1. Customer A spends $1,300 this year at your firm. What is the LTV in 5 years out? Assume 2% interest rates and a 100% probability of retention.

a. What is the answer with a non-constant cash flow?

b. What s the answer with constant cash flow?

2. Your firm has the following probabilities of retention (from the previous year) for someone who first shops in your store in year X:

Year	p(retention)
X	1.00
X+1	0.60
X+2	0.32
X+3	0.90
X+4	0.82
X+5	0.88
X+6	0.97
X+7	0.87
X+8	0.85

a. What is the overall probability of someone from year 0 remaining through year 7?

b. Use this table to provide a more correct answer to question 1.

3. Your firm finds that using a rolling three-year average is the most accurate input for LTV. A customer spent $500 two years ago, $100 last year, and $600 this year. Using a 5% interest rate, what is the LTV for five years out, assuming full retention?