Process X is estimated to have a fixed cost of 40000 per yea

Process X is estimated to have a fixed cost of $40,000 per year and a variable cost of $60 per unit in year 1, decreasing by $5 per unit per year thereafter. Process Y will have a fixed cost of $65,000 per year and a variable cost of $10 per unit in year 1, increasing by $1 per unit per year thereafter. At an interest rate of 12% per year, how many units must be produced in year 5 for the two processes to break even? The number of units that must be produced is determined by______

Solution

Let, number of units = K

Here, annual worth of process X should be equal to the annual worth of the process Y in year 5.

Annual worth of the process X = 40000 + K*(60 – 5*(A/G, 12%, 5)

Annual worth of the process X = 40000 + K*(60-5*1.775)

Annual worth of the process X = 40000 + K*51.125

Annual worth of process Y = 65000 + K*(10 – 1*(A/G, 12%, 5)

Annual worth of process Y = 65000 + K*(10-1*1.775)

Annual worth of process Y = 65000 + K*8.225

At breakeven level,

40000 + K*51.125 = 65000 + K*8.225

Or

K = (65000-40000)/(51.125-8.225)

K = 582.75 or 583 units

So, break even quantity in year 5 will be 583 units approx.