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

Year $1$ Cash Flow

PV of $$100$ due in $1$ year @ $r=5\mathrm{.}0\%$:$\frac{\text{\$}100}{1\mathrm{.}051}=$$$95\mathrm{.}24$

PV of $$100$ due in $1$ year @$r=10\mathrm{.}0\%$:$\frac{\text{\$}100}{{1\mathrm{.}100}^1}=$$$90\mathrm{.}91$

Percentage change due to different $r=\frac{\text{\$}90\mathrm{.}91-\text{\$}95\mathrm{.}24}{\text{\$}95\mathrm{.}24}=-4\mathrm{.}5\%$

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 $$100$ due in $20$ ycars @$r=10\mathrm{.}0\%$:$\frac{\text{\$}100}{{1\mathrm{.}100}^{20}}=$$$14\mathrm{.}86$

Percentage change due to different $r=\frac{\text{\$}14\mathrm{.}86-\text{\$}37\mathrm{.}69}{\text{\$}37\mathrm{.}69}=-60\mathrm{.}6\%**$

What is the percentage change in the PV of $$100$ due in $1$ year when the interest rate changes from $5\%$ to $10\%?($Move the slider to $10\%.)$

a$.$ Decreases by $60\mathrm{.}6\%$

b$.$ Decreases by $4\mathrm{.}33\%$

c$.$ Decreases by $4\mathrm{.}5\%$

d$.$ Does not change

e$.$ Increases by $4\mathrm{.}5\%$

f$.$ Increases by $60\mathrm{.}6\%$

What is the percentage change in the PV of $$100$ due in $20$ years when the interest rate $($cost of capital$)$ changes from $5\%$ to $10\%?$

a$.$ Decreases by $60\%$

b$.$ Decreases by $22\mathrm{.}83\%$

c$.$ Does not change

d$.$ Increases by $22\mathrm{.}83\%$

f increases by $60\mathrm{.}6\%$

Select$-$

The impact of interest rate changes in the PV of $$100$ due in $20$ years compared to the PV of $$100$ due in one year are:

a$.$ smaller because interest rate changes have a greater impact on the near$-$term cash flows than distant cash flows.

b$.$ the same because the cash flow is the same.

c$.$ greater because interest rate changes have a greater impact on distant cash flows than near$-$term cash flows.

d$.$ sometimes less and sometmes more depending on the interest rate.

Selact $B$

If the interest rate is less than $5\%,$ then the PVs for both the one$-$year and $20-$year investments:

a$.$ Decrease because the interest rate is lower.

b$.$ Increase because the investments are discounted at a lower rate.

c$.$ Do not change becasue the investment amount is the same.

d$.$ Might elther increase or decrease.