I am managing a conference at my college. My fixed costs are $15,000. I must pay the 10 speakers $700 each, and the college union $300 per conference participant for food and lodging costs. I am charging each conference participant who is not also a speaker $900, which includes the conference fee and their food and lodging costs. How many paid registrants need to attend for me to break even?© BrainMass Inc. brainmass.com December 24, 2021, 10:31 pm ad1c9bdddf
SOLUTION This solution is FREE courtesy of BrainMass!
Please see the attached Excel sheet as well as the explanation below, and let me know if you have questions.
The idea of this problem is to equate costs to revenues. There is one variable: the number of paying (non-speaker) participants. By varying the number of paying participants, we can find the number necessary to make costs equal revenues -- or in other words, to break even.
We have a $15,000 fixed cost, a $700 cost for each of 10 speakers, and a $300 cost per participant (this includes the 10 speakers AND the unknown number of non-speaker participants). On the other side of the equation, we have $900 of revenue for each non-speaker participant. So we let the number of non-speaker participants be the variable, and examine the effect on the difference between costs and revenues. We want this difference to be 0.
If we were solving with pencil and paper, we'd write 15,000 + 10(700) + (X + 10)300 = X(900), and solve for X. The equivalent in Excel is to define the variable in the yellow cell and make a guess for it, say 10 non-speaker participants. Then we lay out the rest of the problem using formulas which refer to the yellow cell (these are the two blue cells). Next we put the difference between the two sides of the equation in the orange cell.
Finally, we use Goal Seek with
Set cell: C16
To value: 0
By changing cell: C2
This is saying we need to equate costs and revenues by changing the number of non-speaker participants. Excel quickly finds the solution of 41.67, which is also what you'd get if you solve the algebraic equation above.
So 42 paying participants is the minimum number needed to break even.© BrainMass Inc. brainmass.com December 24, 2021, 10:31 pm ad1c9bdddf>