The equations below show the discounted or present value of cash flows either one year or twenty years in the future. The first equation 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 equation compares the two discounted values. Change the slider and observe whether the discounted value of the one-year cash flow changes more or less quickly than the discounted value of the twenty-year cash flow. Year 1 Cash Flow PV of $100 due in 1 year @ r=5.0%:$1001.051=$95.24\text {PV of } \$100 \text{ due in 1 year @ } r = 5.0\% : \large{\frac {\$100} {1.05^1}} \normalsize = \$95.24PV of $100 due in 1 year @ r=5.0%:1.051$100=$95.24 PV of $100 due in 1 year @ r=5.0%:$1001.0501=$95.24\text {PV of } \$100 \text{ due in 1 year @ } r = 5.0\% : \large{\frac {\$100} {1.050^1}} \normalsize = \$95.24PV of $100 due in 1 year @ r=5.0%:1.0501$100=$95.24 Percentage change due to different r=$95.24−$95.24$95.24=0.0%\text {Percentage change due to different } r = \large \frac {\$95.24 - \$95.24} {\$95.24} \normalsize = 0.0\%Percentage change due to different r=$95.24$95.24−$95.24=0.0% Year 20 Cash Flow PV of $100 due in 20 years @ r=5.0%:$1001.0520=$37.69\text {PV of } \$100 \text{ due in 20 years @ } r = 5.0\% : \large{\frac {\$100} {1.05^{20}}} \normalsize = \$37.69PV of $100 due in 20 years @ r=5.0%:1.0520$100=$37.69 PV of $100 due in 20 years @ r=5.0%:$1001.05020=$37.69\text {PV of } \$100 \text{ due in 20 years @ } r = 5.0\% : \large \frac {\$100} {1.050^{20}} \normalsize = \$37.69PV of $100 due in 20 years @ r=5.0%:1.05020$100=$37.69 Percentage change due to different r=$37.69−$37.69$37.69=0.0%\text {Percentage change due to different } r = \large \frac {\$37.69 - \$37.69} {\$37.69} \normalsize = 0.0\%Percentage change due to different r=$37.69$37.69−$37.69=0.0% 5101520%Int=5 1. 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%.) Decreases by 60.6% Decreases by 4.33% Decreases by 4.5% Does not change Increases by 4.5% Increases by 60.6% -Select-abcdefItem 1 2. 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%? Decreases by 60% Decreases by 22.83% Does not change Increases by 22.83% Increases by 60.6% -Select-abcdeItem 2 3. 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: smaller because interest rate changes have a greater impact on the near-term cash flows than distant cash flows. the same because the cash flow is the same. greater because interest rate changes have a greater impact on distant cash flows than near-term cash flows. sometimes less and sometmes more depending on the interest rate. -Select-abcdItem 3 4. If the interest rate is less than 5%, then the PVs for both the one-year and 20-year investments: Decrease because the interest rate is lower. Increase because the investments are discounted at a lower rate. Do not change becasue the investment amount is the same. Might either increase or decrease. -Select-abcdItem 4

