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?

Rationale

$126,034

To afford the equipment costing $200,000 in six years, the company must deposit $126,034 today into an investment account earning 8% compounded annually. This amount represents the present value of the future cost, considering the time value of money over six years at the specified interest rate.

A ($125,482) YOUR ANSWER

This value represents the present value calculated using an eight-year timeframe, which is not applicable to the company's plan to purchase the equipment in six years. The time period is critical in determining the present value, and using the incorrect duration will yield an inaccurate deposit amount.

B ($126,034) CORRECT

This is the correct deposit amount needed today to ensure that the company can afford the $200,000 equipment in six years, calculated using the appropriate present value factor for six years at an 8% interest rate.

C ($108,054) YOUR ANSWER

This amount is derived from an incorrect present value calculation using an eight-year period, which underestimates the required deposit. The present value factor of 0.54027 reflects the time value of money over a longer duration, leading to a significantly lower present value than needed for a six-year investment.

D ($104,000) YOUR ANSWER

This option does not represent any present value calculation related to the given figures. It appears to be an arbitrary number and does not align with the correct financial calculations needed for this investment scenario.

Conclusion

In summary, to ensure the company can purchase the equipment for $200,000 in six years at an 8% interest rate compounded annually, a deposit of $126,034 today is necessary. This amount correctly reflects the present value of the future cost, taking into account the specified interest rate and investment duration. The other options either rely on incorrect timeframes or miscalculations, emphasizing the importance of precision in financial planning.

$126,034

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