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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.

Respuesta :

Edufirst

Answer:

1. Future value:

  • $249,743.36

2. Present value:

  • $198,254.33

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:

1. Future value in three years

  • 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

2. Present value at rate of 8% compounded annually

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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