Question
Pam's Pet Palace is considering an investment in dog grooming equipment that would increase cash receipts by $12,000 annually. The initial cost of the equipment is $50,000. The equipment has an estimated 10 year life and will have a $5,000 salvage value. Using a discount rate of 8%, and the tables in the appendix, what is the net present value of this equipment?
Multiple choice question.
$82,835
$32,835
$35,520
$30,520
Multiple choice question.
$82,835
$32,835
$35,520
$30,520
Answers
GPT-4o mini
To calculate the net present value (NPV) of the dog grooming equipment investment, we can follow these steps:
1. **Calculate the Present Value of Annual Cash Flows**:
The annual cash inflow is $12,000. To find the present value of these cash inflows over 10 years at a discount rate of 8%, we use the present value of annuity formula.
The present value of an annuity formula is:
\[
PV = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)
\]
Where:
- \( C \) = Annual cash inflow ($12,000)
- \( r \) = Discount rate (8% or 0.08)
- \( n \) = Number of years (10)
Plugging in the numbers:
\[
PV = 12000 \times \left( \frac{1 - (1 + 0.08)^{-10}}{0.08} \right)
\]
Using a financial calculator or present value annuity table for an 8% discount rate for 10 years, we find the factor is approximately 6.7101.
\[
PV = 12000 \times 6.7101 = 80,521.20
\]
2. **Calculate the Present Value of Salvage Value**:
The salvage value is $5,000 at the end of 10 years. The present value formula for a single sum is:
\[
PV = \frac{FV}{(1 + r)^n}
\]
Where:
- \( FV \) = Future value ($5,000)
- \( r \) = Discount rate (0.08)
- \( n \) = Number of years (10)
Plugging in the numbers:
\[
PV = \frac{5000}{(1 + 0.08)^{10}} = \frac{5000}{2.1589} \approx 2315.54
\]
3. **Calculate Total Present Value**:
Now summing the present value of the cash inflows and salvage value:
\[
Total PV = PV_{\text{annual}} + PV_{\text{salvage}} = 80,521.20 + 2315.54 \approx 82,836.74
\]
4. **Subtract the Initial Investment**:
Finally, we subtract the initial cost of the investment:
\[
NPV = Total PV - Initial Investment = 82,836.74 - 50,000 = 32,836.74
\]
Rounding this to the nearest whole number gives:
\[
NPV \approx 32,837
\]
Thus, the net present value of the equipment is approximately **$32,835**.
Therefore, the correct answer is:
**$32,835**.
1. **Calculate the Present Value of Annual Cash Flows**:
The annual cash inflow is $12,000. To find the present value of these cash inflows over 10 years at a discount rate of 8%, we use the present value of annuity formula.
The present value of an annuity formula is:
\[
PV = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)
\]
Where:
- \( C \) = Annual cash inflow ($12,000)
- \( r \) = Discount rate (8% or 0.08)
- \( n \) = Number of years (10)
Plugging in the numbers:
\[
PV = 12000 \times \left( \frac{1 - (1 + 0.08)^{-10}}{0.08} \right)
\]
Using a financial calculator or present value annuity table for an 8% discount rate for 10 years, we find the factor is approximately 6.7101.
\[
PV = 12000 \times 6.7101 = 80,521.20
\]
2. **Calculate the Present Value of Salvage Value**:
The salvage value is $5,000 at the end of 10 years. The present value formula for a single sum is:
\[
PV = \frac{FV}{(1 + r)^n}
\]
Where:
- \( FV \) = Future value ($5,000)
- \( r \) = Discount rate (0.08)
- \( n \) = Number of years (10)
Plugging in the numbers:
\[
PV = \frac{5000}{(1 + 0.08)^{10}} = \frac{5000}{2.1589} \approx 2315.54
\]
3. **Calculate Total Present Value**:
Now summing the present value of the cash inflows and salvage value:
\[
Total PV = PV_{\text{annual}} + PV_{\text{salvage}} = 80,521.20 + 2315.54 \approx 82,836.74
\]
4. **Subtract the Initial Investment**:
Finally, we subtract the initial cost of the investment:
\[
NPV = Total PV - Initial Investment = 82,836.74 - 50,000 = 32,836.74
\]
Rounding this to the nearest whole number gives:
\[
NPV \approx 32,837
\]
Thus, the net present value of the equipment is approximately **$32,835**.
Therefore, the correct answer is:
**$32,835**.