The equations below show the discounted or present value of cash flows either one year or twenty years in the future. The first equation 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 equation compares the two discounted values. Change the slider and observe whether the discounted value of the one-year cash flow changes more or less quickly than the discounted value of the twenty-year cash flow. Year 1 Cash Flow PV of $100 due in 1 year @ r=5.0%:$1001.051=$95.24\text {PV of } \$100 \text{ due in 1 year @ } r = 5.0\% : \large{\frac {\$100} {1.05^1}} \normalsize = \$95.24PV of $100 due in 1 year @ r=5.0%:1.051$100=$95.24 PV of $100 due in 1 year @ r=5.0%:$1001.0501=$95.24\text {PV of } \$100 \text{ due in 1 year @ } r = 5.0\% : \large{\frac {\$100} {1.050^1}} \normalsize = \$95.24PV of $100 due in 1 year @ r=5.0%:1.0501$100=$95.24 Percentage change due to different r=$95.24−$95.24$95.24=0.0%\text {Percentage change due to different } r = \large \frac {\$95.24 - \$95.24} {\$95.24} \normalsize = 0.0\%Percentage change due to different r=$95.24$95.24−$95.24=0.0% Year 20 Cash Flow PV of $100 due in 20 years @ r=5.0%:$1001.0520=$37.69\text {PV of } \$100 \text{ due in 20 years @ } r = 5.0\% : \large{\frac {\$100} {1.05^{20}}} \normalsize = \$37.69PV of $100 due in 20 years @ r=5.0%:1.0520$100=$37.69 PV of $100 due in 20 years @ r=5.0%:$1001.05020=$37.69\text {PV of } \$100 \text{ due in 20 years @ } r = 5.0\% : \large \frac {\$100} {1.050^{20}} \normalsize = \$37.69PV of $100 due in 20 years @ r=5.0%:1.05020$100=$37.69 Percentage change due to different r=$37.69−$37.69$37.69=0.0%\text {Percentage change due to different } r = \large \frac {\$37.69 - \$37.69} {\$37.69} \normalsize = 0.0\%Percentage change due to different r=$37.69$37.69−$37.69=0.0% 5101520%Int=5 1. 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%.) Decreases by 60.6% Decreases by 4.33% Decreases by 4.5% Does not change Increases by 4.5% Increases by 60.6% -Select-abcdefItem 1 2. 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%? Decreases by 60% Decreases by 22.83% Does not change Increases by 22.83% Increases by 60.6% -Select-abcdeItem 2 3. 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: smaller because interest rate changes have a greater impact on the near-term cash flows than distant cash flows. the same because the cash flow is the same. greater because interest rate changes have a greater impact on distant cash flows than near-term cash flows. sometimes less and sometmes more depending on the interest rate. -Select-abcdItem 3 4. If the interest rate is less than 5%, then the PVs for both the one-year and 20-year investments: Decrease because the interest rate is lower. Increase because the investments are discounted at a lower rate. Do not change becasue the investment amount is the same. Might either increase or decrease. -Select-abcdItem 4

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Year 1 Cash Flow

PV of $100 due in 1 year @ r=5.0%:$1001.051=$95.24\text {PV of } \$100 \text{ due in 1 year @ } r = 5.0\% : \large{\frac {\$100} {1.05^1}} \normalsize = \$95.24PV of $100 due in 1 year @ r=5.0%:1.051$100=$95.24

PV of $100 due in 1 year @ r=5.0%:$1001.0501=$95.24\text {PV of } \$100 \text{ due in 1 year @ } r = 5.0\% : \large{\frac {\$100} {1.050^1}} \normalsize = \$95.24PV of $100 due in 1 year @ r=5.0%:1.0501$100=$95.24

Percentage change due to different r=$95.24−$95.24$95.24=0.0%\text {Percentage change due to different } r = \large \frac {\$95.24 - \$95.24} {\$95.24} \normalsize = 0.0\%Percentage change due to different r=$95.24$95.24−$95.24=0.0%

Year 20 Cash Flow

PV of $100 due in 20 years @ r=5.0%:$1001.0520=$37.69\text {PV of } \$100 \text{ due in 20 years @ } r = 5.0\% : \large{\frac {\$100} {1.05^{20}}} \normalsize = \$37.69PV of $100 due in 20 years @ r=5.0%:1.0520$100=$37.69

PV of $100 due in 20 years @ r=5.0%:$1001.05020=$37.69\text {PV of } \$100 \text{ due in 20 years @ } r = 5.0\% : \large \frac {\$100} {1.050^{20}} \normalsize = \$37.69PV of $100 due in 20 years @ r=5.0%:1.05020$100=$37.69

Percentage change due to different r=$37.69−$37.69$37.69=0.0%\text {Percentage change due to different } r = \large \frac {\$37.69 - \$37.69} {\$37.69} \normalsize = 0.0\%Percentage change due to different r=$37.69$37.69−$37.69=0.0%

5101520%Int=5

1. 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%.)

Decreases by 60.6%
Decreases by 4.33%
Decreases by 4.5%
Does not change
Increases by 4.5%
Increases by 60.6%

-Select-abcdefItem 1

2. 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%?

Decreases by 60%
Decreases by 22.83%
Does not change
Increases by 22.83%
Increases by 60.6%

-Select-abcdeItem 2

3. 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:

smaller because interest rate changes have a greater impact on the near-term cash flows than distant cash flows.
the same because the cash flow is the same.
greater because interest rate changes have a greater impact on distant cash flows than near-term cash flows.
sometimes less and sometmes more depending on the interest rate.

-Select-abcdItem 3

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

Decrease because the interest rate is lower.
Increase because the investments are discounted at a lower rate.
Do not change becasue the investment amount is the same.
Might either increase or decrease.

-Select-abcdItem 4

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