Question

Problem 1

Your firm, Southern Comfort Corp. (SCC) has $100,000 vested membership fee for its numerous members. The firm additionally has a requirement that members join their lifetime Club whose annual membership fee is $2,000. The fee is expected to increase by 3 percent per year. Disregarding the $100,000 vested membership, assist SCC in determining the following scenarios relative to its member recruitment. .

Show your calculations for the scenarios.

   

1. Would you buy a $65,000 lifelong membership to the club that can be passed down to your descendants in perpetuity? You can earn 6 percent on a long-term bank deposit with the same dollar amount, comparatively.
   
   
   
2. What discount rate would make you indifferent in terms of the lifelong family membership purchase?
   

     c. What annual membership fees would make you indifferent toward the purchase?

    d. What lifelong membership price would make you indifferent?

Answer 1

a) Present value of the annual membership fee if one takes lifelong membership (perpetuity) assuming that the amount is to be paid at the end of the year

= 2000/1.06+2000*1.03/1.06^2+ ... + ...

=2000/1.06 / (1- 1.03/1.06)

=$66666.67

As the lifelong membership is available for $65000, it should be bought

b) Let the discount rate be r for indifference

then , Present value of the annual membership fee

=2000/(1+r) / (1- 1.03/(1+r))

= 2000/(r-0.03) = 65000

=> r =6.0769% or 6.08%

c)

Let the annual membership fee be $A per year for indifference

then , Present value of the annual membership fee

=A/1.06 / (1- 1.03/1.06)

= A/0.03 = 65000

=> A =$1950

d) If lifelong membership fee were $66666.67 (as calculated in a) above) , we would be indifferent towards the purchase