Hi pheifer!
In order to answer this question, you must find the present value of
both arrangements. Once you know it, the best arrangement is the one
with the highest present value. In the following links you can find
more information on present value and the formula to calculate it.
Understanding the Time Value of Money
http://www.investopedia.com/articles/03/082703.asp
Net Present Value
http://www.prenhall.com/divisions/bp/app/cfldemo/CB/NetPresentValue.html
So let's condier each arrangement:
1) $6,250 per month for two years, interest rate is 8% per year,
compunded monthly.
First, we must convert the interest rate to a monthly rate. The yearly
interest rate is 8%; therefore, 8/12=0.666% is the interest rate per
month. Let's assume that we are at the beggining of the month, and the
first payment will be received at the beggining of the next month
(that is, one month from now). The present value of the first payment
is then:
6,250/(1+0.0066) = 6,209.02
This mean that if you were paid 6,209.02 today, you could have the
same 6,250 in one month, due to interests. The present value of the
second payment is:
6,250/(1+0.0066)^2 = 6,168.30
(the ^ means "to the power of"). That is, if you were paid 6,168.30
you could have 6,250 in two months. Since the interest rate is
compounded monthly, the first month you would have
6,168.30*(1.0066)=6,209.02, and reinvesting that amount for a month at
the same interest rate would give you a total of
6,209.02*(1.0066)=6,250.
The same reasoning can be applied to every payment. Therefore, the
present value of all the payments is:
6250/(1.0066)^1 + 6250/(1.0066)^2 +
+ 6250/(1.0066)^3 + 6250/(1.0066)^4 + ... + 6250/(1.0066)^24
Although this is quite tedious to calculate by hand, it's easy to do
in some computer programs, such as Excel. The result is $138,190.89.
That's the present value of the first arrangement.
2) $4,600 per month for two years, plus $30,000 now, 8% yearly
interest rate, compounded monthly.
Here we use exactly the same reasoning as before. Again, I'll assume
that the first payment is due one month from today, but the $30,000
payment is today. Therefore, the present value of this arrangement is:
30000 + 4600/(1.0066)^1 + 4600/(1.0066)^2 + ... + 4600/(1.0066)^24
Notice that the 30000 aren't discounted by the interest rate, because
they are received today. This sum gives $131,708.
Finally, since the present value of the first arrangement is greater
than the second one (138,190 vs. 131,708) it's more convenient to take
the first one; namely, to receive $6,250 per month for two years, with
no signing bonus.
Google search strategy
present value
://www.google.com.ar/search?q=present+value&ie=UTF-8&oe=UTF-8&hl=es&meta=
I hope this helps! If you have any doubt regarding my answer (such as
how to setup a sheet in Excel to perform the calculations), please
request a clarification before rating it. Otherwise I await your
rating and final comments.
Best wishes!
elmarto |
