Shureido is one of the top$-$rated brands of karate gis $($uniforms$)$ worldwide. The company plans

to launch three new gis of different cuts and weights. The Kumite gi is lighter weight and the

coolest of the three. The Kata model will be medium weight for a good "snap" and cut looser

than the Kumite gi$,$ The Advanced is the heavy$-$weight model with loudest snap, but less

breathable than the Kata gi$,$ Shureido expects to sell the Kumite, Kata, Advanced gis, in the ratio

$9$:$7$:$5$ respectively. The prices of the gis will be $$120,$$$185,$ and $$240,$ and have variable costs of

$$45,$$$60,$ and $$75,$ respectively. They plan to spend $$400,000$ in design and $$1,000,000$ in

promotion to acquire $20,000$ new customers.

a$.$ Calculate the breakeven quantities for each gi$,$ model. $[3]$

b$.$ Assume the replacement cycle for gis is roughly a year, and the probability that these

customers repurchase from Shureido the following year is $78\%,83\%,90\%$ respectively,

and the discount rate is $5\%$ annually. Calculate the CLV for customers in each segment.

$($Hint: $M=$ total contribution for each segment from part a$.AC=F\frac{C}{?}$ total number of

customers$)($Note: Just use the same AC for each segment$)[6]$

c$.$ Suppose the company is considering mailing out a $$20$ birthday coupon to encourage

loyalty. What is the minimum retention rate for each segment required to maintain the

same CLV found in part b $($hint: New M $=$ Old M $-$ RS$).[3]$

New $r=\frac{(CLV+AC)(1+d)}{(\text{N}\text{e}\text{w}M+CLV+AC)}$

d$.$ If the company is considering spending $$2\mathrm{.}3M$ next year targeted to an audience of

$6,000$ customers on a single segment, what would be the breakeven acquisition rate for

each segment to justify spending $$2\mathrm{.}3M.$ How many customers does that work out to$?$

$($hint: Number of customers $=$ BAR $x$ targeted audience$).[2]$

Breakeven Acquisition Rate $=\frac{\text{A}\text{c}\text{q}\text{u}\text{i}\text{s}\text{i}\text{t}\text{i}\text{o}\text{n}\text{S}\text{p}\text{e}\text{n}\text{d}\text{i}\text{n}\text{g}}{CLV}$

e$.$ Assume that Shureide spent the $$2\mathrm{.}3M$ on an ad campaign and it was able to gain a total

of $3,250$ new customers. The company also gave a discount of $$15$ off the first order for

this new batch of customers. Please calculate the CLV for each of the segments in this

new batch. Assume that the first $AC$ is now a sunk cost paid off by the first batch. $($Hint:

Start with CLVs from part $b$ and subtract $AC.$ New batch $AC=ad$ cost per customer $+$

first$-$time discount $-$ original AC$).[6]$