Math in Hospitality

Lodging - Occupany Ratios

Occupancy ratios measure the success of a hotel in selling guest rooms. In order to measure occupancy ratios you must know the number of rooms available for sale; the number of rooms sold; the number of guests; the number of guests per room and the net rooms revenue.

Occupancy percentage is determined by dividing the number of rooms occupied by the number of rooms available. This tells how many rooms have been sold.

Multiple Occupancy rates is determined by dividing the number of rooms occupied by more than one guest by the number of rooms occupied. This helps forecast food and beverage revenue, indicate linen requirements, and analyze average daily room rates

The ADR (average daily rate) is determined by dividing the rooms revenue by the number of rooms sold. Room revenue varies so utilizing the total revenue helps the management know how much revenue is up on a daily basis.

RevPAR (revenue per available room) is calculated by dividing the actual room revenue by the number of available rooms. RevPAR measures the revenue generated by the hotel.

RevPAC (revenue per available customer) is the revenue generated by the hotel in relationship to the number of customers at the hotel. It is calculated by dividing the actual room revenue by the number

Food Service - Yield Tests

http://beveragecost.com/Forms/Kitchen%20Calculations.pdf

A.P. AP is the food as it is purchased.

E.P. EP is the edible portion. You might purchase a 6 oz filet (AP), but after the fat is trimmed off you have 5 oz (EP).

Yield and Yield factor or yield percentage is the amount of food that is usable. It is always under 100%. For example, if you purchase a head of lettuce and clean and core it the yield is probably around 75% because you tossed the core and the outer leaves leaving only 75% of the head for use.

Common Produce Yield Factors can be found at: http://menuforprofit.com/mfp_files/mfp_cc_files/ProducePercentageYields.pdf

Three steps for calculating yield when all trim is waste. First weight the trim (trim loss), then subtract the trim loss from the AP weight to get the yield weight then divid the yield weight by the AP weight to get the yield percentage.

The yield factor will always be some number less than 1 and the yield percentage will always be less than 100%.

Which is always higher when costing a recipe? A.P. or E.P.? EP is always higher. EP divided by the yield percentage equals the AP quantities

Fat collections companies; Fat removal company http://www.business.com/directory/food_and_beverage/restaurants_and_foodservice/equipment_and_supplies/recycling/animal_fat_and_oil/weblistings.asp http://www.qsrmagazine.com/articles/news/story.phtml?id=5535 Trans fat removal of food

Cooked Yield Test http://www.restaurantowner.com/public/805.cfm

Shrinkage, percent of shrinkage, total percent of increase Shrinkage is the loss from pre-cooked weight to the as-served weight. The percent of shrinkage is the ratio of shrinkage to the raw weight.

Using Yield Tests for Purchasing To use yield test for purchasing you first calculate the yield percentage. That is the EP divided by the AP. Then, you divide the amount needed EP by the yield percentage to determine the amount to purchase. Be sure to include employees skill level, the menu and what you can use the left over product for, the storage capacity and the customers desires.

Food Service - Inventory and Food Cost Percentages

What is an inventory? Why is an accurate inventory necessary? http://www.restaurantowner.com/public/243.cfm

An inventory is the amount of product kept on hand to be able to prepare food items as planned. An accurate inventory gives you enough product but not too much product so as to have excess money sitting on shelves.

Perpetual inventory is a running inventory showing what is on hand, what has been purchased and what has been used.

Physical inventory is the actual product that is physically on hand

Shrinkage refers to any product that reduces your inventory such as theft, waste or deterioration of product. The amount of product minus any waste/theft etc. equals the shrinkage amount

Food costs are the cost of the product It is important to know at all times you’re your food costs are so that you do not operate in the red.

http://www.starchefs.com/business_tools/learning_materials/html/food_cost.shtml

Food cost percentage is the food cost divided by the sales prce. An industry average of 25-35% is common http://www.restaurantreport.com/features/ft_stratpos1.html

Value of comparing food cost percentages for other months in the same year or the same month in previous years? By comparing food cost percentages you can have an accurate assessment of how the operation is doing. If food cost is up then it can be evaluated. Are the actual costs higher this year and sales price is the same or is there pilferage or waste that is causing food cost to not be in line. Food cost percentage helps operators know how they are doing.

