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

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  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?

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?

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?

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?

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?

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?

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.