$($B$)$ Value of Loyal Customer $($VLC$)$

$VLC=(P)(CM)(RF)(BLC)$

where $BLC=\frac{1}{D}R$; defection rate $+$ retention rate $=1$

If customer defection rate $=12\%,$ contribution margin $=18\%,$ repurchasing frequency $=$ once every five years, and price $=$$$820$ per unit.

$($a$)$ What is the BLC$?$

$($b$)$ What is the VLC$?$

$($c$)$ What is the VLC if the defective rate is reduced to $6\%?$

$($d$)$ What is the VLC if the defective rate is reduced to $3\%?$