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 $343. 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.

Step 1

The lemonade stand had cash flow last year (year 0) of $343. 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%.

C_{0} = $ 343

g = 6%

r = 19%

Step 2

Valuation using Gordan Growth Model = C_{0} x (1 + g) / (r - g) = 343 x (1 + 6%) / (19% - 6%) = $ 2,796.77

Step 3

If this value is to be paid by an annuity A over n = 5 years then PV of all the annuities, today wil...

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