Use the present and future value tables provided in this week’s reading to solve the situations depicted below:1. Bob’s Music Store is doing well in the area. He has some excess cash in the bank account and is looking at different alternatives that might bring more return than the meager rate his bank is offering. He currently receives 2% interest from his bank, which we will use to determine the net present value of each alternative. He has narrowed it down to two options:Alternative A: The first option is to upgrade and customize his computer system. The cost will be $3,000. He expects to save $1,800 per year in labor costs as a result of the additional automation.He also believes he will be able to sell any computer hardware for $500 at the end of the 3-year horizon he is looking at before having to upgrade once again.Alternative B: The second option is to expand his current inventory by offering a new line of guitars.The initial outlay of the expansion is $8,000. He expects current annual sales of $80,000 to increase by 5% per year. In addition, he will have to pay $500 to renovate his current sales floor to accommodate the additional inventory. He is using the same 3-year horizon as in the first option.What is the net present value of each alternative?2. Margo of Margo’s Curios is looking for ways to increase her sales and, hopefully, her net income.She is considering two alternatives which she believes will result in increased business. Her current investments earn 4% and she plans to use a 4-year horizon to determine the best approach.Option A: Her first option is to increase her current advertising expense of $1,800 per year by 15%. As a result, she expects her annual sales of $25,000 to increase by 2% and her annual labor cost of $4,800 to also increase by 2%.Option B: Her second option is to pay for a new website design. It will cost $300 up front and $300 per year in maintenance. She expects this to increase her annual sales by 2% per year.Calculate the net present value of each alternative.What is the net present value of each alternative?2. Margo of Margo’s Curios is looking for ways to increase her sales and, hopefully, her net income.She is considering two alternatives which she believes will result in increased business. Her current investments earn 4% and she plans to use a 4-year horizon to determine the best approach.Option A: Her first option is to increase her current advertising expense of $1,800 per year by 15%. As a result, she expects her annual sales of $25,000 to increase by 2% and her annual labor cost of $4,800 to also increase by 2%.Option B: Her second option is to pay for a new website design. It will cost $300 up front and $300 per year in maintenance. She expects this to increase her annual sales by 2% per year.Calculate the net present value of each alternative. The table provided demonstrates the "Future Value of an Annuity". It shows how different interest rates affect the future value of an annuity over specific periods. The columns represent various interest rates (from 1% to 10%), while the rows represent the periods (1 to 20, and an additional row for 36).Here's a detailed breakdown:### Interest Rates:- 1%- 2%- 3%- 4%- 5%- 6%- 7%- 8%- 9%- 10%### Periods:1. **Period 1**: Values range from 1.0000 at 1% to 1.1000 at 10%.2. **Period 2**: Values range from 2.0100 at 1% to 2.1000 at 10%.3. **Period 3**: Values range from 3.0301 at 1% to 3.3100 at 10%.4. **Period 4**: Values range from 4.0604 at 1% to 4.6410 at 10%.5. **Period 5**: Values range from 5.1010 at 1% to 5.1051 at 10%.The pattern continues, with each period showing increased future values as both the period length and interest rate rise.### Final Period Displayed:- **Period 36**: Values range from 46.973 at 1% to 299.127 at 10%.The numbers in the table represent the accumulated future value of an annuity for each combination of interest rate and period. Lower interest rates and shorter periods result in smaller future values, while higher interest rates and longer periods significantly increase the future value of the annuity.This table is essential for understanding how annuities grow over time with varying interest rates, helping in financial planning and investment decisions. # Interest Tables for Present and Future Values## Understanding the Time Value of MoneyThis educational guide provides comprehensive tables to aid in calculating the present and future values of money based on different interest rates and periods.### 1. Present Value Table#### Present Value of a Lump Sum Payment (Compound Interest)- **Interest Rates**: Ranging from 1% to 10%- **Periods**: From 1 to 20The table shows the present value factor for a lump sum payment received in the future. Each cell corresponds to the factor you multiply with a future sum to determine its present value at a specific interest rate over a given number of periods.#### Key Points: - Higher interest rates reduce the present value of future sums.- Longer periods reduce the present value of future sums.### 2. Present Value of a Periodic Payment (Annuity)- **Interest Rates**: Ranging from 1% to 10%- **Periods**: From 1 to 20This section includes the present value factor for an annuity, which is a series of equal payments made at regular intervals. Each factor helps calculate the present value of an annuity based on rate and period.#### Key Points:- The present value of an annuity increases with more periods.- Higher interest rates decrease the present value of an annuity due to the time value of money.### How to Use the Tables- **Determine the appropriate interest rate** (column) and period (row).- Locate the intersection to find the present value factor.- Multiply the future value by this factor to find the present value.This tool is essential for understanding financial decisions, investment appraisals, and pricing bonds or loans. Understanding how to use these tables is crucial for anyone involved in finance, economics, or accounting.

