Knowledge Matters Math

Angel plans to get his new product into Walmart. If he plans to sell 10,000 units to Walmart at $45 each, but Walmart negotiates a 20% discount, how much revenue has Angel lost compared to his original plan?

$90,000

You have a net lease for $350 per month. You are responsible for the taxes, which are $6,000 per year. What is your monthly rent?

$850

Your business plan calls for sales of $45,000 in year 1 with compound growth of 30% per year thereafter. What are your projected sales for year 10? The formula for compound growth is E = B x (1 + R)T, where E is ending value, B is beginning value, R is rate of growth, and T is the amount of time.

$477,202

Your sole proprietorship makes $90,000 per year in profits. Your average federal tax rate is 24% and your state tax rate is 6%. How much of your profits do you get to keep?

$63,000

You have heard that customers will try a new caterer if the price is 20% below their existing caterer. Your competitor prices a luncheon at $800. What does your price need to be to get customers to try your business?

$640

If the average crowdfunding campaign investment is about $90 and the average number of investors is about 80, what is the best approximation of the average amount raised in a crowdfunding campaign?

$7,200

As a corporation, you want to distribute money to shareholders as a dividend. If the dividend is taxed at a rate of 20% and the dividend is $1 per share, how much money will a shareholder of 10,000 shares get after-tax?

$8,000

Your plan projects revenue of $5,000, $8,000, and $10,000 in years 1 through 3. Expenses are projected to be $9,000 for each of years 1 through 3. If your only funding need is the gap between revenue and expenses, which is the best estimate of your maximum cumulative funding need?

$4,000

Profit is revenue minus expenses. If your profit is $3,000 and your revenue is $50,000, what are your expenses?

$47,000

You have savings of $157,000. After talking it over with your spouse, you agree to risk no more than 30% on your new business idea. How much do you have to invest in the business?

$47,100

You have a loan for $200,000 at 8.5% annual simple interest. What is your monthly interest payment?

$1,417

You have a net lease. Your rent is $1,000 per month. Taxes and maintenance total $500 per month. What is your total monthly payment?

$1,500

An entrepreneur wants $500,000 for one third of her company. How much does she think the company is worth?

$1,500,000

You hope to have revenue of $4,000 and a gross margin percentage of 40%. What is your dollar gross margin? (Gross margin is revenue less direct product costs.)

$1,600

You plan on using cost-based pricing. The cost of your product is $10, and you are planning a 30% mark-up. What should the price of your product be?

$13.00

Your break-even point is 3,000 units. You make $5 on each unit; that is, your price minus variable cost is $5. What are your fixed costs? Use the formula: Break-even Point = Fixed Costs / (Price - Variable Cost)

$15,000

You estimate your annual revenue to be 50,000 + 20,000y, where y is the number of years in business. What is your estimated revenue in 5 years?

$150,000

Demand for electrical services in your area is $12 million per year. It is expected to grow 10% compounded annually over the next 5 years. What will demand be in 5 years? The formula for compound growth is E = B x (1 + R)T, where E is ending value, B is beginning value, R is rate of growth, and T is the amount of time.

$19,326,120

Your business loan has a variable interest rate. Next month the annual rate will jump from 6.3% to 7.8%. Your balance is $1,620,000. How much will your monthly payment go up?

$2,025

You are going into business with 4 equal partners (not counting yourself). If in 6 years, the business is making a profit of $1,000,000, what is your share?

$200,000

You expect your expenses to grow non-linearly over time by the following formula: expenses = 4,000 + 20,000 x (1.5)t where t is the number of months in business. What are your estimated expenses after 6 months?

$231,813

Your research finds 5,400 potential customers for your bowling alley, and you think each is willing to spend $10, five times per year, to bowl. What is the total potential revenue represented by these customers?

$270,000

You have signed a percentage lease with a base rent of $2,000 per month and a variable payment of 2% of revenue. If your revenue for the month is $50,000, what is your total rent for the month?

$3,000

If you raised $400,000 in a stock sale and gave up 12% of your company, what was the implied valuation of the company?

$3,333,333

You estimate that your new business's revenue will grow at a compounded rate of 30% each month for the first 6 months. If your third month's revenue is estimated at $5,000, what is your second month's revenue? (Round to the nearest dollar.)

$3,846

Three smoothie shops exist in your town with annual sales of $300,000; $344,000; and $412,000. What is the average of their sales?

$352,000

Your plan calls for using apprentice plumbers in place of fully licensed plumbers for some jobs. If the apprentice plumbers are 60% as productive as licensed plumbers and licensed plumbers cost $60 per hour, what is the most you should pay for apprentice plumbers?

$36

The Small Business Administration guarantees some loans. The fee for this can range up to 3.75%. On a $1M business loan, how high could the fee be?

$37,500

You are giving your pitch and state that you'll get 30% of this new $1.3 billion market in 2 years. A member of the audience laughs. What did you just say your year two revenue would be?

$390,000,000

Your company has equity of $580,000 and total liabilities of $340,000. What is your company's debt-to-equity ratio?

