Question

Ch 11: Exploring Finance Visualizations -Short-Term versus Long-Term Cash Flows 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%: $100 105$95.24 PV of $100 due in 1 year @ r = 5.0%: $100 1.050! $95.24 $95.24-$95.24 $95.24 Percentage change due to different r = = 0.0% Year 20 Cash Flow $100 1.0520 $37.69 PV of $100 due in 20 @r 5.0%: years PV of $100 due in 20 years @ r = 5.0% : $100 1.05020 $37.69 $37.69-$37.69 $37.69 Percentage change due to different r = = 0.0%
Hi this is all one question.

Answer 1

Answer 1)

Time = 1 year

Amount = $100

PV when r = 5%

PV = 100 / (1 + 5%)^1

PV = $95.24

PV when r = 10%

PV = 100 / (1 + 10%)^1

PV = $ 90.91

Hence, % change = (90.91 - 95.24) * 100 / 95.24

Change = - 4.55%

Hence option C (Decrease by 4.5%)

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Answer 2)

Time = 20 year

Amount = $100

PV when r = 5%

PV = 100 / (1 + 5%)^20

PV = $ 37.69

PV when r = 10%

PV = 100 / (1 + 10%)^20

PV = $ 14.86

Hence, % change = (14.86 - 37.69) * 100 / 37.69

Change = - 60.56%

Hence option A (Decrease by 60%)

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Answer 3)

Correct option is Option C. We can see that time period increases the denominator value and hence PV is more small if interest rate changes in long term compared to short term

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Answer 4)

Correct option is Option B. PV for both will increase as the denominator in formula will be smaller and hence higher PV.