

$\%$

$=$

$$$

$10\mathrm{.}1827]$

Year

$-$

$6\text{'}$

s cash flows

$=$

$$$

$10\mathrm{.}4372[$

$

$10\mathrm{.}1827$

$$x

$102\mathrm{.}5$

$\%$

$=$

$$$

$10\mathrm{.}4372]$

Year

$-$

$7\text{'}$

s cash flows

$=$

$$$

$10\mathrm{.}70[$

$

$10\mathrm{.}4372$

$$x

$102\mathrm{.}5$

$\%$

$=$

$$$

$10\mathrm{.}70]$

$$

$2$

$.$

Assume that the appropriate discount rate for both perpetuities described in Question

$1$

$$is

$9$

$\%$

$.$

$$Calculate the present value of the expected future payments from each of these securities

$.$

$($

please answer Question

$2$

$$using the results of Question

$1)$