Aura Industries purchased land by paying $25,000 cash on the purchase date and agreeing to pay $25,000 for each of the next ten years beginning one-year from the purchase date. Aura's incremental borrowing rate is 10%. The land reported on the balance sheet is closest to: (FV of $1, PV of $1, FVA of $1, and PVA of $1)

Note: Use the appropriate factor(s) from the tables provided.

Question

Aura Industries purchased land by paying $25,000 cash on the purchase date and agreeing to pay $25,000 for each of the next ten years beginning one-year from the purchase date. Aura's incremental borrowing rate is 10%. The land reported on the balance sheet is closest to: (FV of $1, PV of $1, FVA of $1, and PVA of $1) Note: Use the appropriate factor(s) from the tables provided.Single choice

A

$121,375.

B

$96,375.

C

$275,000.

D

$178,614.

Note: Use the appropriate factor(s) from the tables provided.

BlackTom AI · Accepted Answer

Payments after the purchase form an ordinary annuity; the land’s cost equals the $25,000 cash paid today plus the present value of ten annual $25,000 payments discounted at Aura’s incremental borrowing rate of 10%.

1) Relevant concepts
- Use the present value (PV) of an ordinary annuity because payments of $25,000 occur at the end of each year for 10 years (first payment one year from purchase).
- Discount rate = incremental borrowing rate = 10%.
- Formula for PV of an ordinary annuity: PVA = PMT × [(1 − (1 + r)^−n) / r].
- Total asset value = cash paid today + PVA of future payments.

2) Step-by-step reasoning
- Compute the annuity present value factor for n = 10, r = 10%.
- Multiply that factor by the annual payment ($25,000).
- Add the $25,000 paid immediately.

3) Calculations (all intermediate steps)
- Compute (1 + r)^n = (1.10)^10 ≈ 2.5937424601.
- Compute (1 + r)^−n = 1 / 2.5937424601 ≈ 0.3855432894.
- Annuity factor = (1 − 0.3855432894) / 0.10 = 0.6144567106 / 0.10 = 6.144567106.
- PV of 10 payments = 25,000 × 6.144567106 ≈ 153,614.17765.
- Add immediate cash: 153,614.18 + 25,000.00 = 178,614.17765.
- Round to nearest dollar = $178,614.

4) Why this is correct
- The calculation correctly treats the ten future payments as an ordinary annuity and discounts them at the appropriate 10% rate; adding the immediate cash gives the full present cost of the land. The computed PV matches standard PVA table values (approx. 6.1446 for 10 periods at 10%).

5) Why the other choices are incorrect
- $121,375 and $96,375 are far too low; they would imply much smaller annuity factors or use incorrect discounting (e.g., wrong rate or number of periods).
- $275,000 equals the undiscounted sum (25,000 × 11) and incorrectly ignores the time value of money.

6) Conclusion
The present value of the land is $178,614, which matches the provided correct answer.

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