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Answered: Calculate the net present value of each…

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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Use the present and future value tables provided in this week’s reading to solve the situations depicted below: 1. Bob’s Music Store is doing well in the area. He has some excess cash in the bank account and is looking at different alternatives that might bring more return than the meager rate his bank is offering. He currently receives 2% interest from his bank, which we will use to determine the net present value of each alternative. He has narrowed it down to two options: Alternative A: The first option is to upgrade and customize his computer system. The cost will be $3,000. He expects to save $1,800 per year in labor costs as a result of the additional automation. He also believes he will be able to sell any computer hardware for $500 at the end of the 3-year horizon he is looking at before having to upgrade once again. Alternative B: The second option is to expand his current inventory by offering a new line of guitars. The initial outlay of the expansion is $8,000. He expects current annual sales of $80,000 to increase by 5% per year. In addition, he will have to pay $500 to renovate his current sales floor to accommodate the additional inventory. He is using the same 3-year horizon as in the first option. What is the net present value of each alternative? 2. Margo of Margo’s Curios is looking for ways to increase her sales and, hopefully, her net income. She is considering two alternatives which she believes will result in increased business. Her current investments earn 4% and she plans to use a 4-year horizon to determine the best approach. Option A: Her first option is to increase her current advertising expense of $1,800 per year by 15%. As a result, she expects her annual sales of $25,000 to increase by 2% and her annual labor cost of $4,800 to also increase by 2%. Option B: Her second option is to pay for a new website design. It will cost $300 up front and $300 per year in maintenance. She expects this to increase her annual sales by 2% per year. Calculate the net present value of each alternative.What is the net present value of each alternative? 2. Margo of Margo’s Curios is looking for ways to increase her sales and, hopefully, her net income. She is considering two alternatives which she believes will result in increased business. Her current investments earn 4% and she plans to use a 4-year horizon to determine the best approach. Option A: Her first option is to increase her current advertising expense of $1,800 per year by 15%. As a result, she expects her annual sales of $25,000 to increase by 2% and her annual labor cost of $4,800 to also increase by 2%. Option B: Her second option is to pay for a new website design. It will cost $300 up front and $300 per year in maintenance. She expects this to increase her annual sales by 2% per year. Calculate the net present value of each alternative.

The table provided demonstrates the "Future Value of an Annuity". It shows how different interest rates affect the future value of an annuity over specific periods. The columns represent various interest rates (from 1% to 10%), while the rows represent the periods (1 to 20, and an additional row for 36).

Here's a detailed breakdown:

### Interest Rates:
- 1%
- 2%
- 3%
- 4%
- 5%
- 6%
- 7%
- 8%
- 9%
- 10%

### Periods:
1. **Period 1**: Values range from 1.0000 at 1% to 1.1000 at 10%.
2. **Period 2**: Values range from 2.0100 at 1% to 2.1000 at 10%.
3. **Period 3**: Values range from 3.0301 at 1% to 3.3100 at 10%.
4. **Period 4**: Values range from 4.0604 at 1% to 4.6410 at 10%.
5. **Period 5**: Values range from 5.1010 at 1% to 5.1051 at 10%.

The pattern continues, with each period showing increased future values as both the period length and interest rate rise.

### Final Period Displayed:
- **Period 36**: Values range from 46.973 at 1% to 299.127 at 10%.

The numbers in the table represent the accumulated future value of an annuity for each combination of interest rate and period. Lower interest rates and shorter periods result in smaller future values, while higher interest rates and longer periods significantly increase the future value of the annuity.

This table is essential for understanding how annuities grow over time with varying interest rates, helping in financial planning and investment decisions.

# Interest Tables for Present and Future Values

## Understanding the Time Value of Money

This educational guide provides comprehensive tables to aid in calculating the present and future values of money based on different interest rates and periods.

### 1. Present Value Table

#### Present Value of a Lump Sum Payment (Compound Interest)

- **Interest Rates**: Ranging from 1% to 10%
- **Periods**: From 1 to 20

The table shows the present value factor for a lump sum payment received in the future. Each cell corresponds to the factor you multiply with a future sum to determine its present value at a specific interest rate over a given number of periods.

#### Key Points:
- Higher interest rates reduce the present value of future sums.
- Longer periods reduce the present value of future sums.

### 2. Present Value of a Periodic Payment (Annuity)

- **Interest Rates**: Ranging from 1% to 10%
- **Periods**: From 1 to 20

This section includes the present value factor for an annuity, which is a series of equal payments made at regular intervals. Each factor helps calculate the present value of an annuity based on rate and period.

#### Key Points:
- The present value of an annuity increases with more periods.
- Higher interest rates decrease the present value of an annuity due to the time value of money.

### How to Use the Tables

- **Determine the appropriate interest rate** (column) and period (row).
- Locate the intersection to find the present value factor.
- Multiply the future value by this factor to find the present value.

This tool is essential for understanding financial decisions, investment appraisals, and pricing bonds or loans. Understanding how to use these tables is crucial for anyone involved in finance, economics, or accounting.

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