Almendarez Corporation is considering the purchase of a machine that would cost $240,000 and would last for 10 years. At the end of 10 years, the machine would have a salvage value of $21,500. By reducing labor and other operating costs, the machine would provide annual cost savings of $37,000. The company requires a minimum pretax return of 10% on all investment projects. (Ignore income taxes.)
Click here to view Exhibit 13B-1 and Exhibit 13B-2, to determine the appropriate discount factor(s) using the tables provided.
The net present value of the proposed project is closest to: (Round your intermediate calculations and final answer to the nearest whole dollar amount.)
$(130,000)
$13,256
$(4,336)
$(19,683)
A company has provided the following data concerning a proposed project (Ignore income taxes.):
Initial investment $ 10,000
Annual cost savings $ ?
Salvage value $ 0
Life of the project 8 years
Discount rate 14 %
Net present value $ 1,300
Click here to view Exhibit 13B-1 and Exhibit 13B-2, to determine the appropriate discount factor(s) using the tables provided.
The annual cost savings must be closest to: (Round your intermediate calculations to 3 decimal places.)
$1,875
$4,024
$3,704
$2,436
The Correct Answer and Explanation is :
To solve both of these questions, we need to calculate the Net Present Value (NPV) of the proposed projects. Let’s break down both situations and find the correct answers step by step.
First Question: Almendarez Corporation’s Machine Purchase
Given:
- Initial investment = $240,000
- Salvage value = $21,500
- Annual cost savings = $37,000
- Life of the machine = 10 years
- Required rate of return = 10% (discount rate)
- We need to find the net present value (NPV) of this investment.
Step 1: Use the Present Value of Annuities formula to find the NPV.
The formula for NPV is:
[
NPV = \text{Initial Investment} + \left( \text{Annual Savings} \times \text{Present Value Factor for Annuity} \right) + \left( \text{Salvage Value} \times \text{Present Value Factor for a Single Sum} \right)
]
Present Value Factor for Annuity (PVA) for 10 years at 10% can be found using Exhibit 13B-1. It is 6.14457.
Present Value Factor for a Single Sum (PV) for 10 years at 10% can be found in Exhibit 13B-2. It is 0.38554.
Step 2: Apply the values to the NPV formula:
[
NPV = -240,000 + (37,000 \times 6.14457) + (21,500 \times 0.38554)
]
[
NPV = -240,000 + 227,343.09 + 8,281.16
]
[
NPV = -240,000 + 235,624.25
]
[
NPV = -4,375.75
]
Thus, the closest value for the NPV is approximately $(4,336).
Second Question: Annual Cost Savings Calculation
Given:
- Initial investment = $10,000
- Salvage value = $0
- Life of the project = 8 years
- Discount rate = 14%
- NPV = $1,300
- We need to find the annual cost savings.
Step 1: Use the Net Present Value formula.
The formula is the same as before:
[
NPV = \text{Initial Investment} + \left( \text{Annual Savings} \times \text{Present Value Factor for Annuity} \right)
]
Using Exhibit 13B-1, the Present Value Factor for Annuity (PVA) for 8 years at 14% is 4.946.
Step 2: Set up the NPV equation:
[
1,300 = -10,000 + (\text{Annual Savings} \times 4.946)
]
Rearranging:
[
\text{Annual Savings} \times 4.946 = 11,300
]
[
\text{Annual Savings} = \frac{11,300}{4.946} = 2,283.58
]
Thus, the closest annual cost savings is $2,436.
Conclusion:
- The Net Present Value of the proposed project by Almendarez Corporation is closest to $(4,336).
- The annual cost savings for the second project is closest to $2,436.
These calculations show how the present value factors (from the tables) are used to determine NPV and how cost savings are calculated for an investment.