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.

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