LOST sponsors a 5-day camping trip. LOST provides a $3,000 grant and collects $350 per camper. The program expects 150 campers and the following expenses: Campground fees, $6,500 for 3 days, Transportation fees $3925 with 60 person capacity, Outdoor equipment rental $45 per camper, meals $55 per camper per day. Determine the break-even number of campers.

Can you help?  

At College-Cram, we try to make things easier for you with our financial ratios series. We have assembled the most used ratios in chapters covering:

• Liquidity Ratios
• Profitability Ratios
• Debt Management Ratios
• Asset Management Ratios
• Dividend/Market Value Ratios

and placed them in our Finance and Business Math libraries.

For me, the biggest frustration I had with all the ratios wasn't how the math worked, but where to find the numbers and then how to use them. Our eight ratios covering Profitability do a much better job of teaching than the printed examples found in the financial ratios chapters in my Finance textbook.

Each Profitability Ratio Cramlet™ works in conjuction with the financial statements found in the Finance and Business Math libraries. (In fact, each ratio Cramlet has the required financial statements embedded into the Cramlet itself for easy reference.) Each ratio Cramlet begins with a brief explanation of what the ratio is designed to achieve and how it is to be used. The Cramlet walks you through each step of solving the ratio by finding (and clicking) the appropriate numbers on the corresponding financial statements. In other words, you don't just plug in numbers -- you go find the numbers from the financial statements, further developing your understanding of where the numbers come from.

The Basic Earning Power Ratio Cramlet™, for example, explains that the ratio is intended for direct comparison of similar firms that use different financing strategies or have different tax situations. It then walks you through selecting the correct items from the Income Statement and Balance Sheet to determine the EBIT:

With the EBIT calculated, you are then prompted to find the total assets on the Balance Sheet. The final step calculates the Basic Earning Power Ratio, with a brief explanation of how to interpret the ratio for usage within the appropriate industry.

As an added feature in all the ratio Cramlets, you can change the values and click "Next" to recalculate the ratio. (This is useful for checking homework or continued repetition, helping you master the steps for the Basic Earning Power Ratio.)

Profitability Ratios are one of our more popular series of financial ratio Cramlets™ within the Finance and Business Math libraries of College-Cram. Check them out and see how easy financial ratios can be.

Dear Professor Cram:

ABC Corp has 500,000 of debt outstanding, and it pays an interest rate of 10% annually. Annual sales of 2 million with a tax rate of 30% and a net profit margin of 5%. What is the ABC Corp TIE ratio? Somehow I missed the boat on this one. Can you help?

John S., US Navy

Thanks for your question, John. You may want to review some of our Debt Management Ratios. What you are looking for with Times Interest Earned, or TIE, is ABC Corp's ability to pay interest payments out of earnings.

First, let's calculate the interest payment. With $500,000 in debt at 10% annual interest, multiplying the two together gives us $50,000 in annual interest expenses. Earnings for $2,000,000 in sales, with 5% profit margin, is $100,000 in profit (before taxes). (Remember, figure the ratio BEFORE taxes because interest is a deductible expense and reduces taxes.)

So, what is the answer? $100,000 in earnings divided by $50,000 in interest yields a TIE ratio = 2.

As always with financial ratios, this value should be compared with TIE ratios for other companies in ABC Corp's industry to help put it in perspective. Anything less than 1.0 means the company isn't earning enough to pay the interest in their debt. A higher industry average than company value could either mean that this company uses more debt than the industry average, or that their earnings are inferior to the industry average. This is why one ratio by itself doesn't tell the whole story.

Dear Professor Cram:

Can you explain to me the concept of ratio analysis and the limitations of ratio analysis? Thanks!

Ken S., Hong Kong

Thanks for your question, Ken. In Finance, ratio analysis is generally used to compare the performance or position of a single company with other companies or with an industry.

