Mgt201 GDB No. 1 solution

A few days ago, Mr. A has purchased a lottery. Fortunately, he has received a letter from the lottery officials that he has won that lottery. Additionally, it has been mentioned in the letter that he has to choose between one of the two given alternatives as his Prize money: 

A:Rs. 4,000 every year for next 10 years or;  

B:Rs. 54,000 after 10 years. His opportunity cost is 11%. 

Required: Find the value of each alternative. Which alternative is acceptable for Mr. A and why?

Solution:

Option A
=4000/1.11+4000/(1.11^2)+4000/(1.11^3)+4000/(1.11^4)+4000/(1.11^5)+4000/(1.11^6)+4000/(1.11^7)+4000/(1.11^8)+4000/(1.11^9)+4000/(1.11^10)
= 23556.93

Option B
= 54000/(1.1^10)
= 20819.34

Option A is Acceptable as it has high Present Value 

Here in option B calculation is as follows:

54000/(1.11)^10
=19017.96
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Another Solution:

This is annuity concept so first we bring all the values to one common point and then compare. Here first we find the present value of Alternative A and then find the present value of B and compare which ever is higher that will be acceptable.


Value of alternative A= =4000/1.11+4000/(1.11^2)+4000/(1.11^3)+4000/(1.11^4)+4000/(1.11^5)+4000/(1.11^6)+4000/(1.11^7)+4000/(1.11^8)+4000/(1.11^9)+4000/(1.11^10)
= 23556.93

Value of alternative B= 54000/(1.1^10)
= 20819.34

Alternative that is acceptable= Option A

Reason= Because Option A will be higher in present value than option B