Lennon Hearth Products manufactures glass door fireplace screens that have two types of mounting brackets for the frame. And L-shaped bracket is used for relatively small fireplace openings, and a U-shaped bracket is used for all others. The company includes both types of brackets in the box with the product, and the purchaser discards the one not needed. The cost of these two brackets with screws and other parts is $3.50. If the frame of the fireplace screen is redesigned, a single universal bracket can be used that will cost $1.20 to make. However, retooling will cost $6000. In addition, inventory write-downs will amount to another $8000. If the company sell 1200 fireplace units per year, should the company keep the old brackets or to with the new ones, assuming the company uses an interest rate of 15% per year and it wants to recover its investment in 5 years? Use the present worth method.

Question

Lennon Hearth Products manufactures glass door fireplace screens that have two types of mounting brackets for the frame. And L-shaped bracket is used for relatively small fireplace openings, and a U-shaped bracket is used for all others. The company includes both types of brackets in the box with the product, and the purchaser discards the one not needed. The cost of these two brackets with screws and other parts is $3.50. If the frame of the fireplace screen is redesigned, a single universal bracket can be used that will cost $1.20 to make. However, retooling will cost $6000. In addition, inventory write-downs will amount to another $8000. If the company sell 1200 fireplace units per year, should the company keep the old brackets or to with the new ones, assuming the company uses an interest rate of 15% per year and it wants to recover its investment in 5 years? Use the present worth method.

Answer 1

We will be happy to critique your thinking. This can be done on a spreadsheet.

Answer 2

To determine whether the company should keep the old brackets or switch to the new universal brackets, we need to calculate the present worth of both options and compare them.

Let's define the following variables:
- PV = Present Worth
- NPV = Net Present Value
- I = Initial investment
- A = Annual cost
- n = Number of years
- r = Interest rate

1. Present Worth of the Old Brackets:
- Initial investment (retooling cost) = $6000
- Annual cost (inventory write-downs) = $8000
- Number of years (recovery period) = 5
- Interest rate = 15%

Using the present worth formula:
PV = I + A * (1 - (1 + r)^(-n)) / r

PV (Old Brackets) = $6000 + $8000 * (1 - (1 + 0.15)^(-5)) / 0.15
PV (Old Brackets) ≈ $6000 + $8000 * (1 - 0.4972) / 0.15
PV (Old Brackets) ≈ $6000 + $4016.8 / 0.15
PV (Old Brackets) ≈ $6000 + $26778.67
PV (Old Brackets) ≈ $32778.67

The present worth of using the old brackets is approximately $32778.67.

2. Present Worth of the New Brackets:
- Initial investment (retooling cost) = $6000
- Annual cost (cost of making universal bracket) = $1.20 * 1200
- Number of years (recovery period) = 5
- Interest rate = 15%

Using the present worth formula:
PV = I + A * (1 - (1 + r)^(-n)) / r

PV (New Brackets) = $6000 + ($1.20 * 1200) * (1 - (1 + 0.15)^(-5)) / 0.15
PV (New Brackets) ≈ $6000 + $1440 * (1 - 0.4972) / 0.15
PV (New Brackets) ≈ $6000 + $718.8 / 0.15
PV (New Brackets) ≈ $6000 + $4792
PV (New Brackets) ≈ $10792

The present worth of using the new brackets is approximately $10792.

Now, we can compare the present worth of both options:

If PV (Old Brackets) > PV (New Brackets), the company should keep the old brackets.
If PV (Old Brackets) < PV (New Brackets), the company should switch to the new brackets.

In this case, $32778.67 > $10792, which means the present worth of keeping the old brackets is greater than that of switching to the new brackets. Therefore, the company should keep the old brackets.