There are several groups of ratios that each serve different purposes:

• Liquidity Ratios provide measures of how easily a firm can meet its obligations.
• Profitability Ratios indicate the earnings and profitability potential of a company.
• Asset Management Ratios measure how efficently a company can turn its assets into sales.
• Debt Management Ratios indicate how leveraged a company is in terms of debt, and how well it can handle that debt with its assets and operating income.
• Dividend/Market Value Ratios measure how well a company uses its assets to generate earnings for its investors.

Ratios can provide meaningful comparisons of companies in similar industries or of a company in a single industry. As such, financial ratios should be evaluated in comparison to other companies in the same industry. For example, a dividend ratio of 5.2 means nothing by itself, and means very different things if the industry average is 22.5 as opposed to 1.5. For businesses that have operations in more than one industry, ratio analysis is less meaningful.

Also, keep in mind that ratio analysis does not tell the entire story. There may be good business reasons to support management's decision to reduce or increase liquidity or fixed assets in a different manner than the rest of the industry. Having a single ratio out of line with an industry, therefore, does not necessarily mean there is a problem.

Here is an overview on Ratio Analysis. 

Dear Professor Cram:

A man deposits 1200 at the end of each year into a savings account that earn 6.75% interest compounded annually. After 4 years he made no more deposits. What would be the balance in the account 3 years from the last deposit?

Eva, Faulkner University

Thanks for your question, Eva.

This is a future value of an annuity problem, complicated by making payments at the END of the periods, but not payments for the whole time. So we have to break it up into pieces: years with deposits, and years without deposits. First, let's lay out what we know about the payments. I usually do this on a timeline, but those are hard to type....

• End of first year - deposit $1,200
• End of second year - deposit $1,200
• End of third year - deposit $1,200

"After 4 years he made no more deposits." Hmmm - so did he make the 4th deposit or didn't he? I hate problems that are ambiguous. If you had his bank statement, it wouldn't be ambiguous... OK, I am going to assume he DID make the 4th deposit at the end of the 4th year, and after 4 years (of deposits) he made no more deposits.

• End of fourth year - deposit $1,200

The next thing we know is we flash forward three years from the last deposit (hmmm, did he really make that 4th deposit? makes a difference in the answer...) and we need to know the balance at the end of the 7th year.

Here is one way to solve this problem: Let's build it a year at a time.

At the end of the first year - he just has the deposit, no interest yet. OK, that is $1,200.

At the end of the second year, he should have the first deposit, plus a year's worth of interest at 6.75% ($1,200.00 x 0.065 = $78.00), plus the new deposit of $1,200.00. Let's add those up:

$1,200.00 1st deposit
$1,200.00 new deposit at the end of the second year
+ $ 78.00 interest during the second year
$2,478.00 at the end of the second year

This third year, he will be due interest on that whole balance of $2,478.00 from last year:

($2,428.00 x 6.75% = 161.07) [it went up by MORE than the 78.00 per $1,200 because of interest on interest - now we have compounding going on!]

$2,478.00 at the end of the second year - our starting balance
$1,200.00 deposit at the end of the third year
+ $161.07 interest during the third year
$3,839.07 at the end of the third year

You get the idea. Now repeat for fourth year (if he really made that 4th deposit - darned ambiguous word problems).

Once you have the ending balance after the last deposit, now we just add interest each year for three more years. You can either:

1. Take the ending balance from those payment years and now add 6.75% to it for each year and repeat three times; OR

2. If you can handle exponents, you can do all three years in one fell swoop. For each year it is the old balance x 1.0675 for the new ending balance. For three years that is the old balance x 1.0675 x 1.0675 x 1.0675 which is the old balance x (1.0675)³.

I hope this helps. Let us know if you need anything else.

Dear Professor Cram:

Can you explain how to solve for fixed costs, variable costs, and total costs?

Renee, Bahamas

Thanks for your question, Renee.

Since I don't know how much you already know, let's start with some definitions.

• Fixed costs are those costs which do not change as production or sales change within a relevant range.
• Variable costs are directly proportional to sales or production volumes.
• Mixed costs have components of both but can be divided into their fixed and variable components.

The challenge is identifying costs and determining whether they are fixed, variable, or mixed (and then splitting out the mixed into fixed and variable.)

