The Ultimate Professor
The Ultimate Professor
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Here is a sample:
I evaluated the three options Sally Hamilton has to choose from and this is what I came up with: (Although I think my calculations are correct, please feel free to critique and correct my errors!)
Option 1 gives Sally a $50,000 cash bonus paid now. I chose to evaluate this amount to see what the future value would be in 6 years, since the other options are based on 6 years. The future value at 6 years and earning 6% came to $70,926.
Option 2 is an annuity due, with the first $10,000 paid now, and another $10,000 paid each year over the next 6 years. I used the FVAD chart, with 6 periods at 6% and the future value came to $73,938. Based on these numbers, the Present Value of option 2 is $52,123.
Option 3 is a deferred annuity. To calculate the annuity, I used the FVA chart for 3 periods at 6% x $22,000 which gave me a total future value of $70,039. For the present value I used the $70.039 total, used the Present Value chart for 2 periods at 6% and got a Present value of $62,335.
Based on my calculations, it would be more profitable for Sally Hamilton to chose option 2 as her return on her investment would be greater than if she chose either other option. Although the present value is greater for option 3 than the others, I don’t think Sally should look too much at this number because the only real present value she should go by is option 1 which would give her the entire bonus immediately. But based on the calculations, Sally would earn more choosing option 2 than the other options and therefore should go with that option.
The questions I’m still a little confused about, and which would make a difference in my calculations are this: For option 2, because it is an annuity due and the payments are made at the beginning of the period, should my number of periods actually be 5 instead of 6? And for option 3, because it is an ordinary annuity the first payment is made at the end of the third period, when I drew this out on a number line it appeared to me that I should use 2 periods instead of three to obtain the present value of the deferred annuity. Is this correct, or should I have used 3 periods when calculating the present value?
Thanks everyone for your help in figuring this out!
