Sarah has been given the following choice of inheritance packages by her parents

Question

Sarah has been given the following choice of inheritance packages by her parents: Package A is composed of $10,000 today and $15,000 one year from today. Package B is composed of $15,000 today and $9,000 one year from today. (a)* Assuming that the borrowing and deposit rates of interest are identical, identify the conditions under which Sarah should take Package A, and the conditions under which she should take package B. (b)* Still assuming that the two rates of interest are identical, identify the conditions under which Sarah is better off when the interest rate changes from 25 percent to 20 percent. (c)* Assuming that the deposit rate is 0 percent and that the borrowing rate is 100 percent, construct the budget lines associated with both of these packages and show that it is impossible to say which package Sarah should choose without information regarding her preferences. (d)* Assuming that the borrowing rate exceeds the deposit rate, identify the circumstances under which Sarah should choose package A, the circumstances under which she should choose package B, and the circumstances under which you need information regarding her preferences to determine which package she should choose.

Explanation / Answer

It is a time value like problem

PV(present value) of package A = 10000 + 15000/(1+r)

PV of package B = 15000 + 9000/(1+r)

Accept package B when PV of B > PV of A

15000 + 9000/(1+r) > 10000 + 15000/(1+r)

so solving it we get r > 20%

at r < 20 % accept A

B) at 25 % she is accepting B.But at 20 % both A and B have same PV so she can accept any of the two

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