By reviewing costs at two different production or sales levels, it is possible to determine the variable rates (just like finding the slope of a line in algebra.)

Variable Costs = (cost per unit) X (number of units)

Total Costs = (fixed costs) + (variable costs)

Here is a simplistic example to demonstrate the concept:

Bogus Manufacturing Company - selected data

• Five sales reps are paid 5% commissions plus $500 monthly salary each
• Utilities cost $1,000 per month plus $0.10 per unit manufactured
• Materials cost is $0.75 per unit
• Equipment cost $500,000 and has an expected life of 3,000,000 units with no salvage value
• Rent is $10,000 per month
• Other salaries are $20,000 per month

From these, we can identify the fixed and variable costs:

• Five sales reps are paid 5% commissions plus $500 monthly salary each
  Fixed Costs = $500/month X 5 sales reps = $2,500 per month
  Variable Costs = 5% of sales
• Utilities cost $1,000 per month plus $0.10 per unit manufactured
  Fixed Costs = $1,000 per month
  Variable Costs = $0.10 per unit produced
• Materials cost is $0.75 per unit
  Variable Costs = $0.75 per unit produced (under GAAP this will go into inventory until sold and then show up in the Cost of Goods Sold - I am going to ignore that in this example and recognize the cost as we use the materials)
• Equipment cost $50,000 and has an expected life of 3,000,000 units with no salvage value
  Depreciation here will be on units of production method at rate of $500,000/3,000,000 units = $0.1667 per unit in Variable Costs
• Rent is $10,000 per month Fixed Costs
• Other salaries are $20,000 per month Fixed Costs

Let's group the costs:

• Fixed Costs
  • $ 2,500 per month for 5 sales reps
  • $ 1,000 per month Utilities
  • $ 10,000 per month Rent
  • + $20,000 per month Salaries
  • $33,500 per month Fixed Costs

• Variable Costs
  • $ 0.05 per unit sales commissions (5%)
  • $ 0.75 per unit produced Materials
  • $ 0.10 per unit Utilities
  • + $0.1667 per unit Depreciation
  • $1.0167 per unit Variable Costs

Now that we have identified the cost components, let us solve for Total Cost. Let's expand the example data:

• Manufacture and sell 100,000 units at a Selling Price of $3.50 per unit during one month
• Fixed Costs are $33,500
• Variable Costs are 5% of sales + $1.0167/unit

From this data, we can find variable costs (VC) and total costs (TC)

• [Sales are $350,000 (100,000 units @ $3.50 each)]
• VC = 5% X $350,000 + 100,000 X $1.01667
• VC = $17,500 + $101,667 = $119,167
• TC = FC + VC
• TC = $33,500 + $119,167 = $152,667

From this, we know a lot of things. We can calculate their profit. We can even figure what sales are required to just break even called Break Even Point.

I hope this helps. Let us know if you need anything else.

Dear Professor Cram:

When annual sales, variable cost, contribution margin, fixed costs, and operating income are all known, how can the number of units be determined?

Elias, Baker College

Thanks for your question, Elias.

The categories you mention are actually more information than is required, but that is not unusual in word problem assignments. I am going to show how to do it using my own example, since you didn't give me a specific problem to solve. (This way I can use nice round numbers that I know won't get hung up on long division.) Here is my example - let's say:

• annual sales are $1,000,000
• variable cost is $100 per unit
• contribution margin is 50%
• fixed costs are $100,000
• operating income is $400,000

With sales of $1,000,000 and operating income of $400,000, operating expenses had to be $600,000. Since we know $100,000 of those expenses were fixed costs, the balance of $500,000 in operating expenses had to be variable costs. These came at a rate of $100 per unit, so we sold 5,000 units. Just that simple!

Are we really there yet? Do the rest of the numbers work? We haven't used the contribution margin, have we? Let's check that. I think we need the selling price. We had $1,000,000 in sales and we said that was from 5,000 units, so there must have been a selling price of $200 each. Variable cost was $100, leaving a contribution margin of 50%. Well OK, then...

I hope this helps. Let us know if you need anything else.