AZ - More Real Estate Math

Cheryl bought her home three years ago for $217,000. Assuming her home appreciated at the 3% rate typical of her current market, how much is her home worth now?

$237,121.76

Nearly 25 years ago, the Fredericksons purchased a house for $42,000. The tax assessor recently appraised the property at $320,000. If the property tax assessment ratio is 25%, what's the assessed value of the home?

$80,000

Depreciation

Loss in property value from any cause

Debt coverage ratio calculation

Mortgage loan payment amount x number of payments in a year

Appreciation calculation

Original value x appreciation % = appreciation amountOriginal value + appreciation amount = new value

Depreciation calculation

Original value x depreciation % = depreciation amountOriginal value ‒ depreciation amount = new value

You're working with a seller whose home was valued at $100,000 a couple of years ago. Through some market research, you've discovered that this area is seeing an appreciation rate of about 2% per year. What is the value after three years?

$106,121

Using a calendar year, what would the daily rate be if annual taxes are $4,662? Round to the nearest cent.

$12.77

Jordan bought an apartment unit a year ago for $144,000. He learned that the average annual appreciation rate for the area is 3%. Assuming his apartment appreciates at that rate, how much is it worth now?

$148,320

The Waltons' Property Tax The Walton family got a great deal on their home. They bought it for $101,297, and the tax assessor recently appraised it for $162,000. If the assessment ratio is 25%, and the tax rate is 3.2%, what are their annual property taxes?

$162,000 x 25% = 40,500 40,500 x 3.2% = 1,296

Beverly bought a commercial piece of property two years ago for $19,000. Based on the average annual commercial depreciation rate, how much is the property worth today?

$18,024 Commercial property depreciates fully in 39 years, or at a rate of 2.6% per year. Multiply the original value by 97.4% (100% - 2.6%): $19,000 × 0.974 = $18,605 for the first year. Then repeat for the second year: $18,605 × 0.974 = $18,024.84.

The Callahan's house has an assessed value of $60,000. The tax rate for their area is 3.8%. What will the Callahan's tax bill be for the year?

$2,280

The Smyths' Property Tax The Smyths purchased their home 10 years ago for $180,000. The tax assessor recently appraised the property at $205,000. If the property tax assessment ratio is 25%, what's the assessed value of the home?

$205,000 x 25% (.25) = $51,250

Calculating Appreciation Yes! $200,000 x 0.05 is $10,000. Based on this, what is the value of James' property after one year?

$210,000

Candice's house cost $207,000 when she bought it two years ago. The average appreciation rate for her area is 1.5%. Assuming that her home appreciates at this rate, how much is it worth now?

$213,256

Calculating Appreciation You got it: $210,000 x 0.05 is $10,500. Based on this, what is the value of James' property after two years?

$220,500

Sally is in the process of buying a property, and the sale closes on June 15. The seller already paid the water bill for June, which was $46.80. How much does Sally owe to the seller at closing for the prepaid water bill?

$23.40

What is the current value of a property that was purchased two years ago for $260,000, assuming an annual appreciation rate of 2%?

$270,504

The tax assessor just appraised Monique and Darrell's home at $145,000. The assessment ratio for their property is 25%. What is the assessed value of Monique and Darrell's property?

$36,250 $145,000 × 0.25 (25% in decimal form) = $36,250.

Leona bought her home just over two years ago for $350,000. Assuming her home appreciated at the 3% rate typical of her current market, how much is her home worth now?

$371,315 A shortcut for these calculations is to multiply the beginning balance each year by 1.03 (103% in decimal form): Year one: $350,000 × 1.03 = $360,500. Year two: $360,500 × 1.03 = $371,315.

When prorating annual HOA fees of $1,500 using the statutory calendar, what's the daily rate, rounded to the nearest cent?

$4.17

When prorating annual property taxes of $2,400 using the statutory calendar, what's the daily rate, rounded to the nearest cent?

$6.67

Finnegan pays $1,000 a year in HOA fees. The fees are due on a quarterly basis. He paid the HOA in January for the quarter, but sold his home and closed on March 1. How much will the buyer owe Finnegan for the prepaid HOA fees?

$83.33

Troy, a seller, paid his $3,600 annual property tax bill upfront in January. He sold his property and closing occurred on October 1. How much will the buyer owe Troy for taxes, assuming a statutory year?

$900

Capitalization rate calculation

(Income / property's value) x 100

The water and sewer for a property closing on January 10 is billed in arrears. Assuming the sellers own the property the day of closing, which formula(s) can be used to calculate their prorated debit using the calendar year method?

(Monthly expense ÷ 31 days) × 10 days

Proration, What the Seller Owes That's right, a statutory year is 360 days. According to this type of year, each month has 30 days and each year has 360 days. What are the daily expenses for the HOA fees?

