# Lesson 8 Exercises – Capitalization: Converting an Income Stream into Value (The Income Approach to Value)

## Appraisal Training: Self-Paced Online Learning Session

1. Capitalization is the process of:
1. Forecasting future yields of a property
2. Calculating value from price
3. Deducting expenses to find net assets
4. Converting an income stream into a value indicator

#### Solution:

d. Converting an income stream into a value indicator

Explanation: The answer is (d). Capitalization is any method used to convert an income stream into a value. The two primary methods of income capitalization are direct capitalization and yield capitalization.

1. Which is a key variable of income capitalization?
1. Capitalization rate used to convert a multiplier into value
2. Capitalization rate or factor used to convert income into value
3. Overall rate used to convert a multiplier into value
4. None of the above

#### Solution:

b. Capitalization rate or factor used to convert income into value

Explanation: The answer is (b). There are three key variables of income capitalization: income to be capitalized, the capitalization rate or factor used to convert the income into a value indicator, and the time period over which the income is to be realized.

1. In yield capitalization:
1. You convert future benefits (income) into present value by dividing a single year's income estimate by an appropriate capitalization rate.
2. You convert future benefits (income) into present value by discounting each future benefit at an appropriate yield rate.
3. You convert future benefits (income) into present value by capitalizing each future benefit by an appropriate capitalization rate.
4. Both a and b above

#### Solution:

b. You convert future benefits (income) into present value by discounting each future benefit at an appropriate yield rate.

Explanation: The answer is (b). Yield capitalization is used to convert future benefits into present value by discounting each future benefit at an appropriate yield rate. The other method of income capitalization is direct capitalization which is used to convert an estimate of a single year’s income expectancy into an indicator of value.

1. In direct capitalization:
1. You convert an estimate of a single year's income expectancy into present value by dividing the income expectancy by an appropriate rate or by multiplying the income estimate by an appropriate factor.
2. You convert future benefits (income) into present value by discounting each future benefit at an appropriate yield rate.
3. You convert future benefits (income) into present value by capitalizing each future benefit by an appropriate capitalization rate.
4. Both a and b above

#### Solution:

a. You convert an estimate of a single year’s income expectancy into present value by dividing the income expectancy by an appropriate rate or by multiplying the income estimate by an appropriate factor.

Explanation: The answer is (a). Direct capitalization is used to convert future benefits (a single year's income expectancy) into present value in one step by either dividing the income estimate by a rate or by multiplying the income estimate by a factor.

1. If the subject property has a net operating income of \$55,000, what is its indicated value using the capitalization rate of 0.1125?
1. \$367,000
2. \$400,000
3. \$489,000
4. \$550,000

#### Solution:

c. 489,000

Explanation: The answer is (c). As shown in Example 8-1, Value = Income ÷ Rate.
Value = \$55,000 ÷ .1125 = \$489,000 (rounded).

1. An investor purchases a rental home for \$100,000. If they expect to receive a 6 percent return on their investment, how much is the annual rent they expect to receive?
1. \$3,000
2. \$6,000
3. \$1,666,667
4. \$500

#### Solution:

b. \$6,000

Explanation: The answer is (b). As shown in Example 8-2, Income = Rate × Value.
Income = 0.06 × \$100,000 = \$6,000

1. A property with a net operating income of \$30,500 was appraised at \$350,000.  At what rate was the income capitalized (rounded to the nearest whole percentage)?
1. 0.0085 =  1%
2. 0.08 = 8%
3. 0.09 = 9%
4. 0.1148 = 11%

#### Solution:

c. 0.09 = 9%

Explanation: The answer is (c). As shown in Example 8-3, Rate = Income ÷ Value.
Rate = \$30,500 ÷ \$350,000 = 0.087 (rounded to 0.09, or 9 percent).

