Compound Interest and Real Estate Valuation

Compound Interest:

• Compound interest is calculated on the principal plus accumulated interest from previous periods (“interest on interest”).
• Simple interest is calculated only on the principal.
• Simple Interest Example: Principal: 1000 Riyal, Annual interest rate: 10%, Duration: 2 years. Year 1: 1000 * 0.10 = 100 Riyal. Year 2: 1000 * 0.10 = 100 Riyal. Total interest: 200 Riyal. Total amount after 2 years: 1200 Riyal.
• Compound Interest Example: Principal: 1000 Riyal, Annual interest rate: 10%, Duration: 2 years. Year 1: 1000 * 0.10 = 100 Riyal. Amount after year 1: 1100 Riyal. Year 2: 1100 * 0.10 = 110 Riyal. Total interest: 210 Riyal. Total amount after 2 years: 1210 Riyal.
• The compounding period is the time interval when interest is added to the principal to calculate new interest (annually, semi-annually, quarterly, monthly, or daily).
• Example: 1000 Riyal at 12% annual interest compounded monthly has a monthly interest rate of 12%/12 = 1%.
• Compound Interest Formula: FV = PV (1 + i/n)^(nt), where FV = Future Value, PV = Present Value, i = Annual interest rate, n = Number of times interest is compounded per year, t = Number of years.
• Example: Invest 5000 Riyal at 8% annual interest compounded quarterly for 5 years. PV = 5000, i = 0.08, n = 4, t = 5. FV = 5000 (1 + 0.08/4)^(4*5) = 7429.74 Riyal.
• Hoskold Method (Sinking Fund Method): Calculates the present value of annual capital recapture payments assuming they are deposited in a sinking fund earning a safe rate of return. Primarily used for valuing depleting assets like mines and natural resources. Formula: PV = A / (r + Isf), where PV = Present Value, A = Annual capital recapture payment, r = Required rate of return, Isf = Interest rate on the sinking fund.
• Inwood Method: Assumes the present value of investment recapture from income stream depends on a single discount rate. It assumes that the annual payment (assuming a level annuity) is accumulating compound interest and is amortized or “paid off” just like a loan.

Real Estate Valuation Methods:

• Real estate valuation methods estimate the fair market value of a property.
• Sales Comparison Approach: Compares the property to similar properties recently sold in the same area, adjusting sale prices for differences in features, location, and condition.
• Cost Approach: Estimates the cost to replace the property with a new one, then subtracts depreciation.
• Income Approach: Estimates the income the property is expected to generate, then applies a capitalization rate to convert the income into value.

Income Approach:

• The income approach is used for commercial and investment properties. The property’s value is directly proportional to the income it can generate.
• Steps: 1. Estimate Net Operating Income (noi❓) by subtracting operating expenses from potential gross income. 2. Select a Capitalization Rate (Cap Rate). 3. Calculate Value: Value = NOI / Cap Rate.
• Example: A commercial property generates an NOI of 100,000 Riyal annually, and the cap rate is 8%. Value = 100,000 / 0.08 = 1,250,000 Riyal.
• The capitalization rate should reflect the risks and market conditions.

Measures of Central Tendency:

• Appraisers use averages to determine prevailing values in a neighborhood, average rental rates, and gross rent multipliers.
• Common methods for measuring central tendency (average) are the mean, median, and mode.

In the sample of values ​​listed below:

1
2
3
4
4

• 2.8 is the arithmetic mean
• 3 is the median
• 4 is the mode
• 1-4 is the range
• Mean: The arithmetic average is calculated by adding all values ​​in the sample to arrive at a sum and then dividing by the number of elements in the sample. Real estate agents use this method when referring to the “average” square footage or “average” price.
• Median: The middle value in a sample of values. In the sample above, 3 is the median because there are an equal number of values ​​above and below it (two above and two below). Real estate publications often refer to the median housing price in a particular state, city, or county.
• Mode: The most frequently occurring value in a sample. In the sample above, 4 is the mode. The modal prices of similar dwellings will be of interest to the appraiser in developing comparisons.
• Range: The difference between the lowest and highest number in the sample. For example, appraisers will be interested in the lowest and highest prices paid for homes in the neighborhood.
• Standard Deviation: A mathematical formula that measures how much prices vary from the mean (arithmetic mean). For example, a small standard deviation means that most prices are almost identical. The greater the standard deviation, the greater the difference in prices.