.97 per day

Which Is Which? Let's start with the basics. What are appreciation and depreciation? 1) An increase in a property's value 2) A decrease in a property's value

1) Appreciation 2) Depreciation

What Do We Do First? Before we begin, let's identify the steps we need to take in order to solve this problem. 1) Calculate the daily rate. 2) Find out the number of days in the proration period. 3) Multiply the number of days in the time period by the daily rate.

1) Step one 2) Step two 3) Step three

Proration, What the Seller Owes Right, the seller is responsible for the fees from January 1 to June 15, the day of closing. So, how many days is this?

165 days

Assuming that the seller pays for the date of closing, if closing is July 7, how many days will the seller be responsible for paying using a statutory year?

187 days

Over how many years is a residential income-producing property depreciated?

27.5 years

How many days are in the month of February when using statutory year proration method?

30

A statutory year is ______ days.

360

Proration, What the Seller Owes Let's look at an example: Closing is June 15 and the HOA fees are $350 for the calendar year. These are based on the statutory year (30 days in each month) and they've not been paid for the current year. The buyer and seller must split this fee based on the amount of time each will be in the home for the current year. Let's break this down into smaller steps. If a statutory calendar is being used, how many days are there in a year?

360 days

Reconciliation

A balancing of both sides of the Closing Disclosure

What's depreciation?

A decrease in property value

Proration

A division of expenses and income between buyer and seller according to who owes what to whom

Which of these items wouldn't be prorated?

A down payment

What's a Proration? Which of these is the best definition of a proration?

A proportionate calculation based on who actually owes an expense for a given period of time

Calculating Appreciation Cheryl bought her home three years ago for $217,000. Assuming her home appreciated at the 3% rate typical of her current market, how much is her home worth now?

A shortcut for this calculation is to multiply the starting value by 1.03 to get the ending balance plus appreciation. For the above example: $217,000 x 1.03 = $223.510. Then multiply that value by 1.03 to get the value at the end of the following year, and so on, for as many years as you're calculating appreciation. $237,121.76

What is a proration?

An amount apportioned according to use

Capitalization rate

An estimate of value or return on investment. This number tells investors how much income a property is generating as a percentage of the property's value

What's the definition of appreciation?

An increase in property value

Appreciation

Increase in property value

Debt coverage ratio (a.k.a., debt service coverage ratio)

Investors use this number to determine if a property is generating enough income to pay a property's mortgage

Prepaid items

Items a seller paid in advance and that the buyer must reimburse at closing, e.g., utilities

What are accrued expense items?

Items to be divided proportionately between the buyer and seller that the seller owes

Proration, What the Seller Owes Correct. Based on a 360-day calendar, $350 is divided by 360 to find the daily rate. Now, we will calculate the number of days the seller will owe for the year. How many days does the seller have to pay for HOA fees?

Jan 1 to June 15

What's the Seller Paying? Almost finished. What's the seller going to pay at closing? Round to the nearest cent. Again, our problem: Closing is March 12. Annual taxes are $1,200. How much does the seller have to pay at closing if using a statutory year, assuming the seller has not yet paid any taxes?

Multiply the number of days in the time period by the daily cost ($3.33 x 71 days =$236.43).

Number of Days Now that you have the daily rate, let's find out how many days are in the proration period. Here's the problem again so you don't have to click back a slide: Closing is March 12. Annual taxes are $1,200. Assuming the seller does NOT pay for the date of closing, how much does the seller have to pay at closing if using a statutory year, assuming the seller has not yet paid any taxes? How many days will the seller be responsible for?

This problem is using a statutory year, so we have 60 days, plus 11 days in March (remember, the seller does NOT pay the day of closing in this transaction). 71 days

Net to seller

The amount the seller gets after the mortgage payoff, broker commission, and other closing costs have been deducted

Assessed value

The dollar amount to which the local tax rate is multiplied to determine property tax owed

Which of the following is NOT a number you need to calculate property taxes?

The original purchase price

Accrued expenses are prorated items that are paid at closing by whom?

The seller

Depreciated Value Let's try a calculation. An investor purchased a commercial property for $1 million, with a building worth $800,000. What's its depreciated value after one year?

This is a commercial property. It depreciates over 39 years, giving us a depreciation rate of 2.6%. 800,000 x 2.6% = 20,800 800,000 - 20,800 = $779,200

Danette hasn't paid the first quarter water bill on her property. It was due on April 1. She's closing with the buyer, Jason, on April 1. What type of expense is this and how will it appear on the settlement statement?

This is an accrued expense, and will appear as a seller debit and a buyer credit.

What's the Buyer Paying? We're at the final step. What's the buyer going to pay at closing? Round to the nearest cent. From the last question, remember that the seller owes $236.43 and the annual taxes are $1,200.

To find the answer, take the annual taxes owed and subtract what the seller must pay ($1,200 ‒ $236.43). The buyer would owe $963.57

Of the following, which is considered a typical accrued adjustment?

Unpaid real estate taxes

Which of the following is a typical accrued adjustment?

