Time Value of Money - Six Functions of a Dollar
Using Assessors’ Handbook Section 505 (Capitalization Formulas and Tables)
Appraisal Training: Self-Paced Online Learning Session

# Lesson 6: Present Worth of \$1 Per Period

In order to solve the following problems you will need to refer to AH 505 to look up the factors in the compound interest tables. Before you start, please print the problems using the "Print Questions" button below so you can work through the problems on your own. After you work through the problem, the solution can be viewed by clicking on the blue plus sign immediately following the question. Additionally, when you have completed all the problems, you may print all of the solutions using the "Print Questions with Answers" button below.

## Problem 1

Solve for present value using the correct PW\$1/P factor:

Solution

## Problem 2

Jim took out a standard 30-year mortgage loan for \$200,000 with monthly payments of \$1,199.10; interest rate of 6%. Eight years later, he sold the house. What was the remaining balance on the loan when he sold? (Hint: At any point in time, the remaining balance on an amortizing mortgage loan is equal to the present value of the remaining loan payments discounted at the contract rate of interest.)

Solution

## Problem 3

When the contract rent under a lease is less than the market rent, there is a leasehold advantage in favor of the tenant. This is sometimes called the "bonus value" in the lease. If a tenant is able to freely assign or sublease his interest to another tenant, he may be able to capture the bonus value. The annual contract rent for a property is \$180,000; the annual market rent is \$225,000. There are 5 years remaining in the lease. What is the estimated bonus value in the lease? Assume an annual interest (discount) rate of 5%. (Hint: Bonus value can be estimated by discounting the difference between the market and contract rent over the remaining term of the lease.)

Solution

## Problem 4

An income property generates an expected annual net income of \$1,250,000; this income is expected to remain level over an expected 8-year holding period. The estimated value of the property at the end of the holding period -- its reversionary value -- is \$12,500,000. Assuming an interest (discount) rate of 12%, estimate the value of the property using discounted cash flow (DCF) analysis. (Hint: The essence of DCF analysis is that a property´s value is equal to the present value of the property´s expected market net income over the holding period, plus the present value of the property´s expected reversionary value at the end of the holding period, with the income discounted at a yield rate, or expected rate of return, required by market participants.)

Solution

## Problem 5

Mary will retire in 20 years and after she retires she wants to be able to withdraw \$10,000 at the end of each year for 10 years from her retirement account. How much should she invest in equal annual deposits over the next 20 years to fund her retirement account? Assume that her first deposit occurs a year from today and that the annual interest rate throughout is 9%.

Solution

## Problem 6

A taxable possessory interest (TPI) involves the private use of publicly-owned property. Under certain conditions, the right to possession held by a private possessor is taxable, even though the underlying fee interest held by the public owner is exempt. One way of valuing a taxable possessory interest is called the income approach – direct method. In this method, the estimated value of the TPI is equal to the present value of the expected net market rent to the public owner over the possessor´s reasonably anticipated term of possession (in essence, the duration of the TPI). Suppose that a private possessor leases government-owned land. The net market rent is \$12,000 per year. The reasonably anticipated term of possession is 20 years. Using an interest (discount) rate of 10%, estimate the value of the TPI using the income approach – direct method.

Solution