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Nana76 [90]
4 years ago
12

Anna owns Home Antiques, whose value is $160,000 today assuming normal growth. However, Anna believes the value will grow at 16%

per year for the next three years. She wants to take this rapid growth into consideration when valuing the business for a potential sale. Find the future value of the business in three years, then use that future value to find the present value at a rate of 8% compounded annually.
Business
1 answer:
mr Goodwill [35]4 years ago
7 0

Answer:

1. Future value:

  • <u>$249,743.36</u>

2. Present value:

  • <u>$198,254.33</u>

The goal is to find the present value of the business: $198,254.33. The future value is calculated as an intermediate step to calculate the present value.

Explanation:

<u />

<u>1. Future value in three years</u>

  • Value today: $160,000
  • Value in one year with grow at 16% ⇒ multiply by 1.16
  • Value in two years with grow at 16% ⇒ multiply by 1.16²
  • Value in three years with grow at 16% ⇒ multiply by 1.16³

  • Future value in three years: $160,000 × 1.16³ = $249,743.36

<u />

<u>2. Present value at rate of 8% compounded annually</u>

The present value is calculated discounting the future value at the given rate:

  • Present value = $249,743.36 / (1.08)³ = $198,254.33
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Correct question:

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