Problem $5$ $-14$ Present Values (LO $2$ ) $\newline$ What is the present value of the following cash-flow stream if the interest rate is $6 \% ?$ Note: Do not round intermediate calculations. Round your answer to $\mathbf{2}$ decimal places $\newline$ \begin{tabular}{cc} $\newline$ Year & Cash Flow \\ $\newline$ \hline $1$ & $\$ 200$ \\ $\newline$ $2$ & $400$ \\ $\newline$ $3$ & $300$ $\newline$ \end{tabular}

Full solution

Q. Problem

5

-14

Present Values (LO

2

)

\newline

What is the present value of the following cash-flow stream if the interest rate is

6 \% ?

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

\mathbf{2}

decimal places

\newline

\begin{tabular}{cc}

\newline

Year & Cash Flow \\

\newline

\hline

1

\$ 200

\newline

2

400

\newline

3

300

\newline

\end{tabular}

Calculate PV Year $1$ : Calculate the present value of the $\$$ $200$ cash flow received in Year $1$ . $\newline$ Present Value (PV) = Cash Flow / $(1 + r)^n$ $\newline$ Where $r$ is the interest rate ( $6$ % or $0$ . $06$ ) and $n$ is the number of periods ( $1$ year). $\newline$ $PV = \$200 / (1 + 0.06)^1$ $\newline$ $PV = \$200 / 1.06$ $\newline$ $PV = \$188.68$
Calculate PV Year $2$ : Calculate the present value of the $\$$ $400$ cash flow received in Year $2$ . $PV = \frac{\text{Cash Flow}}{(1 + r)^n}$ $PV = \frac{\$400}{(1 + 0.06)^2}$ $PV = \frac{\$400}{(1.06)^2}$ $PV = \frac{\$400}{1.1236}$ $PV = \$356.21$
Calculate PV Year $3$ : Calculate the present value of the $\$$ $300$ cash flow received in Year $3$ . $PV = \frac{\text{Cash Flow}}{(1 + r)^n}$ $PV = \frac{\$300}{(1 + 0.06)^3}$ $PV = \frac{\$300}{(1.06)^3}$ $PV = \frac{\$300}{1.191016}$ $PV = \$251.98$
Sum Total PV: Sum the present values of all cash flows to find the total present value. $\newline$ Total Present Value = PV of Year $1$ + PV of Year $2$ + PV of Year $3$ $\newline$ Total Present Value = $\$188.68$ + $\$356.21$ + $\$251.98$ $\newline$ Total Present Value = $\$796.87$