xploring Finance Visualizations $-$ Short$-$Term versus Long$-$Term Cash Flows

hort$-$lerm versus Long$-$Ierm Cash flows

Sonceptual Overview: Explore how time and the cost of capital affects the net present values of two alternative investments.

The equations below show the discounted or present value of casth flows either one year or twenty years in the fiare. The frst equabion in each set of three shows the discounted value when the interest rate $($or cost of capital$)$ equals $5\%.$ The second equation in each set of three shows the discounted value for an interest rate that is controlled by the slider. The third pquation compares the two discounted values. Change the slider and observe whether the discounted value of the one year cash flow changes more or less quicky than the discounted value of the twenty$-$year cash flow.

Year $1$ Cash Flow

PV of $$100$ due in $1$ year @ $r=5\mathrm{.}0\%$:$\frac{\text{\$}100}{{1\mathrm{.}05}^1}=$$$95\mathrm{.}24$

PV of $$100$ due in $1$ year @ $r=5\mathrm{.}0\%$:$\frac{\text{\$}100}{{1\mathrm{.}050}^1}=$$$95\mathrm{.}24$

Percentage change due to different $r=\frac{\text{\$}95\mathrm{.}24-595\mathrm{.}24}{\text{\$}95\mathrm{.}24}=0\mathrm{.}0\%$

Year $20$ Cash Flow

PV of $$100$ due in $20$ years @ $r=5\mathrm{.}0\%$:$\frac{\text{\$}100}{{1\mathrm{.}05}^{20}}=$$$37\mathrm{.}69$

PV of $$100$ due in $20$ years @ $r=5\mathrm{.}0\%$:$\frac{\text{\$}100}{{1\mathrm{.}050}^{30}}=$$$37\mathrm{.}69$

Percentage change due to different $r=\frac{\text{\$}37\mathrm{.}69-\text{\$}37\mathrm{.}69}{\text{\$}37\mathrm{.}69}=0\mathrm{.}0\%$

$\%$ Int $=5$

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