Food Service - Measurements and Conversions

Weight – What is it? How is it measured?
Weight is the heaviness of something and it is measured in pound, ounces etc. Weight can refer to dry or liquid weight

Volume – What is it? How is it measured?
Volume is the space that is taken up. It is measured by height x width x length

Count – What is it? Give examples of foods sold by count.
Count is individual item such as apples, eggs, oranges, tomatoes etc.

Are weight and volume equal?
Weight and volume are not equal. 8 ounces of of raisins may not equal one cup of raisins

Imperial Measurement System – What is it and where is it used?
This is a measurement system used in Great Britain and Canada that uses pounds and ounces for weight and pints and fluid ounces for volume.

U.S. Measurement Systems – What is it and where is it used?
This is a measurement system that uses pounds for weight and cups for volume. It is used in the US.

Metric Measurement System – What is it and where is it used?
The metric system is used worldwide and uses the decimal system.

Go to: http://englishplus.com/grammar/00000058.htm to see the abbreviations for measurements. These are necessary to read recipes.

Some common equivalencies are:
3 tsp. = 1 tbsp (T)
2 T = 1 fluid ounce
16 T = 1 C (8fl.ounces)
1/4 C = 4 T (2fl. ounces)
1/2 C = 8 T (4fl. ounces)
1 C = 16 T (1/2 pint or 8fl. ounces)
2 C = 1 pint (16fl. ounces)
1 quart = 2 pint (4 cups or 32fl ounces)
1 gallon = 4 quart (8 pt or 16 cups or 128fl ounces)

Go to: http://www.infoplease.com/ipa/A0001723.html to see metric conversion.

Resources

Online Conversion: http://www.onlineconversion.com/
Cooking Basics: http://www.pioneerthinking.com/measure.html
Measurement Conversion: http://www.metric-conversions.org/measurement-conversions.htm

Food Service - Recipe Conversion

Quantity – How much portion size does each individual need and then how much do you need to purchase based on how many individuals will be fed.

Cost – How much does each portion cost and then how much “other expenses” do you have that equal the total cost to produce that food item.

Merchandising – How will you plate the item for an appealing plate?

Yield – Yield is the usable portion of a product. If the chicken breast has no waste then you have 100% yield. If 25% of the chicken breast is fat then you have 75% yield.

What do inaccurate conversions lead to? Inedible food, waste or food shortages

How do you convert the Total Yield? You divide the desired new yield by the old yield to obtain a conversion factor, then you multiply each ingredient by the conversion factor to establish your new amount. For example if you have a recipe for 10 people and you want to prepare it for one person you divide 1 by 10 = 1/10…..then you multiply 1/10 times every ingredient in your recipe to convert the recipe to one portion. Be sure when doing conversions to have numerator and denominator in the same unit.

Need help in changing decimals to fractions? Go to: http://www.homeschoolmath.net/worksheets/fraction-decimal.php

What are some conversions problems? When you are converting recipes you must take into account equipment, evaporation, recipe errors and time. You might need larger or smaller equipment that in turn affects the quality because evaporation occurs differently in different cooking vessels. In addition, a recipe can have errors that are not obvious in small quantities but that really affect the recipe when produced in bulk……please note that with herbs and spices you generally need to use experience…rather than conversion factors when increasing a recipe. And, finally, it is important to adjust the time properly. Experience again plays a role in factoring cooking times.

Resources

Recipe Conversion Basics: http://allrecipes.com/HowTo/Recipe-Conversion-Basics/Detail.aspx
Recipe Adjuster: http://www.fruitfromwashington.com/Recipes/scale/recipeconversions.php
Conversions: http://www.pastrywiz.com/conversion.htm
Recipe Adjustment (pdf): http://www.fns.usda.gov/TN/Resources/rec_adjust.pdf
Portion size conversions: http://www.mypyramid.gov/

Food Service - Unit and Recipe Costing

Unit Cost – AP means as purchase. AS means as served and EP means edible portion. Generally the amount purchased is not the amount used for a single recipe….For example you purchase a dozen eggs for $1.20. The unit cost is 10 cents. If you purchase a 50 pound bag of flour and the price is $10.00 for 50 pounds then the flour is $1.00 per pound thus the unit cost is $1.00.

