Tristan\'s Toys invested in a new manufacturing system. The initial cost was $29

Question

Tristan's Toys invested in a new manufacturing system. The initial cost was $298936. Annual costs are projected to be $185138, increasing by 15% each subsequent year. The system will require a substantial overhaul of $43650 at the end of year 9. The line is estimated to have a lifespan of 15 years.

The company projects it will sell 88736 units the first year, with the number of units sold increasing by 38663 units each subsequent year. What is the minimum price that the company must charge per unit to breakeven on the investment? Use a MARR of 1% compounded annually to make the calculation.

Enter your answer as follows: 12.34 - round to two decimal places

Do not use a dollar sign ("$").

Explanation / Answer

Initial Investment = 298936

PV of annual cost = (185138/(0.01-0.15))*(1 – 1.15^15/1.01^15) = 7,946,194.05

PV of overhaul = 43650/1.01^9 = 39,910.93

Assume unit price be P

Annuity factor = (1/0.01)*(1 – 1/1.01^15) = 13.865053

1st value is 88736 and increases 38663 each year subsequently; this is a varying annuity.

PV of units sold = 88736*13.865053 + 38663*(13.865053 – 15/1.01^15)/0.01

PV of units sold = 4,883,249.73

PV of revenue generated = 4,883,249.73 P

NPV = -298936 - 7,946,194.05 - 39,910.93 + 4,883,249.73 P

As P increases, NPV increases.

P is minimum when NPV = 0

P = (298936 + 7,946,194.05 + 39,910.93)/ 4,883,249.73 = 1.696624

Unit price = $1.70

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