Consider the followingdata:

(Click the icon to view thedata.)

Requirement

Customer 421

Initial acquisition cost

$ 400

$400

n= number of years retained

6

r= retention rate for each of the n years retained

0.8

0.8

Cost of capital

0.1

0.1

Upper M Subscript t

Mt = margin from customer in year t

Upper M 1

M1

$ 200

$200

Upper M 2

M2

370

370

Upper M 3

M3

375

375

Upper M 4

M4

390

390

Upper M 5

M 5= 305

305

Upper M 6

M 6

410

410

c 1

c 1

90

90

c 2

c 2

80

80

c 3

c 3

80

80

c 4

c 4

80

80

c 5

c 5

70

70

c 6

c 6

70

70

Compute the customer lifetime value for Customer 421 based on the data above for the first six years of the customer relationship. Costs (c Subscript t

ct) were incurred to promote customer retention to a rate of 0.8

0.8 in years 1 through 6.

Begin by determining the general formula for calculating customer lifetime value(CL V). (Abbreviation not alreadydefined: Cost of capital= i)

Modifying Above CL V equals Summation from t equals 1 to t equals n Start Fraction left parenthesis Upper M Subscript t Baseline minus c Subscript t Baseline right parenthesis x left parenthesis retention rate Subscript t Baseline right parenthesis Superscript t minus 1 Over left parenthesis 1 plus i right parenthesis Superscript t End Fraction minus Initial acquisition cost With

CL V=t=1

t=n

Mtctxretentionratter1(1+i)tInitialacquisitioncost

Next calculate the discounted net cash flows for each year and in total. (Round all amounts in your calculation to four decimalplaces, XXXIX.)

Discounted

t

net cash flows

1

2

3

4

5

6

Total