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Hi John
Can you please help me with the following question?
A newspaper reader has won first prize in a national competition and they have a choice as to how they take the prize:
1. They can take $90,000 per annum indefinitely starting in 3 years’ time
2. They can take a lump sum of $910,000 in 1 year’s time
Assuming a cost of capital is 10%, which would you advise and why?So the answer is Statement 2 because it is worth more in present value terms.
Would you know how to solve it, because I cant understand solution from the BPP
Regards
MartaI assume that you are happy with the idea that the best is the one with the greatest present value?
For choice 2, you get the present value by discounting the 910,000 by the 1 year discount factor at 10%.
For choice 1, there are two ways of getting the present value (both giving the same answer, apart from rounding difference because the tables only go to 3 decimal places).
Method 1 is to calculate the discount factor for 1 to infinity (which is 1/r, or in this case 1/0.1)
and then subtract the annuity discount factor for 2 years at 10%.
This will leave you with a factor for 2 to infinity.Method 2 is to calculate the discount factor for 1 to infinity (as above).
If it had been 1 to infinity, then this would give a PV now. However, because it starts 2 years late (time 3 instead of time 1), you then need to multiply by the ordinary 2 year factor at 10% to account for the extra 2 years.Both methods give the same answer (apart from rounding) so use whichever method you find the more obvious to you.
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