Depreciation is the “decrease in value”

of physical properties with the passage

of time.
 Property is depreciable if:
• it is used in business or held to produce
income (van, printing machine…)
• it is something that wears out, decays, gets
used up, becomes obsolete...
• it is not inventory.
 Depreciation: Book Value

The Book value of an asset is its first cost minus the total
depreciation taken against it to date.
In economic analysis, the only use of book value is to compute
taxes as we will see later.

t
BVt = Cost basis -  d j
j=1

BVt : Book value of the depreciated asset at the end of time t

dj: sum of depreciation deductions taken from 0 to time t.
 Modified Accelerated Cost Recovery
System (MACRS) method

 The Modified Accelerated Cost Recovery System (MACRS) is the

principle method for computing depreciation for property in
engineering projects.

 Consists of two systems for computing depreciation deductions:

1. The General Depreciation System (GDS)- the main system

2. The Alternative Depreciation System (ADS)
Provides longer recovery period and uses only
straight-line method of depreciation
Depreciation Methods: MACRS - GDS

Using MACRS-GDS is easy!

1. Determine the asset’s recovery period

2. Use the appropriate column that matches the
recovery period to find the recovery rate, rk, and
compute the depreciation for each year as

Where B is the cost basis, and, rk, the recovery rate

 MACRS: GDS or ADS- Half-year convention

HALF-YEAR TIME CONVENTIONS FOR MACRS DEPRECIATION CALCULATIONS

 All assets placed in service during the year are treated as if use
began in the middle of the year ,half year depreciation is
allowed

 If asset is disposed of before the full recovery period is used,

only half of the normal depreciation deduction can be taken
for that year
 Depreciation Methods: MACRS - GDS

Example

A firm purchased and placed in service a new electronic component for

$100,000 . Use a GDS 5 years recovery period

a- Determine the depreciation deduction in the 4th year

b- Determine the Book value at the end of year 4
c- Determine the Book value at the end of year 5 if the component is
disposed at that time
Solution

a) depreciation at year 4?

cost recovery allowance for year 4 is 0.1152,

depreciation deduction d4= 0.1152 x $100,000= $11,520

b) book value at year 4?

t
BVt = Cost basis -  d j
j=1
b)BV4= $100,000 - $100,000 (0.2+0.32+0.192+0.1152)
=$17,280
c) BV5= $100,000 - $100,000 (0.2+0.32+0.192+0.1152+ (0.5* 0.1152)
=$11,520
 MACRS Disposition

For property depreciated according to the half-year convention,

only half- the depreciation is allowed for the year of
disposition.

Residential rental property and nonresidential real estate use a

midmonth convention. For example, real property sold in
March will take 2.5/12 of that year’s depreciation.
 Gain (loss ) on disposal
The disposal of a depreciable asset can result in a gain or loss
based on the sale price (market value) and the current book
value

A gain is often referred to as depreciation recapture,

and it is generally taxed as the same as ordinary
income.
An asset sold for more than it’s cost basis results in a
capital gain.
 Pause and solve

Y Casting and Molding company, sold a piece of equipment

during the current tax year for $78,600. This equipment
had a cost basis of $190,000 and the accumulated
depreciation was $139,200.

Based on this information, what is the gain (loss) on

disposal?
 Solution

MV= $78,600

BV at the time of sale = $190,000 - $139,200= $50,800

Gain (loss) on disposal= MV –BV,

the gain (loss) on disposal= $78,600 - $50,800= $27,800

Taking taxes into account changes our expectations of
returns on projects, so our MARR (after-tax) is lower.
 After Tax Cash Flow - ATCF

After-tax economic analysis is generally the same as before-

tax analysis, just using after-tax cash flows (ATCF) instead of
before-tax cash flows (BTCF).

The analysis is conducted using the after-tax MARR .

 After Tax Cash Flow - ATCF

Cash flows are typically determined for each year using the
notation below.

Rk = revenues (and savings) from the project

during period k
Ek = cash outflows during k for deductible
expenses
d k = sum of all noncash, or book, costs
during k, such as depreciation
t = effective income tax rate on ordinary
income
Tk = income tax consequence during year k

ATCFk = ATCF from the project during year k

 After Tax Cash Flow - ATCF

Some important cash flow formulas.

