estimate the value of a loyal customer of a loyal volvo automobile owner. assume the contribution margin is…

estimate the value of a loyal customer of a loyal volvo automobile owner. assume the contribution margin is 0.32, the purchase price is $70,000, the repurchase frequency is every six years, and the customer defection rate is 21 percent. do not round intermediate calculations. round your answer to the nearest dollar.

estimate the value of a loyal customer of a loyal volvo automobile owner. assume the contribution margin is 0.32, the purchase price is $70,000, the repurchase frequency is every six years, and the customer defection rate is 21 percent. do not round intermediate calculations. round your answer to the nearest dollar.

Answer

Explanation:

Step1: Calculate the annual contribution margin

The contribution margin per - purchase is the purchase price times the contribution margin ratio. The purchase price is $P = 70000$ and the contribution - margin ratio is $r=0.32$. So the contribution margin per purchase $CM_p=P\times r = 70000\times0.32=22400$. The repurchase frequency is every 6 years, so the annual contribution margin $CM_a=\frac{CM_p}{6}=\frac{22400}{6}=\frac{11200}{3}$.

Step2: Calculate the customer lifetime value (CLV)

The customer defection rate is $d = 0.21$. The formula for the customer lifetime value of a non - discounting case is $CLV=\frac{CM_a}{d}$. Substitute $CM_a=\frac{11200}{3}$ and $d = 0.21=\frac{21}{100}$ into the formula: [ \begin{align*} CLV&=\frac{\frac{11200}{3}}{\frac{21}{100}}\ &=\frac{11200}{3}\times\frac{100}{21}\ &=\frac{1120000}{63}\ &\approx17778 \end{align*} ]

Answer:

$17778$