Question

Your niece, Sally, is a lemonade stand mogul. Her lemonade stand has been the most successful in the neighborhood for the last 5 years. She’s ready to get out. She wants to sell her lemonade stand to her younger sister, Rachel. Rachel contracts you, the business major, to advise her in the transaction. The lemonade stand has no valuable assets, so its value is derived solely from the ability to generate cash flows. The lemonade stand had cash flow last year (year 0) of $357. Cash flow has been growing steadily, and is expected to continue growing steadily for the foreseeable future (aka, infinitely), at 6% per year. The applicable discount rate is 19%. However, Rachel doesn’t have much cash on hand and will have to finance the purchase of the lemonade stand as a 5-year annuity to Sally. How much will Rachel have to pay Sally per year over the next five years to take over the lemonade stand? Round to nearest cent.

Answer 1

Cash Flow Generated by lemonade stand = $ 357 in year 0

Perpetual Growth Rate of Cash Flows = 6 % per annum and Applicable Discount Rate = 19 %

Therefore, Expected Cash Flow Next Year (year 1) = [357 x 1.06] = $ 378.42

The value of lemonade stand today should equal the total present value of the stand's perpetual constant growth cash flows discounted at the applicable discount rate.

Therefore, Current Value of Stand = V0 = 378.42 / (0.19 - 0.06) = $ 2910.92

Now the stand is purchased for V0 through a 5-year annuity finance option. It is assumed that the annuity financing also has 19% as the discount rate.

Let the annual annuity be $P

Therefore, 2910.92 = P x (1/0.19) x [1-{1/(1.19)^(5)}]

P = 2910.92 / 3.0576 = $ 952.0179 ~ $ 952.02