An invoice generally shows :
Item Number Quantity Unit Description Size Price Amount
123 2 Flat Heirloom tomato 5x30ea 20# $10.00 $20.00

For invoice templates visit: http://office.microsoft.com/en-us/templates/ct101172551033.aspx

Total Recipe Cost – The total recipe cost is determined by deciding what quantity you need for the recipe and then adding all of the ingredient costs together. For example:

Your recipe for 6 servings is:

12 eggs
8 oz milk
1 bunch parsley
2 oz cheese

Twelve eggs cost $1.00; 8 ounces of milk costs $.50; one bunch of parsley is $.30; and 2 ounces of cheese is .$60 ….the total recipe is $2.40. You get 6 portions from this so each portion costs $.40.

Once you have the total recipe cost then you can determine how many portions you can get from that recipe and have your cost per portion. If your total recipe is costing $5.00 and you can get 5 portions from the recipe then your portion cost is $1.00.

View the Recipe Costing Form below.

Recipe Costing Form

What is portion? – The portion amount is the amount actually sold to the customer.

There are Two types of labor: Direct and Indirect – Direct labor is labor that is involved in producing the food. Indirect labor is labor that is used in auxillary areas such as cleaning the facility, ordering product etc.

What is Prime Cost? – Prime cost is the total cost of preparing a food item for sale. It is the portion cost plus the direct cost.

Resources

Trade Calculations – Recipe and Portion Cost: http://www.members.shaw.ca/gwall/tradecalc/porcost.htm
Recipe Cost Calculator: http://sensetosave.com/frugal-tools/recipecostcalc/

Food Service - Controlling Food Costs

Menu – The menu is the most important consideration in controlling food cost. The menu stabilizes what you are producing. It is the basis of your calculations and much effort and thought should go into the menu development.

Purchasing and Ordering – Purchasing and ordering is important because the necessary amount of product must b e on hand, but too much product is wasted inventory that is not producing income. It is also important to have specifications so that you can shop vendors for the best price. Accurate, detailed specs help you specify exactly what you are purchasing.

Receiving – Receiving is critical, All items must be counted and accurately received. It is important that the specified product is received and that an accurate count is verified. In addition it is important that the receiver puts away the product in a timely manner to insure freshness and safety.

Storing – Storage is important. Proper temperatures must be maintained. FIFO (First in, first out) insures the product being utilized is fresh. Storage areas should be kept clean and monitored on a regular basis to insure product quality.

PARSTOCK (PAR) – It is important to maintain a Par stock so that product is always on hand. One can determine the par stock by keeping records of use and knowing that each week 4 cans of tomato sauce will be used generally.

Kitchen Procedures – Kitchen procedures are important to maintaining cost control

1. Establishing Standard Portions helps the kitchen staff know how much to serve and in turn how much each serving costs.
2. Waste must be monitored. Overcooking or theft must be evaluated on a regular basis to prevent excess waste
3. Percentage of Sales can be established overall on the menu. With careful monitoring it can be established that appetizers contribute 10% of sales, desserts 20% of sales etc. This will help in purchasing and ordering as well as monitoring food cost.
4. Sales and Service is also important in monitoring food cost. Charging the right price is critical to maintaining appropriate food costs, and upselling allows high profit items to contribute to sales.

Resources

Controlling Food Costs: http://www.armsco.com/freejul9.htm
http://www.hotel-online.com/Trends/Payne/Articles/FoodCostSteps.html
Receiving and Storing of Food: http://www.allfoodbusiness.com/Safe_Food_Storage.php
Receiving Safe Food: http://www.uri.edu/ce/ceec/pdfs/toolbox_receiving.pdf
Food Storage Guide: http://www.ag.ndsu.edu/pubs/yf/foods/fn579-1.htm

Food Service - Menu Pricing

Cost-Based Menu Pricing can be done in several ways…

Factor Pricing requires one to know the cost of the item and the desired food cost percentage. The cost divided by the food cost percentage equals the selling price.

Prime Cost Pricing is the food cost plus the direct labor. This equals prime cost. Divide the prime cost by the desired prime cost percentage to determine the selling price

The psychological Impact of Pricing is very important.

Last digits of 9 and 5 give a perception of being a better value

Number of digits is important too. Three digits is perceived as a better value than 4 digits. $9.99 vs. $10.00.

The Spread in menu prices should be considered as well. The highest priced item on the menu should not be more than double the lowest priced item on the menu.

Resources

How to Price Your Restaurant Menu: http://restaurants.about.com/od/menu/a/foodcost.htm
Menu Tools: http://www.menutools.com/faq.php

Quiz