# Topic 14.1: Basic Real Estate Computations >

### Learning Objectives

After successfully completing this topic, you will be able to
• compute real estate sales commissions, and
• calculate the percent of profit or loss, given the original cost of the investment, the sale price and the dollar amount of profit or loss.

### Sales Commissions

It’s widely known in the real estate industry that even those of us who profess to be terrible at math can quickly calculate how much we’ll make on a sale. That may be because we calculate it more often, but is more likely because we’re personally interested in the calculation. To work out commission problems, we should envision the commission equation below.

Part ÷ Total x Rate, or, the shortened form: P ÷ T x R

Cover what you want to find and you’ll see the formula.

To find the commission, cover the P and the formula appears as T x R

#### Example—to find the commission

A broker sells a house for \$350,000. His commission rate is 7%. What’s the commission at closing?

Cover the P in the formula to get T x R
T x R = P \$350,000 x .07 = \$24,500

#### Example—to find the rate

A broker sold his listing for \$300,000 and gets a commission of \$18,000. What was the commission rate?(cover the R in the formula.)

Cover the R in the formula to get P ÷ T
P ÷ T = R \$18,000 ÷ \$300.000 = .06 (6%)

#### Example—to find the price

A broker received a commission of \$23,800. The commission rate was 7%. What was the price?

Cover the T in the formula to get P ÷ R
P ÷ R = T \$23,800 ÷ .07 = \$340,000

### Commission Splits Between Brokers

In most cases, a cooperating broker sells the listing, so there is a split between brokers.

#### Example—to find the commission on a cooperating sale

A broker has listed a house with a 7% commission and offers a 50% commission split to cooperating brokers. Another broker sells the house for \$350,000. What is the selling broker’s commission at closing?

First, get the total commission:
Cover the P in the formula to get T x R
T x R = P \$350,000 x .07 = \$24,500
Then, divide the commission between the brokers: \$24,500 x .50 = \$12,250

#### Example—to find a sales associate’s commission on a cooperating sale

You’ll be given the commission split between the brokers, then the split between the broker and the sales associate.

A broker lists a house with a 6% commission and offers a 50% commission split to cooperating brokers. A sales associate in another office sells the house for \$265,000. The sales associate receives 60% of the commission received by her broker. What is the sales associate’s commission?

First, get the total commission.
Cover the P in the formula to get T x R
T x R = P \$265,000 x .06 = \$15,900
Then, divide the commission between the brokers: \$15,900 x .50 = \$7,950.
Then, get the sales associate’s share: \$7,950 x .60 = \$4,770

#### Example—to find the sales price given the sales associate’s commission

A sales associate sells a house for \$240,000. His commission of \$4,320 is 30% of the total commission. What is the total commission percentage?

\$4,320 is 30% of the total commission. To find the total commission:

\$4,320 ÷ .30 = \$14,400.
Cover the R in the formula to get P ÷ T = R
P ÷ T = R \$14,400  ÷  \$240,000 = .06, or 6%

#### Example—to find the total commission on a sliding scale listing

Some brokerage firms have established a graduated listing commission structure because it takes as much work to list and sell an inexpensive home as it does a larger home. A broker’s commission rate is based on a sliding scale as follows: 8% on the first \$50,000 value, 7% on the second \$50,000, 6% on the next \$150,000, and 5% on all over \$250,000. The broker sells his own listing for \$425,000. What is the broker’s commission, and what is the commission rate?

The commission is calculated as follows

To get the commission rate, divide commission by price: \$25,250  ÷  \$425,000 = .059 or 5.9%

### Calculating Selling Price, Cost and Profit

When a person sells a property, the profit is calculated by subtracting the cost from the sales price.

#### Example of calculating profit from a sale

When a person sells a property, profit is calculated by subtracting the cost from the sales price. Assume a man sells his property for \$340,000. He paid \$230,000 six months earlier. His profit is calculated as follows: \$340,000 price – \$230,000 cost = \$110,000 made (profit).

#### How to calculate the percent profit on a sale:

Part ÷ Total x Rate, or, the shortened form: P ÷ T x R

To calculate the percent profit, cover the R to get P ÷ T = R

#### Example—to find the percent profit on a sale

In the example above, the seller made \$110,000 profit on the sale of a property that cost \$230,000. Always use the cost as the “total” in the formula.

Cover the R in the formula to get P ÷ T
P ÷ T = R     \$110,000  ÷  \$230,000 = .478, or 47.8%

#### Example—to find the percent loss on a sale

A woman bought a building site six months ago for \$40,000. She sold it last week for \$33,500. What was the dollar loss? What was her percentage loss? Always use the cost as the “total” in the formula. The loss is the “part” in the formula.

Her dollar loss was \$6,500: \$40,000 – \$33,500 = \$6,500.

To calculate her percent loss, cover the R in the formula to get P ÷ T
P ÷ T = R  \$6,500  ÷  \$40,000 = .162, or 16.2%

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