1. A small apartment complex valued at \$300,000 earns a monthly net income of \$3,000. What is the overall capitalization rate?
1. 1 percent
2. 6 percent
3. 12 percent
4. 20 percent

#### Solution:

c. 12 percent

Explanation: The answer is (c). As shown in Example 8-3, Rate = Income ÷ Value.
Income = \$3,000 × 12 = \$36,000 per year.
Rate = \$36,000 ÷ \$300,000 = 0.12, or 12 percent.

1. A small office building valued at \$300,000 earned a net operating income of \$52,000 annually. What is the direct capitalization rate?
1. 3 percent
2. 5.2 percent
3. 17.3 percent
4. 20 percent

#### Solution:

c. 17.3 percent

Explanation: The answer is (c). As shown in Example 8-3, Rate = Income ÷ Value.
Rate = \$52,000 ÷ \$300,000 = 0.173, or 17.3 percent.

1. Which of the following estimates would result in a direct capitalization rate of 20 percent?
1. Potential gross income \$100,000; value \$500,000
2. Effective gross income \$100,000; value \$500,000
3. Net operating income \$100,000; value \$500,000
4. Cash flow \$100,000; value \$500,000

#### Solution:

c. Net operating income \$ 100,000; value \$500,000

Explanation: The answer is (c). As shown in Example 8-3, Rate = Income ÷ Value.
Rate = \$100,000 ÷ \$500,000 = 0.20, or 20 percent.

1. A building with an annual net operating income of \$8,000 is valued at \$80,000. Estimate the value of the building if the capitalization rate is increased by one percentage point?
1. \$53,300
2. \$72,700
3. \$80,000
4. \$80,900

#### Solution:

b. \$72,700

Explanation: The answer is (b). \$8,000 net operating income and \$80,000 value means the capitalization rate used was 10 percent. If the capitalization rate is increased by one percentage point, the new value would be \$8,000 ÷ 0.11, or \$72,700 (rounded).

1. Analysis of recent comparable sold properties indicates a gross rent multiplier around 6.75. You know that the subject property's gross rental income is \$68,000 annually. What is the approximate value of the property?
1. \$459,000
2. \$10,074
3. \$38,250
4. \$750,000

#### Solution:

a. \$459,000

Explanation: The answer is (a). As shown in Example 8-4, Value = Income × Multiplier.
Value = \$68,000 × 6.75 = \$459,000

Questions 13 and 14 are based on the following information.

An office building recently sold for \$2,000,000. Given the following information:

Gross Income:
\$400,000
Vacancy factor:
8 percent
Expenses:
45 percent of effective gross income
Annual mortgage payment:
\$165,000
Equity:
\$500,000
1. What is the overall rate of return for the property?
1. 8.3 percent
2. 9 percent
3. 10 percent
4. 10.12 percent

#### Solution:

d. 10.12 percent

Explanation: The answer is (d). The overall rate of return cannot be calculated without first calculating the anticipated Net Operating Income [NOI]. In this problem, the NOI is \$202,400. This is calculated by subtracting the vacancy allowance as well as the expenses from the gross income. Net operating income divided by sale price equals the overall rate of return for the property: \$202,400 ÷ \$2,000,000 = 10.12 percent. For a quick review of OverAll Rates, see Demonstration 8‑3, on page 4; a more extensive discussion of OverAll Rates will begin in Lesson 11.

1. What is the indicated gross income multiplier?
1. 4
2. 5
3. 7.5
4. 10.12

#### Solution:

b. 5

Explanation: The answer is (b). As shown in Example 8-5, Multiplier = Value ÷ Income.
Multiplier = \$2,000,000 ÷ \$400,000 = 5

1. A commercial office building with a sale price of \$1,000,000 has a gross rent multiplier of 10. What is gross potential income of the property?
1. \$100,000
2. \$10,000,000
3. \$8,333
4. \$120,000,000

#### Solution:

a. \$100,000

Explanation: The answer (a). As shown in Example 8-6, Income = Value ÷ Multiplier.
Income = \$1,000,000 ÷ 10 = \$100,000.