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The projected annual sales of an LED keychain are projected to be 25,000 the first year...

The projected annual sales of an LED keychain are projected to be 25,000 the first year and increase by 10,000 per year until 55,000 are sold during the fourth year. Sales are then predicted to decrease by 5,000 per year in the fifth year and each year therafter until 25,000 are sold in the tenth year.

Proposal A is to purchase manufacturing equipment costing $100,000 with an estimated salvage value of $20,000 at the end of 10 years.

Proposal B is to purchase manufacturing equipment costing $245,000 with an estimated salvage value of $50,000 at the end of 10 years. The variable manufacturing cost per unit under proposal A is estimated to be $0.80, but only $0.25 under proposal B.

1. If the interest rate is 9% what is the Present Equilavent cost of each proposal for a 10-year production period?

2. Which proposal should be accepted for a 10-year production period?

Solutions

Expert Solution

1.

Proposal A:
Year 0 1 2 3 4 5 6 7 8 9 10
Initial cost -100000
Annual variable cost -20000 -28000 -36000 -44000 -40000 -36000 -32000 -28000 -24000 -20000
Salvage Value 20000
Net cash flow -100000 -20000 -28000 -36000 -44000 -40000 -36000 -32000 -28000 -24000 0
Rate of interest 9%
Discounting factor 1 0.917431 0.84168 0.772183 0.708425 0.649931 0.596267 0.547034 0.501866 0.460428 0.422411
Present Value -100000 -18348.6 -23567 -27798.6 -31170.7 -25997.3 -21465.6 -17505.1 -14052.3 -11050.3 0
Present Equivalent Cost -290955
Working:
Year 1 2 3 4 5 6 7 8 9 10
Unit sales 25000 35000 45000 55000 50000 45000 40000 35000 30000 25000
Variable cost per unit 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80
Annual variable cost 20000 28000 36000 44000 40000 36000 32000 28000 24000 20000
Proposal B:
Year 0 1 2 3 4 5 6 7 8 9 10
Initial cost -245000
Annual variable cost -6250 -8750 -11250 -13750 -12500 -11250 -10000 -8750 -7500 -6250
Salvage Value 50000
Net cash flow -245000 -6250 -8750 -11250 -13750 -12500 -11250 -10000 -8750 -7500 43750
Rate of interest 9%
Discounting factor 1 0.917431 0.84168 0.772183 0.708425 0.649931 0.596267 0.547034 0.501866 0.460428 0.422411
Present Value -245000 -5733.94 -7364.7 -8687.06 -9740.85 -8124.14 -6708.01 -5470.34 -4391.33 -3453.21 18480.47
Present Equivalent Cost -286193
Working:
Year 1 2 3 4 5 6 7 8 9 10
Unit sales 25000 35000 45000 55000 50000 45000 40000 35000 30000 25000
Variable cost per unit 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
Annual variable cost 6250 8750 11250 13750 12500 11250 10000 8750 7500 6250

2.

Since the Present Equivalent Cost of Proposal B is less than for Proposal A, Proposal shall be accepted.

ekkarill92 answered 1 year ago
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