Question

Predatory Lending Inc. sells financial services (high interest micro loans) through independent agents. Good agents generate $2,000 in net revenue in the first year, a figure that grows at 5% annually. Poor agents, on the other hand, produce $1,000 in year one and 20% less revenue each successive year. There is no way to tell in advance whether an agent will be good or bad. In the past, about 40% of new agents have turned out to be good and 60% poor. Of the good agents, 50% are loyal, they tend to like the work and remain with the company with a 90% probability year to year, and 50% are not loyal, they leave Predatory Lending and go to work for a competitor after the first year. Similarly, 80% of the poor agents are loyal (i.e., the competition wouldn’t hire them) and have a 90% probability of staying with the firm year to year and 20% drop out after the first year and go back to school. (For simplicity, assume that revenues from agents that drop out in year one are not discounted.)

Given that recruiting and training costs are $5,000 per new agent:

a) What is the CLV of each of the 4 possible types of agents (good loyal/ non-loyal and bad loyal / non-loyal? (Assume a 10% discount rate)

b) Can Predatory Lending Inc. remain in business given it current operating situation?

CLV formula: Gross margin * (Retention rate / [1+ Rate of discount – (Retention rate * (1 + Growth Rate))] – Costs

CLV= m{r/[1 + i-r(1+ g)]}-C

Answer 1

Answer:

Predatory Lending Inc.

a)

Good-Loyal

Good-Non Loyal

Net revenue in the 1st year =

$2,000

Net revenue in the 1st year =

$2,000

Annual growth rate =

5%

Less: Recruiting and training costs =

$5,000

The number of years is assumed to be a perpetuity

Life time value (LTV) of Good-Non Loyal =

($3,000)

as it is a going-concern.

The Life time value is the present value of perpetual

revenues less the recruiting and training costs.

Formula:

Present value of a growing perpetuity = C1/(r-g)

where: C1 = Cash flows in year 1 =$2000

r = Discount rate = 10%

g = growth rate = 5%

PV of growing perpetuity [$2,000/(10%-5%)]

$ 40,000

Less: Recruiting and training costs

$5,000

Life time value (LFV) with 100% probability

$ 35,000

Life time value (LFV) with 90% probability

$ 31,500

Poor-Loyal

Poor-Non Loyal

Net revenue in the 1st year =

$1,000

Net revenue in the 1st year =

$1,000

Growth rate (decrease rate) =

-20%

Less: Recruiting and training costs =

$5,000

As the Loyal agents continue with the firm for ever, the

Life time value (LTV) of Poor-Non Loyal =

($4,000)

revenues generated by them is a perpetuity.

Present value of a growing perpetuity = C1/(r-g)

Here, growth rate = -20%

PV of declining perpetuity [$1,000/(10%-(-20%)]

$3,333.33

Less: Recruiting and training costs

$5,000

Life time value (LFV) with 100% probability

($1,666.67)

Life time value (LFV) with 90% probability

($1,500.00)

b)

Can predatory Lending Inc. continue in business given its current operating situation?

We have to find out the expected Life time values of all these 4 types of agents incorporating

all the possible probabilities.

Expected probability of Good-Loyal [40% good * 50% loyal * LTV with 90% probability]

$ 6,300

Expected probability of Good-Non-Loyal [40% good * 50% non- loyal * LTV ]

($600)

Expected probability of Poor-Loyal [60% Poor * 80% loyal * LTV with 90% probability]

($720)

Expected probability of Poor-Non-Loyal [60% poor * 20% non- loyal * LTV ]

($480)

Net expected value

$ 4,500

Yes. The firm can continue in the business as the net expected value is positive.