SOLUTION: You are the owner of an apartment building that is being offered for sale for $1,500,000. You receive an offer from a prospective buyer who wants to pay you $500,000 now, $500,000

Question 591561: You are the owner of an apartment building that is being offered for sale for $1,500,000. You receive an offer from a prospective buyer who wants to pay you $500,000 now, $500,000 in 6 months, and $500,000 in 1 year.
a. What is the actual present value of this offer, considering you can earn 12% interest compounded monthly on your money?
b. If another buyer offers to pay you $1,425,000 cash now, which is a better deal?
c. Because you understand the "time value of money" concept, you have negotiated a deal with the original buyer from part a, whereby you will accept the three-payment offer but will charge 12% interest, compounded monthly, on the two delayed payments. Calculate the total purchase price under this new agreement.
d. Now, calculate the present value of the new deal, to verify that you will receive the original asking price of $1,500,000 for your apartment building.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the present value of 1.5 million is equal to 1.5 million if it is all payed up front.
the present value of 1.425 million is equal to 1.425 million if it is all payed up front.
the present value of .5 million payed up front and .5 million payed in 6 months and .5 million payed in 12 months would be equal to:
.5 million plus .5 million / (1.01)^6 plus .5 million / (10.1)^12 which would be equal to:
.5 million plus .4710226176 million plus .4437246126 which is equal to:
1.41474723 million.
the best you're going to do is if the 1.5 million is payed up front.
the next best you're going to do is if you accept the 1.425 million offer.
the last best you're going to do is if you accept the 3 payment plan and don't charge interest on the deferred payments.
if you accept the deferred payment offer but charge 12% interest compounded monthly on the deferred payments, then you will make the following:
.5 million on the part that is paid up front.
.5 million * (1.01)^6 on the part that is paid in 6 months.
.5 million * (1.01)^12 on the part that is paid in 12 months.
the present value of that is equal to:
.5 million on the first part.
plus .5 million * (1.01)^6 / (1.01)^6 = .5 million on the second part.
plus .5 million * (1.01)^6 / (1.01)^12 = .5 million on the third part>
this will total 1.5 million which is the original asking price.
the payment of 1.5 million up front is equivalent to paying in 3 parts with interest being charged for the 3 parts, so you will make the same money.
the bottom line is:
1.5 million up front is a present value of 1.5 million.
1.5 million in 3 payments and being charged 1% per month for the deferred payments still gives you a present value of 1.5 million.
1.425 million present value is next in line.
1.41 million present value is next in line.
the deferred payment plan that charges 1% interest for each deferred month of payment is equivalent to 1.5 million up front and is the preferred plan if deferred payments are to be considered.

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