28. A company plans on purchasing a new piece of equipment in six years. The equipment is expected to cost $200,000. In planning for this purchase, the company will deposit an amount of money into an investment account earning 8% compounded annually. Using an 8% interest rate, the implied annual interest is $200,000 * 0.08 = $16,000. The following information is given: Assuming an annual interest rate of 8% for eight years is appropriate, the present value of the deposit is $200,000 * 0.62741 = $125,482. Assuming an annual interest rate of 8% for six years is appropriate, the present value of the deposit is $200,000 * 0.63017 = $126,034. Assuming an annual interest rate of 8% for eight years is appropriate, the present value of the deposit is $200,000 * 0.54027 = $108,054. How much does this company need to deposit today?
Answer: B
The company needs to deposit $126,034 today.
To purchase the equipment expected to cost $200,000 in six years, the company must make a present value deposit of $126,034 today, calculated using an 8% interest rate for six years.
A) $125,482
This option reflects the present value calculation using an interest rate for eight years, which is not appropriate for this scenario. The equipment is being purchased in six years, thus using an eight-year term results in an incorrect present value.
B) $126,034
This option is correct as it represents the present value of $200,000 calculated using the appropriate six-year time frame at an 8% interest rate. The calculation accurately reflects the amount that needs to be deposited today to achieve the future cost of the equipment.
C) $108,054
This amount is derived from an incorrect present value calculation using an inappropriate interest rate for eight years. It underestimates the amount needed to reach the future cost of the equipment, making it an unsuitable choice.
D) $104,000
This option is not based on any provided calculations and does not correspond to a proper present value formula for the equipment purchase. As such, it is not a valid answer in this context.
Conclusion
The correct answer of $126,034 is based on the correct application of the present value formula for a six-year investment at an 8% interest rate. All other options fail to meet the criteria due to either incorrect time frames or calculations, making them unsuitable for the company's planning needs.