0.59

You are evaluating a pitch, and the founder says his product has a gross margin of $45 per unit and he has fixed expenses of $50,000. What is his break-even sales volume?

1,112

You project revenue to start at $5,000 for the first month and grow by $200 each month thereafter. You project expenses to begin at $7,000 per month and grow by $50 per month. In what month will you break even (revenue equal to expenses)?

14

70 of 500 respondents say they would visit a trampoline park. What percentage of respondents is this?

14%

You are planning to finance your start-up with a bank loan of $400,000 and equal contributions of $50,000 each in cash from a group of partners. You need $1.2M for the start-up. How many partners, including yourself, do you need to recruit?

16

A software start-up is pitching to raise money to write code. They need a team of four coders for two years, and each coder costs $100,000 per year. Their app will sell for $0.25. How many do they need to sell just to cover the coding cost?

3,200,000

You are looking at two locations. Traveling to downtown from Location A involves 3 miles of backroads at 30 MPH. Traveling to downtown from Location B involves 1 mile of backroads at 30 MPH and 5 miles of highway at 60 MPH. Which location has the shorter trip to downtown?

A

Venture capitalists often seek a return of 10 times their investment in 7 years. Approximately what is this compound annual rate of return? To make Z times return in Y years, where R is the compound rate of return: Z = (1 + R)Y

39%

Your business plan calls for delivering 6,000 haircuts in year 3. If one stylist works 250 days per year and does 5 cuts per day, how many stylists will you need?

5

You are asking investors for $100,000 each and promising to distribute to them profits of $15,000 each for the first 4 years and $25,000 each per year thereafter. Which of the following is closest to the number of years it will take for investors to get their money back?

5.6

You are in a 98 story building taking the elevator to the top from the bottom. Each story is 15 feet. The elevator travels at 29.33 feet per second. How long do you have for your elevator pitch?

50 seconds

Tyreek pitches four investors. They agree to each invest $25,000 and value Tyreek's company at $200,000. How much of the company will Tyreek still own after the investment?

50%

You hear a pitch where the founder says he'll reach $30 million in sales in 5 years. His first year sales are projected at $5 million. Which is closest to the compound growth rate he is implying? The formula for compound growth is E = B x (1 + R)T, where E is ending value, B is beginning value, R is rate of growth, and T is the amount of time.

56%

Your research of competitors shows prices of $45, $78, $13, $125, and $66. If you throw out the highest and lowest data points (outliers), what is the mean of the remaining prices?

63

If you sell stock in your company for $100,000 and the valuation of your company is $625,000, what percentage of the company will you own after the stock sale?

84%

You count customers going into the 5 pizza shops in your city. You get 56, 98, 43, 112, and 106. What is the median number of customers going into the shops?

98

There are about 30.2 million small businesses in the United States and about 30,000 other larger businesses. What percent of all businesses in the U.S. are small businesses?

99.9%

You have laid out your pricing plan at $185 for a bounce party for 8 kids; your competitor is at $155. A potential investor says she thinks you can get a 30% premium with your new facility. Does she think you should be priced higher or lower than your plan?

Higher

You are counting your competitors in town. This number is a(n):

Integer

Two investors have net worths of $12 million (investor A) and $1 million (investor B). They set their investment limits at 2% and 30% of their net worth, respectively. Which has the higher investment limit?

Investor B

You have data showing demand for plumbing services rising for each of the last five years. This would best be displayed on a:

Line graph

If 60% of the population is female and 30% of females buy physical therapy services, and 70% of men buy physical therapy services, is there more demand for physical therapy from women or men?

Men

Demand for plumbing services for the last 3 years, from furthest past to most recent, was $44 million, $42 million, and $38 million. A graph of this trend would have a slope that is:

Negative

As a huge math fan, you think it would be fun to have a prime number of partners in your business (including yourself) and at least 3 partners. If every partner gets one vote on major decisions, can a vote ever end in a tie (2-way, 3-way, 4-way, etc.)?

No

Your uncle is offering to sell you his T-shirt printing business for $1M. You think a multiple of 10X earnings (profit) is fair. His earnings are $69,000 per year. Should you buy it?

No

Which type of chart would best display data on the flavors of ice cream that customers prefer?

Pie chart

Abby can purchase a secondary data report for $500 or create primary data by surveying 300 people at a cost of $1.33 per person. Which is cheaper?

Primary

Which type of technology is best for laying out financial projections?

Spreadsheet

You receive a report that demand for lawncare services (demand) will grow from $900,000 per year to $990,000 and the available crews (supply) will grow from 100 to 120. Which is growing faster (as a percentage), supply or demand?

Supply

One survey has 3 respondents, and another has 100. Which survey is more likely to give accurate data?

The one with the larger sample size

You plan to be at least 5 miles (straight line distance) from your competitor. Your drive there via a route that forms two legs of a right triangle. The legs are 4 miles and 3.5 miles. Are you far enough away?

Yes