Lesson 4 Exercises — Time Value of Money (The Income Approach to Value)

Appraisal Training: Self-Paced Online Learning Session

Check Your Knowledge

  1. You can buy a parcel of real estate today that you estimate will bring $15,000 in 9 years. Assuming your money is worth 9%, how much would you be willing to pay for the property?
Solution:

To determine the amount you would be willing to pay for the property, you use the present worth of 1 factor
$15,000 × 0.460428 (column 4 @ 9% annual; 9 years) = $6,906.42
  1. You deposit $4,000 each year into a retirement account paying 8% interest. How much will you have in 25 years when you retire?
Solution:

To determine the amount you will have in 25 years you use the future worth of 1 per period factor
$4,000 × 73.105940 (column 2 @ 8% annual; 25 years) = $292,423.76
  1. Your company is required to pay into a sinking fund each year in order to meet an obligation that matures in 10 years. The amount of the obligation is $100,000 and you can earn 4% on your deposits. How much must your company deposit each year in order to meet these needs?
Solution:

To determine the amount you must deposit each year to meet the obligation you use the sinking fund factor
$100,000 × 0.083291 (column 3 @ 4% annual; 10 years) = $8,329.10
  1. Your company borrows $150,000 agreeing to pay the balance in 10 years in equal installments to include principal plus 8% interest. What should the payments be?
Solution:

To determine the payment amount, you use the periodic repayment factor
$150,000 × 0.149029 (column 6 @ 8% annual; 10 years) = $22,354.35
  1. At an interest rate of 12%, how long would it take a sum of money to double?
Solution:

To determine how long it would take to double your money, you use the future worth of 1 factor. Go to column 1 at 12% interest; at 6 years the factor is closest to 2.
  1. You can buy a mortgage from a mortgage broker. Mortgage payments are $30,000 per year and there are 16 years to maturity. The broker is asking $325,000 for the note. You already hold similar mortgages and they yield 12%. Should you buy this note?
Solution:

To determine whether you should buy this note, you use the present worth of 1 per period factor.
$30,000 x 6.973986 (column 5 @ 12% annual; 16 years) = $209,219.58.

No, you should not buy this note. The present worth of the income stream is less than the asking price.