Taxable income

Ordinary income tax consequences

After Tax Cash Flow - ATCF
 After Tax Cash Flow - ATCF

Example

Certain new machinery when placed in service is estimated to cost $180,000.

benefits less expenses equals 36,000 per year for 10 years. It will have $30,000
MV at the end of 10th year.

The company elects, MACRS-GDS, with half year convention with a recovery
period of 5years. Effective tax rate is 38%.

If the company uses an after-tax MARR of 10%, develop the after tax cash flow
and calculate the PW.
Is the investment in machinery justified?
 After Tax Cash Flow - ATCF

Depreciation Cash flow for

BTCF Cost Depreciation Deduction Taxable income tax
year (A) basis Rate (B) income (C) (D) ATCF (E)
=basis *rate A-B -t(C) A+D
0 -180,000 --- ---- --- ----- ---- -180,000
1 36,000 180,000 0.2 36,000 0 0=-0.38(c) 36,000
2 36,000 180,000 0.32 57,600 -21,600 8208 44,208
3 36,000 180,000 0.192 34,560 1,440 -547 35,453
4 36,000 180,000 0.1152 20,736 15,264 -5,800 30,200
5 36,000 180,000 0.1152 20,736 15,264 -5,800 30,200
6 36,000 180,000 0.0576 10,368 25,632 -9,740 26,260
7-10 36,000 0 0 36,000 -13,680 22,320
10 30,000 0 30,000 -11,400 18,600
PW(10%) 17,208
IRR 12.4%
30,000 -
0=30,000
Gain or Loss (gain)
 After Tax Cash Flow - ATCF
• Pw(10%)=-180,000 + 36,000(P/F,10,1) + 44,208(P/F,10,2),
+35,453(P/F,10,3)+ 30,200(P/F,10,4)+ 30,200(P/F, 10,5)+
26,260(P/F,10,6) +22,320(P/A,10,4)(P/F,10,6) +
18,600(P/F,10,10)

• PW (10%)= 17,208 >0

• SO investment is justified
 After Tax Cash Flow - ATCF

Example modified

Certain new machinery when placed in service is estimated to cost $180,000.

benefits less expenses equals 36,000 per year .However, the asset will be
disposed at year 5. It will have $30,000 MV at the end of 5 th year.

The company elects, MACRS-GDS, with half year convention with a recovery
period of 5years. Effective tax rate is 38%.

If the company uses an after-tax MARR of 10%, develop the after tax cash flow
and calculate the PW. what will be the BV5? Calculate gain/loss on disposal

Is the investment in machinery still justified?

 After Tax Cash Flow - ATCF

Depreciation Cash flow for

BTCF Cost Depreciation Deduction Taxable income tax
year (A) basis Rate (B) income (C) (D) ATCF (E)
=basis *rate A-B -t(C) A+D
0 -180,000 --- ---- --- ----- ---- -180,000
1 36,000 180,000 0.2 36,000 0 0=-0.38(c) 36,000
2 36,000 180,000 0.32 57,600 -21,600 8208 44,208
3 36,000 180,000 0.192 34,560 1,440 -547 35,453
4 36,000 180,000 0.1152 20,736 15,264 -5,800 30,200
5 36,000 180,000 (0.1152)/2 10, 368 25,632 -9,740 26,260
5 30,000 Gain=9264 -3520 26,480
 Example continued
• BV5= 180,000-(180,000*(0.2+0.32+0.192+0.1152+ 0.1152/2))
= 20,736
• Gain= MV5-BV5=30,000- 20,736= $9264
 After Tax Cash Flow - ATCF
• Pw(10%)=-180,000 + 36,000(P/F,10,1) + Year ATCF (E)
44,208(P/F,10,2), +35,453(P/F,10,3)+ 0 -180,000
30,200(P/F,10,4)+ 26,260 (P/F, 10,5)+
1 36,000
26,480(P/F, 10,5)
2 44,208
3 35,453
• PW (10%) >0 4 30,200
5 26,260
• SO investment is justified
5 26,480