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Direct Marketing LTV Sum Solution Note: The only formula you have to remember is lifetime value of a customer (LTV)! In the sum, you would be given several sources of a firm’s income and expenses - all mixed up - for a certain number of years. Remember to always write the first year mentioned in the sum as the ZEROTH (0th) YEAR AND NOT THE FIRST YEAR. For example, if you have years from 2000-04, then 2000 will be the zeroth year and 2001 will be the first year and so on. Before starting the sum, make two columns ‘Income’ and ‘Expenses’ and list out the names of the incomes and expenses under each of them. Step 1 –You have to club them together, first the income (say under column A) and then the expenses (say under column B), then subtract the total of B from that of A. That gives you your total contribution [C] for each year: Total contribution (yearly) = Total income – Total expenses Step 2 – Take the decimal form of the interest rate, like 10% is 10/100 and therefore 0.1. Then add 1 to it (1+0.1=1.1) Raise that to the power of each year (starting from zero). In the above example, 2000 (year zero) =1.10=1 (the result of any number to the power of zero is 1) 2001 (first year) =1.11=1.1 2002 (second year) =1.12=1.1x1.1=1.21 2003 (third year) =1.13=1.1x1.1x1.1=1.331 or 1.33 2004 (fourth year) =1.14=1.4641 or 1.46 Round off the results to two decimal points, like 1.331=1.33. Find this for each year. Step 3 – Using the values you just found, apply the formula and get the LTV LTV= Ci /(1+d)n Where Ci is the contribution for that particular year, i is the number of years, d is the discount/interest rate or the cost of capital incurred by the company. Basically you have to take the contribution for that year, and divide it by the corresponding figure for that year which you found in step 2. That will give you the lifetime value for that particular year. So if your contribution for year zero (2000) is Rs 5,000, and in step 2 you found the figure for year 2000 to be 1, then the lifetime value for year 2000 will be 5000/1=Rs. 5,000 Step 3 – Add the LTV values of all years and you will find the total customer lifetime value. Example: Given:On 31st March 2004 2005 2006 2007 2008 Sales --- 15,000 27,000 35,000 50,000 Referrals --- 3,000 5,000 8,000 12,000 Telemarketing 4,000 8,000 10,000 15,000 17,000 Discount --- 1000 2000 4000 6000 The rate of interest being paid by the company on loans is 10% Solution: Life Time Value=LTV= Ci / (1+d)n where Ci=net contribution for the year i i=number of years of an existing customer or an expected customer D=discount rate, interest rate, cost of capital Here; D=10% - Given Decimal form of the interest rate = 10% is 10/100 = 0.1 On march 31st 2004 2005 2006 2007 2008 Sales - 15,000 27,000 35,000 50,000 (+)Referrals - 3,000 5,000 8,000 12,000 Total Income (I) - 18000 32000 43000 62000 Telemarketing 4,000 8000 10000 15000 17000 (+)Discounts - 1000 2000 4000 6000 Total Expense (E) 4,000 9000 12000 19000 23000 Contribution (I-E) -4,000 9000 20000 24000 39000 LTV= Y0 + Y1 + Y2 + Y3 + Y4 = -4000/(1+0.1)0 + 9000/(1+0.1)1 + 20000/(1+0.1)2 + 24000/(1+0.1)3 + 39000/(1+0.1)4 = -4000 + 9000/1.1 + 20000/1.21 + 24000/1.33 + 39000/1.46 = -4000 + 8181.81 + 16528.92 + 18045.11 + 26712.32 = 65468.16