Suppose that there are 5 possible investment projects that can be undertaken in the macroeconomy: Projects A - E. For simplicity, each project has an up-front cost of $100, and the project lasts for just one year: there is no depreciation (d = 0), and we'll suppose (silly!) that the machine just vaporizes at the end of the year it's installed. So, there are 3 relevant details: the up-front cost ($100); the (real) revenue each project returns one year later, and the real interest rate. The following table summarizes:ProjectCost (today)(real) revenue in 1 year from todayPV of the (real) revenue when the real interest rate is…2%4%6%A$100$101$99.02 B$100$103 $97.17C$100$105 D$100$107 $102.88 E$100$109 Complete the missing cells in the table, which involves figuring out the present value of the one-year-ahead revenue for each project, and for each of the three interest rate (r) options.
Question
Suppose that there are 5 possible investment projects that can be undertaken in the macroeconomy: Projects A - E. For simplicity, each project has an up-front cost of 100); the (real) revenue each project returns one year later, and the real interest rate. The following table summarizes:ProjectCost (today)(real) revenue in 1 year from todayPV of the (real) revenue when the real interest rate is…2%4%6%A10110097.17C105 D107 100$109 Complete the missing cells in the table, which involves figuring out the present value of the one-year-ahead revenue for each project, and for each of the three interest rate (r) options.
Solution
To complete the table, we need to calculate the present value (PV) of the future revenue for each project at each interest rate. The formula for calculating the present value is:
PV = FV / (1 + r)^n
where:
- FV is the future value (the revenue in 1 year from today),
- r is the interest rate, and
- n is the number of periods (in this case, 1 year).
Let's calculate the missing cells:
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For project B at 4% interest rate: PV = 99.04
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For project B at 6% interest rate: PV = 97.17
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For project C at 2% interest rate: PV = 102.94
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For project C at 4% interest rate: PV = 100.96
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For project C at 6% interest rate: PV = 99.06
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For project D at 2% interest rate: PV = 104.90
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For project D at 4% interest rate: PV = 102.88
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For project D at 6% interest rate: PV = 100.94
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For project E at 2% interest rate: PV = 106.86
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For project E at 4% interest rate: PV = 104.81
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For project E at 6% interest rate: PV = 102.83
So, the completed table would look like this:
| Project | Cost (today) | (real) revenue in 1 year from today | PV of the (real) revenue when the real interest rate is…2% | 4% | 6% |
|---|---|---|---|---|---|
| A | $100 | $101 | $99.02 | ||
| B | $100 | $103 | $100.98 | $99.04 | $97.17 |
| C | $100 | $105 | $102.94 | $100.96 | $99.06 |
| D | $100 | $107 | $104.90 | $102.88 | $100.94 |
| E | $100 | $109 | $106.86 | $104.81 | $102.83 |
Similar Questions
The point of this question/table (along with the "Bonus" questions that follow) is to think about the relationship the textbook authors call the "investment line" (and which we'll subsequently call the "demand for investment," "investment demand," or equivalently the "demand for loanable funds"). Suppose that there are 5 possible investment projects that can be undertaken in the macroeconomy: Projects A - E. For simplicity, each project has an up-front cost of $100, and the project lasts for just one year: there is no depreciation (d = 0), and we'll suppose (silly!) that the machine just vaporizes at the end of the year it's installed. So, there are 3 relevant details: the up-front cost ($100); the (real) revenue each project returns one year later, and the real interest rate. The following table summarizes:ProjectCost (today)(real) revenue in 1 year from todayPV of the (real) revenue when the real interest rate is…2%4%6%A$100$101$99.02 B$100$103 $97.17C$100$105 D$100$107 $102.88 E$100$109 Complete the missing cells in the table, which involves figuring out the present value of the one-year-ahead revenue for each project, and for each of the three interest rate (r) options.
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