Discounted Cash Flow Homework Problem

Discounted Cash Flow Homework Problems

Please post the answers (and show your work) in the assignments section by midnight the last day of the week assigned.

1. Calculate the future value of 1,535 invested today for 8 years at 6 percent. (5 points) $1535 * 1.5938 = $2,446

2. What is the total present value of the following cash stream, discounted at 8 percent? (5 points)
|Year |Amount |Rate |PV |
|1 | $ 400.00 |0.926 | $ 370.40 |
|2 | $ 750.00 |0.857 | $ 642.75 |
|3 | $ 945.00 |0.794 | $ 750.33 |
|4 | $ 145.00 |0.735 | $ 106.58 |
|5 | $ 78.00 |0.681 | $ 53.12 |
| | |Total | $ 1,923.17 |

3. If you invested $2,000 per year into an IRA for 30 years and received 6 percent return each year, what would the account balance be in 30 years? (8 points) $2,000 * 79.058 = $158,116.37

4. A friend gives you a proposition. If you give him 1,500 dollars today, he will guarantee your receive 12 percent a year for the next 5 years. How much money will you receive from him at the end of 5 years? (8 points) $1,500 * 1.7623 = $2,643.51

5.
You want to buy a new Computer Aided Design (CAD) system for your business. The cost of the system is $150,000 and you expect to save over $40,000 per year in reduced labor costs. Please calculate the net present value of the CAD if your required return is 10 percent and the life of the system is expected to be 5 years. (12 points)

|Investment |Cost savings |Net cash flows |PV @10% |Discount Rate |Year |
| 150,000.00 | | 150,000.00 |(150,000.0000) | |0 |
| | 40,000.00 | 40,000.00 |36,360.00 |0.909 |1 |
| | 40,000.00 | 40,000.00 |33,040.00 |0.826 |2 |
| | 40,000.00 | 40,000.00 |30,040.00 |0.751 |3 |
| | 40,000.00 | 40,000.00 |27,320.00 |0.683 |4
|
| | 40,000.00 | 40,000.00 |24,840.00 |0.621 |5 |
| | |NPV = |1,600.00 | | |

Page 2

6. Your company is considering converting its heating system in the main office from coal to heating oil. The initial cost of removing the coal fired furnace and installing an new oil fired unit is $60,000. The life of the analysis is 7 years. In the past you spent $25,000 per year on coal. The new company says you will spend no more than $15,000 per year on heating oil. If your required return is 12 percent, should you make this investment? Please calculate the net present value of this project. (12 points)

$25,000 per year for coal @ 7 yrs. = $175,000 $15,000 per year for heating oil @ 7 yrs. = $105,000 $175,000 - $105,000 = $70,000.

It will cost $60,000 for tear down and install. The difference is $10,000 and this is not 12% return prior to the investment.

You’ll Take a loss.
|Investment |Cost Savings |PV @12% |Discount Rate |Year |
|60,000.00 | |(60,000.00) | |0 |
| |10,000.00 |8,930.00 |0.893 |1 |
| |10,000.00 |7,970.00 |0.797 |2 |
| |10,000.00 |7,120.00 |0.712 |3 |
| |10,000.00 |6,360.00 |0.636 |4 |
| |10,000.00 |5,670.00 |0.567 |5 |
| |10,000.00 |5,070.00 |0.507 |6 |
| |10,000.00 |4,520.00 |0.452 |7 |
| |NPV = |(14,360.00) | | |

To Break Even:
|Investment |Cost Savings |PV @12% |Discount Rate |Year |
|60,000.00 | |(60,000.00) | |0 |
| |10,000.00 |8,930.00 |0.893 |1 |
| |10,000.00 |7,970.00 |0.797 |2 |
| |10,000.00 |7,120.00 |0.712 |3 |
| |10,000.00 |6,360.00 |0.636 |4 |
| |10,000.00 |5,670.00 |0.567 |5 |
| |10,000.00 |5,070.00 |0.507 |6 |
| |10,000.00 |4,520.00 |0.452 |7 |
| |10,000.00 |4,040.00 |0.404 |8 |
| |10,000.00 |3,610.00 |0.361 |9 |
| |10,000.00 |3,220.00 |0.322 |10 |
| |10,000.00 |2,870.00 |0.287 |11 |
|Break Even Year |10,000.00 |2,570.00 |0.257 |12 |
| |NPV = |1,950.00 | | |