You are negotiating the terms of a legal settlement. You have been given several

Question

You are negotiating the terms of a legal settlement. You have been given several different settlement options. Your average rate of return on the assets you currently hold is 5% and you expect to continue receiving that rate. You have a choice of receiving: A lump sum today of $ 550,000 and payments of $5,000 at the end of the year for the next 5 years (total of 6 payments). Equal payments of $10,000 for the next 10 years at the end of each year (total of 10 payments). Equal payments of $ 16,000 starting today and continuing annually for the next 4 years (total of 5 payments). What is the present value of each alternatives? Explain why receiving money today is better than receiving money today is better than receiving the same money later?

Explanation / Answer

Present value under alternative 1:

Payment received today = 50000 ; payments every year = 5000 ; r= 5% ; n =5

Hence the present value of the payments is 5000 * PVIFA = $ 5000 * 4.329 = $21645

(PVIFA for n=5 ; i=5% is 4.329)

Hence total present value of option 1 = 21645 + 50000 = $ 71645

Present value under alternative 2

Payments = 10000 ; n = 10 ; i = 5%

Present value = 10000 * PVIFA(n=10,i=5%)

PVIFA(n=10,i=5%) = 7.7217

Hence present value = 10000 * 7.7217 = $ 77217

Present value under alternative 3

This is a case of annuity due where payments are made at the beginning of the year. Here we will calculate the present value ordinarily for 4 years and we will add the resultant amount with the payment received now i.e. $ 16000

So Present value of ordinary pauments = 16000 * PVIFA(n=4,i=5%)

PVIFA(n=4,i=5%) = 3.546

So Present value of ordinary pauments = 16000 * 3.546 = $ 56736

Total present value = 56736 +16000 = $ 72736

If we receive money today than receiving the same in future then we will be better off. This is becasue, we would be able to invest a larger sum of money today and see it grow over the years. However when we are receiving money in equal installments at a future date, our window of increaseing that money by compounding investment reduces as we are receiving less payments.

Suppose you will receive $100 today vs you will receive $ 100 after year.

If you receive today and invest it @ say 5%, by the end of year 1 you will have $105

However, if you receive after one year you will receive $ 100 only.

Hence receiving today is a better option becasue time has money value

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