1. What is the discounted value of the account at the beginning of Year 1?
A. $75,000
B. $46,507 Correct
C. $37,500
D. $67,500
Explanation
The present value (PV) is calculated by discounting the future value (FV) back to the beginning of the period. The calculation provided, $75,000 * 0.6208 = $46,560, uses the present value factor for a 10% rate over 5 years (1/(1.10)^5 ≈ 0.620921), resulting in approximately $46,569. Option B ($46,507) is the closest match, likely due to slight rounding differences in the factor used. $75,000 is the future value, not the discounted present value. $37,500 incorrectly applies a simple 50% discount over 5 years, ignoring compound discounting. $67,500 is not supported by any standard present value calculation.
2. A business wishes to discount a future value dollar amount to present value. Which type of interest is used for this calculation?
A. Compound Correct
B. Inflationary
C. Paid
D. Simple
Explanation
Discounting a future value to its present value uses compound interest, reversing compounding by applying a discount rate per period over multiple periods, reflecting the time value of money where interest is earned on prior interest. Inflationary refers to purchasing power loss, not a calculation method. Paid describes disbursed interest, not a calculation type. Simple interest calculates interest only on the principal, without compounding, and is not used for multi-period discounting.
3. A company factored $100,000 of accounts receivables. The factor discounted the receivables by the interest for the one year it planned to take to collect the receivables. Using an annual interest rate of 9%, the present value of the receivables is $100,000 * 0.917 = $91,700. How much cash should the company expect to receive?
A. $91,700 Correct
B. $108,300
C. $100,000
D. $91,000
Explanation
The calculation uses the present value factor for one year at 9% (1/(1.09) ≈ 0.91743), yielding $91,700, which is the cash received upfront. $108,300 represents the future value plus interest, not the discounted amount. $100,000 is the face value, not the discounted amount. $91,000 is an incorrect approximation not using the precise discount factor.
4. 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?
A. $125,482
B. $126,034 Correct
C. $108,054
D. $104,000
Explanation
The equipment is needed in six years, so the correct time period is six years. The present value factor for 8% over six years is 1/(1.08)^6 ≈ 0.63017. Multiplying $200,000 by 0.63017 gives $126,034, the required deposit today. $125,482 uses the eight-year factor (0.62741), which is incorrect. $108,054 uses an incorrect eight-year factor (0.54027). $104,000 is not supported by any present value calculation.
5. A company will receive payments of $8,000 per year for the next five years under a subscription contract. The first payment will be made at the beginning of the contract. Assuming an annual interest rate of 4% is appropriate, the present value of an ordinary annuity is 4.4518 * $8,000 = $35,615 and the present value of an annuity due is 4.6299 * $8,000 = $37,039. Which amount must the company record for this sale in accordance with generally accepted accounting principles (GAAP) if collection is reasonably assured?
A. $0
B. $37,039 Correct
C. $35,615
D. $40,000
Explanation
Since the first payment is received at the beginning, the cash flows represent an annuity due. GAAP requires recording the present value of future cash flows at the contract’s inception when collection is assured. The correct present value for an annuity due at 4% for five periods is $37,039. $35,615 is for an ordinary annuity, assuming end-of-period payments, which is incorrect here. $0 is incorrect as revenue should be recognized. $40,000 is the undiscounted total, ignoring the time value of money.