Unpaid real estate taxes

Gross income multiplier

Used to help estimate the value for income generation of residential properties with five or more units, this number shows the relationship of a property's sale price to its annual gross income

Gross rent multiplier

Used to help estimate the value for income-generating residential properties with one to four units, this number shows the relationship of a property's sale price to its monthly gross rent

In an ideal world, a property's value will increase over time, or ______.

Appreciate

What is the formula used to determine annual property tax?

Assessed value × tax rate

If the buyer owed taxes for 95 days, the seller owed for 270 days, and annual taxes were $4,000, what would the buyer's prorated tax expense be?

$1,041.20

The Daily Rate What is the daily rate? Remember our problem: Closing is March 12. Annual taxes are $1,200. How much does the seller have to pay at closing if using a statutory year, assuming the seller has not yet paid any taxes? Let's compute the daily rate.

$1,200 / 12 = 100 100 / 30 = $3.33

Sally's home appraised at $225,000. The assessment ratio is 20% and the tax rate is 2.8%. What will Sally's tax bill be for her home?

$1,260 Finding the property tax here is a two-step process. First, find the assessed value by multiplying the appraised value by the assessment ratio: $225,000 × 0.20 = $45,000. Then, multiply the assessed value by the tax rate: $45,000 × 0.028 = $1,260.

Calculating Appreciation James purchased a house in an up-and-coming area of town for $200,000. Last year, property values appreciated 5%. That trend is expected to continue for the next few years. Assuming it does, let's determine the new value of James's property after two years. Let's walk through this step by step. First, what is the appreciation amount for the first year?

$10,000

Calculating Appreciation That's right! Now we're into year two. What is the appreciation amount in year two?

$10,500

What are the steps in a proration?

Calculate the daily rate, then multiply rate by the number of days in the proration period.

Statutory proration

Calculations assume 30 days per month or 360 days per year

Calendar year proration

Calculations use the exact number of days in the period (and 365 days per year)

A real estate transaction has a closing date of May 20. The seller, who's responsible for closing costs up to but not including the day of closing, has already paid annual property taxes of $1,949. How will the closing statement reflect the proration for the seller? Use a calendar year proration, and round to the nearest dollar.

Credited $1,207

A real estate transaction has a closing date of August 5. The seller, who's responsible for closing costs up to and including the day of settlement, has not yet paid annual property taxes of $1,290. If proration is based on a statutory calendar, the buyer will be_______ on the closing statement.

Credited $771 The buyer will be credited $771, since $1,290 ÷ 360 = $3.58 daily rate. The buyer is responsible for August 6 through December 31, which is 4 months and 25 days under the statutory calendar, which equals $3.58 × 145 days = $519.10. So, $1,290 - $519.10 = the seller's share of $770.90, or $771 if rounded to the nearest whole dollar.

A decrease in property value over time is called ______.

Depreciation

How do you calculate the monthly rate for annual taxes using a statutory year?

Divide by 12

How do you calculate the daily rate for annual taxes using a calendar year?

Divide by 365

Accrued items

Expenses that are accruing but are not yet payable (e.g., property taxes)

The Murphys' Property Tax The Murphys recently received a property tax bill for $896.00. If the assessed value is $32,000, and the tax ratio is 25%, what's the tax rate percentage? Hint: property taxes = assessed value x tax rate

Property taxes = assessed value x tax rate is the same as property taxes ÷ assessed value = tax rate. $896 ÷ $32,000 = .028 or 2.8%.

Which of these items will be either accrued or prepaid?

Prorated

Proration, What the Seller Owes Great work! January through May (30 days x 5 months = 150 days), plus the 15 days in June. 150 days + 15 days = 165 days. If we know the seller is responsible for 165 days, the buyer must be responsible for 195 days (360 ‒ 165 = 195). The last thing to do is to multiply the days the seller is responsible for by the daily rate. Identify the amount the seller will pay. (Round to the nearest dollar.)

Proration, What the Seller Owes That's right, the seller will pay $160.

Gross income multiplier calculation

Sales price / annual gross income

Gross rent multiplier calculation

Sales price / monthly gross rent

Net to seller calculation

Sales price x (100% ‒ commission %) ‒ mortgage payoff amount

Which Calendar? Let's look at our problem again: Closing is set for March 12. Annual taxes are $1,200. How much does the seller have to pay at closing if using a 360-day year, assuming the seller has not yet paid any taxes? Our problem uses which type of calendar?

Statutory year

Calculating Depreciation Your client purchased a small cottage one year ago for $18,000. If the annual depreciation rate is 3.6%, what is the depreciated value today?

You can use the shortcut for depreciation just like you can for appreciation, except instead of adding to the value, you'll subtract. So in this case, it'd be 100% minus the 3.6% depreciation, which leaves a depreciated value of 96.4%. Multiply that by the purchase price to get the depreciated value ($18,000 x .964 = $17,352). You can use this method for subsequent years, too, if needed. For example, the value at the end of year two would be $17,352 x .964 = $16,727.33. or $18,000 - 3.6% = 648 648 - 18,000 = 17,352