Time Value of Money – Six Functions of a Dollar
Summary
Appraisal Training: Self-Paced Online Learning Session
Assessors' Handbook Section 505, Capitalization Formulas and Tables (AH 505), contains six compound interest functions and corresponding factor tables. Each compound interest function is defined by a formula, which is the basis for calculating the compound interest factors for that function. Each formula requires a periodic interest rate and the number of periods. All of the functions are based on compound interest – interest earned is added to principal and itself earns interest from that time on. The compound interest tables are used to solve time value of money problems and are particularly important when performing calculations as part of the income approach to value, specifically yield capitalization and discounted cash flow analysis.
Lesson 1 presented the concept of the time value of money. It explained that each compound interest formula, and factors derived from it, involves three variables: an interest rate, a term, and a compounding interval. It discussed compound interest versus simple interest. You learned that the effect of compounding depends on the frequency with which the interest is compounded, the periodic interest rate applied, and the number of periods involved. You also learned that using a compound interest factor does one of two things: (1) adds compound interest to a present value to arrive at a future value – referred to as compounding; or (2) subtracts compound interest from a future value to arrive at a present value – referred to as discounting.
In Lesson 2, you learned that the “Future Worth of $1” function is used to compound a single present amount to its future value. You learned how to perform this calculation using the “Future Worth of $1” factors found in column 1 of the AH 505 tables, based on a fixed rate of periodic interest being earned and the number of compounding periods involved.
In Lesson 3, we explained that the “Present Worth of $1” function is used to discount a single future amount to its present amount. You learned how to calculate the present value of a future amount using the “Present Worth of $1” factors found in column 4 of the AH 505 tables based on a fixed rate of periodic interest and the number of discounting periods involved.
In Lesson 4, you learned that the “Future Worth of $1 per Period” function is used to compound a series of periodic equal payments to their future value. You learned how to calculate the future value of a series of equal periodic payments with each payment occurring at the end of the period – an ordinary annuity – using the “Future Worth of $1 per Period” factors found in column 2 of the AH 505 tables.
In Lesson 5, we explained that the “Sinking Fund Factor” function is used to determine the equal periodic payment amount that must be made at the end of each period in a series of future equal payments in order to have the payments compound to a desired amount at the end of the last period. You learned how to use the “Sinking Fund Factor” in column 3 of the AH 505 tables and that it is typically used to determine how much must be set aside in each period in order to grow to a specified amount at the end.
In Lesson 6, you learned that the “Present Worth of $1 per Period” function is used to discount a series of periodic payments to their present value. You learned how to calculate the present value of a series of future equal periodic payments with each payment occurring at the end of the period – an ordinary annuity –using the “Present Worth of $1 per Period” factors found in column 5 of the AH 505 tables.
In Lesson 7, we explained that the “Periodic Repayment” function is used to determine the periodic payment amount necessary to amortize, or repay, a given present value. You learned how to calculate the payment amount that must be made at the end of each period in a series of future equal periods in order to repay the amount borrowed using the “Periodic Repayment” factors found in column 6 of the AH 505 tables.
In Lesson 8, you learned that the “Mortgage Constant” function is used to determine the annualized payment amount per $1 of loan amount, for a fully amortized loan with monthly compounding and payments. You learned how to calculate this annualized payment amount using the “Mortgage Constant” factors found in column 7 of the AH 505 tables. Mathematically, the “Mortgage Constant” factor is simply the monthly “Periodic Repayment” factor multiplied by 12.
In Lesson 9, we discussed “intra-year compounding” – that is, the compounding of interest more than once a year (semi-annual, quarterly, monthly, daily, or even continuously). You learned that when interest is compounded more than once a year, it affects both future and present value calculations: All else being equal, a future value, given intra-year compounding, will always be higher than it would have been with annual compounding and a present value, given intra-year compounding, will always be lower than it would have been with annual compounding.
Finally, in Lesson 10, you learned more about annuities. You learned that an annuity is a series of equal payments made at regular periodic intervals (e.g., monthly or annually). You learned that there are two types of annuities: an ordinary annuity and an annuity due. In an ordinary annuity, the payments occur at the end of the period; in an annuity due, the payments occur at the beginning of the period. You also learned that while the AH 505 tables (columns 2, 3, 5, & 6) are for use in ordinary annuity calculations, the factors in the tables can be mathematically converted to their corresponding annuity due factors.
We hope that you have found the information presented in this learning session beneficial.
Training Credit for Certified Property Tax Appraisers
If you are a certified property tax appraiser or auditor-appraiser working for a California County Assessor's office or the Board of Equalization (BOE), you can obtain training credit for taking this self-paced online learning session. If you wish to obtain training credit, you must complete the examination at the end of this learning session and submit your answers to the BOE using the 'Submit' button at the end of the exam. Completion of this online learning session examination with a score of 70% or higher will qualify for 8 hours of training as required by Revenue and Taxation Code section 671 for certified appraisers who are employees of the state, any county, or city and county.
By submitting the examination, you are attesting to the fact that you have read all the lessons and have performed all the exercises in the “Check Your Knowledge” section of the training. Please do not share your answers with anyone.