370 Chapter 8 Mathematics of PricingHang on—why does something depreciated over 5 years have depreciation percents for 6?
Under MACRS, we assume that all items are put into service halfway through the year, regard-
less of when that actually happens. So the fi rst year of accounting for the computer’s expense is
assumed to only be the fi rst half-year that the computer was in use. The 20% depreciation is not
considered a full year’s worth of depreciation; it is the fi rst half-year’s worth. That is the reason
why the percentage for year 2 is higher than the percentage for year 1; MACRS assumes we are
taking a full 12 months’ worth of depreciation in year 2. At the end of the fi fth year, we have
only taken 4^1 ⁄ 2 years of depreciation, leaving another half year to run into year 6.
Fortunately, the calculation is easier than the explanation!Example 8.4.7 Calculate the depreciation each year for the Cotswold Real Estate
computer, using MACRS.In the fi rst year, the depreciation is (20%)($2,000) $400.
In the second, the depreciation is (32%)($2,000) $640.
In the third, it amounts to (19.2%)($2,000) $384.
In both the fourth and fi fth years, it is (11.52%)($2,000) $230.40.
Finally, in the sixth year the depreciation is (5.76%)($2,000) $115.20.The $400 depreciation in the fi rst year is based on the assumption that the computer was in
use for 6 months. However, the company takes this same $400 depreciation regardless of
how much of the year the computer was actually in use.
This simple example illustrates how MACRS works mathematically. This is a simpli-
fi ed example; as with many things involving the tax code, the specifi c details, exceptions,
and other vagaries of MACRS can be quite involved.EXERCISES 8.4
A. Appreciation- The housing market in Watsonville Falls is hot, and a local real estate agent predicted at a meeting of the chamber of
commerce that prices should rise by an average of 6.3% per year for the foreseeable future. If the average single-family
home costs $273,592 today, what would the agent predict it will be in 5 years? - In August 2006 the price of an ounce of gold was $640. A commentator on a late-night radio program predicted that the price
of gold would rise by an average of 15% per year for the next 5 years. What is he projecting the price will be in August 2011.
B. Percent (Declining Balance) Depreciation- Gary bought a boat for $32,750. If the market value declines at a steady 8% annual rate, what will the boat’s value be
in 5 years? In 10 years? - Renee paid $29,409 for a new truck. She expects that the market value will decline by 11% annually. How much does
she expect to be able to sell it for in 3 years? - A car that cost $21,450 new is worth $11,050 5 years later. What percent depreciation rate would lead to this value?^4
(^4) NOTE: Chapter 6 is not formally a prerequisite for this chapter; however, a precise answer to this question requires use of a formula from that chapter.
Students who have not yet covered Chapter 6 should skip this question.