Question

Beacon Company is considering automating its production facility. The initial investment in automation would be $8.16

million, and the equipment has a useful life of 7 years with a residual value of $1,020,000. The company will use straight-
line depreciation. Beacon could expect a production increase of 46,000 units per year and a reduction of 20 percent in
the labor cost per unit.
Production and sales volume
Sales revenue
Variable costs
Direct materials
Direct labor
Variable manufacturing overhead
Total variable manufacturing costs
Contribution margin
Fixed manufacturing costs
Net operating income
Current (no automation) 89,000 Proposed (automation) 135,000
units
units
Net present value
Per Unit
$94
$19
25
10
54
$ 40
Total
?
1,120,000
?
Per Unit
$94
$19
?
10
?
$ 45
Total
$ ?
P
2,250,000
P
Required:
4. Using a discount rate of 14 percent, calculate the net present value (NPV) of the proposed investment. (Future Value of $1. Present
Value of $1, Future Value Annuity of $1, Present Value Annuity of $1.)
Note: Use appropriate factor(s) from the tables provided. Negative amount should-be indicated by a minus sign. Enter the answer
in whole dollars.

Answer 1

o calculate the net present value (NPV) of the proposed investment, we need to discount the expected cash flows over the 7-year useful life of the automation equipment at a discount rate of 14 percent.

Step 1: Calculate the annual cash flows for each year.

Annual cash flow = Net operating income + Depreciation expense

For the current (no automation) scenario:

Annual cash flow = $3,241,000 + (Initial investment - Residual value) / Useful life

Annual cash flow = $3,241,000 + ($8,160,000 - $1,020,000) / 7

Annual cash flow = $3,241,000 + $1,080,000 / 7

Annual cash flow = $3,241,000 + $154,285.71 ≈ $3,395,285.71

For the proposed (automation) scenario:

Annual cash flow = $4,365,000 + (Initial investment - Residual value) / Useful life

Annual cash flow = $4,365,000 + ($8,160,000 - $1,020,000) / 7

Annual cash flow = $4,365,000 + $1,080,000 / 7

Annual cash flow = $4,365,000 + $154,285.71 ≈ $4,519,285.71

Step 2: Calculate the discount factor for each year using the discount rate of 14 percent.

Discount factor (n=7, i=14%) = 1 / (1 + 0.14)^7

Discount factor (n=7, i=14%) ≈ 0.417439

Step 3: Calculate the discounted cash flows for each year.

Discounted cash flow (year 1) = Annual cash flow (year 1) x Discount factor (n=1, i=14%)

Discounted cash flow (year 1) ≈ $3,395,285.71 x 0.417439 ≈ $1,416,222.33

Discounted cash flow (year 2) = Annual cash flow (year 2) x Discount factor (n=2, i=14%)

Discounted cash flow (year 2) ≈ $3,395,285.71 x (0.417439)^2 ≈ $590,959.12

Repeat the calculation for each year until year 7:

Discounted cash flow (year 3) ≈ $521,343.91

Discounted cash flow (year 4) ≈ $460,269.36

Discounted cash flow (year 5) ≈ $405,700.28

Discounted cash flow (year 6) ≈ $357,037.69

Discounted cash flow (year 7) ≈ $313,504.14

Step 4: Calculate the NPV by summing up all the discounted cash flows:

NPV = Sum of discounted cash flows - Initial investment

NPV ≈ $1,416,222.33 + $590,959.12 + $521,343.91 + $460,269.36 + $405,700.28 + $357,037.69 + $313,504.14 - $8,160,000

NPV ≈ $3,065,037.83 - $8,160,000

NPV ≈ -$5,094,962.17

The net present value (NPV) of the proposed investment, using a discount rate of 14 percent, is approximately -$5,094,962.17. This indicates that the proposed investment is not financially feasible at this discount rate, as it results in a negative NPV.