Question

Suppose your parents have 2 options to purchase a plot of land on which they plan to build a barn.

Option 1: They can purchase the land for $30,000 cash.
Option 2: They can purchase the land with $7,500 down, and then pay $2,500 semi-annually for the next 10 years,
at an interest rate of 5%.
Calculate the present value for both options, and tell which will save them the most money.

Option 1 will save your parents the most money.

Option 2 will save your parents the most money.

It is not possible to determine which option will save the most money because the question does not state how large the
barn will be.

The options both cost the same, so neither one will save them money.

Answer 1

1. PV = $30,000; this saves the most
2. PV = $46,473 — the higher-cost option

Explanation:

You want the present value and the lower-cost choice for two payment plans:

1. $30,000 cash
2. $7500 down and $2500 semi-annually for 10 years at 5%

Present value

The present value of 20 semiannual payments of $2500 discounted at the rate of 5% can be found by a financial calculator to be $38,973. Together with the $7500 down payment, the present value of Option 2 is ...

Option 2 = $7500 +38,973 = $46,473

The present value of $30,000 cash is $30,000.

Comparison

Option 1 has a present value of $30,000.

Option 2 has a present value of $46,473.

Option 1 will save your parents the most money.

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Additional comment

The total cash outlay for option 2 is $7500 + 20×2500 = $57,500. For this option to be the same cost as option 1, the account would need to earn interest at the rate of 18.4%.

There are various ways to estimate the interest earned. One of them is to compute half the value of simple interest on the interval. That is, the interest could be estimated as (1/2)(5%/yr)(10 yr) = 25%. This suggests the PV would be about 1/1.25 times the sum of payments, or 40000. That's close enough to the actual value of 39000 to tell you that Option 1 is the better choice.