Question

A friend has been awarded a settlement in a law suit that specifies he be paid $30,000 at the start of each quarter for the next 6 years. Additionally at the end of year 6 he will receive a one-time payment of $500,000.00. He wishes to renegotiate this settlement to a single lump sum payment due today. If we assume that your friend can earn 8% per annum compounded quarterly on sums invested, what is the minimum amount that he should accept in the renegotiated settlement?

Answer 1

Based on the amount that your friend will be paid every quarter and the amount he will receive at the end of 6 years, the minimum amount he should take is $889,616.

What amount is the minimum your friend should accept?

The amount your friend will receive is constant so this is an annuity. It is an annuity due because it comes at the start of the period.

The minimum amount your friend should take is:

= Present value of annuity due + Present value of end of 6 year payment

The period is:                                                  The rate is:
= 6 years x 4 quarters                                     = 8% / 4 quarters

= 24 quarters                                                   = 2% per quarter

The minimum amount is:

= (Annuity x Present value of Annuity Due interest factor, 2%, 24 periods) + (500,000 x Present value factor, 2%, 24 periods)

= (30,000 x 19.2922) + (500,000 x 0.6217)

= $889,616

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