Problem $5$ $-18$ Present Values (LO $2$ ) $\newline$ A factory costs $\$ 400,000$ . You forecast that it will produce cash inflows of $\$ 120,000$ in year $1, \$ 180,000$ in year $2$ , and $\$ 300,000$ year $3$ . The discount rate is $12 \%$ . $\newline$ a. What is the value of the factory? $\newline$ Note: Do not round intermediate calculations. Round your answer to $2$ decimal places. $\newline$ Value of the factory

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Q. Problem

5

-18

Present Values (LO

2

)

\newline

A factory costs

\$ 400,000

. You forecast that it will produce cash inflows of

\$ 120,000

in year

1, \$ 180,000

in year

2

, and

\$ 300,000

year

3

. The discount rate is

12 \%

\newline

a. What is the value of the factory?

\newline

Note: Do not round intermediate calculations. Round your answer to

2

decimal places.

\newline

Value of the factory

Calculate PV for Year $1$ : To find the value of the factory, we need to calculate the present value of the cash inflows for each year and then sum them up. The formula for the present value (PV) of a future cash inflow is: $\newline$ $PV = \frac{\text{Cash Inflow}}{(1 + r)^n}$ $\newline$ where $r$ is the discount rate and $n$ is the number of years until the cash inflow.
Calculate PV for Year $2$ : First, let's calculate the present value of the cash inflow for year $1$ , which is $\$120,000$ .
$PV_{\text{year1}} = \frac{\$120,000}{(1 + 0.12)^1}$
$PV_{\text{year1}} = \frac{\$120,000}{1.12}$
$PV_{\text{year1}} = \$107,142.86$ (rounded to two decimal places)
Calculate PV for Year $3$ : Next, we calculate the present value of the cash inflow for year $2$ , which is $\$180,000$ .
$PV_{\text{year2}} = \frac{\$180,000}{(1 + 0.12)^2}$
$PV_{\text{year2}} = \frac{\$180,000}{(1.12)^2}$
$PV_{\text{year2}} = \frac{\$180,000}{1.2544}$
$PV_{\text{year2}} = \$143,540.67$ (rounded to two decimal places)
Sum PV for Total Value: Now, we calculate the present value of the cash inflow for year $3$ , which is $\$300,000$ .
$PV_{\text{year3}} = \frac{\$300,000}{(1 + 0.12)^3}$
$PV_{\text{year3}} = \frac{\$300,000}{(1.12)^3}$
$PV_{\text{year3}} = \frac{\$300,000}{1.404928}$
$PV_{\text{year3}} = \$213,564.95$ (rounded to two decimal places)
Sum PV for Total Value: Now, we calculate the present value of the cash inflow for year $3$ , which is $\$300,000$ .
$PV_{\text{year3}} = \frac{\$300,000}{(1 + 0.12)^3}$
$PV_{\text{year3}} = \frac{\$300,000}{(1.12)^3}$
$PV_{\text{year3}} = \frac{\$300,000}{1.404928}$
$PV_{\text{year3}} = \$213,564.95$ (rounded to two decimal places)Finally, we sum up the present values of all cash inflows to find the total value of the factory.
Value of the factory = $PV_{\text{year1}} + PV_{\text{year2}} + PV_{\text{year3}}$
Value of the factory = $\$107,142.86 + \$143,540.67 + \$213,564.95$
Value of the factory = $\$464,248.48$