Question

5) 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 is expected to have sales next year (year 1) of $350. Sales have been growing steadily, and are expected to continue growing steadily for the foreseeable future (aka, infinitely), at 5% per year. The applicable discount rate is 15%. However, Rachel doesn't have much cash 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? a. b. c. d. $894.95 1,044.10 $ 1,582.78 1,846.58

Answer 1

Current Value of lemonade Stand	Annual Sale/(Cost - Growth rate)
Current Value of lemonade Stand	350/(15%-5%)
Current Value of lemonade Stand	3,500
Now will be settled with 5 year annuity so PV of annuity must be 3500
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
3500=	= Annual Payment * (((1-(1 + 15%) ^- 5)) / 15%)
3500=	= Annual Payment * 3.352
Annual payment=	3500/3.352
Annual payment=	1,044.15
So option B is correct