Chapter 11, Problem 43P

To determine

i.

MACRS depreciation.

Answer to Problem 43P

MACRS depreciation is $ 84800.

Explanation of Solution

Given:

Cost of machine = $200000

Useful Life = 10 years.

Calculation:

A 10-year property class with half-yearly convention has been assumed.

MACRS
Year	Depreciation Base ($)	Depreciation Rate (%)	Annual Depreciation ($)	Year-end Book Value ($)
1	2,00,000	10	20,000	1,80,000
2	2,00,000	18	36,000	1,44,000
3	2,00,000	14.4	28,800	1,15,200
TOTAL			84,800

Conclusion:

MACRS depreciation is $ 84800.

To determine

ii.

Straight Line Depreciation.

Answer to Problem 43P

Straight Line Depreciation is $20000 per annum.

Explanation of Solution

Given:

Cost of machine = $200000

Useful Life = 10 years.

Calculation:

SLM depreciation =

$\begin{array}{l}Cost/Usefullife\\ =\frac{\$200000}{10}\\ =\$20,000peryear\end{array}$

Year	Beginning-of-year Book Value ($)	Annual Depreciation ($)	Year-end Book Value ($)
1	2,00,000	20,000	1,80,000
2	1,80,000	20,000	1,60,000
3	1,60,000	20,000	1,40,000
TOTAL		60,000

Conclusion:

Straight Line Depreciation is $20000 per annum

iii.

Sum-of-years-digit depreciation.

Sum-of-years-digit depreciation is $98182.

Given:

Cost of machine = $200000

Useful Life = 10 years.

Calculation:

Sum-of-years-digit depreciation (SOYD)

$\begin{array}{l}=1+2+3+4+5+6+7+8+9+10\\ =55\end{array}$

Depreciation base = $200,000

Annual depreciation in year N = $\text{Depreciation base×}\frac{\left(\text{Number of years remaining at beginning of year N}\right)}{\text{SOYD}}$

SOYD
Year	Depreciation Base ($)	Depreciation Rate	Annual Depreciation ($)	Year-end Book Value ($)
1	2,00,000	10/55	36,364	1,63,636
2	2,00,000	9/55	32,727	1,30,909
3	2,00,000	8/55	29,091	1,01,818
TOTAL			98,182

Conclusion:

Sum-of-years-digit depreciation is $98182.

iv.

Double declining balance depreciation.

Double declining balance depreciation is $ 97600.

Given:

Cost of machine = $200000

Useful Life = 10 years.

Calculation:

SLM Depreciation rate =

$\begin{array}{l}\frac{1}{UsefulLife}\\ =\frac{1}{10}\\ =0.1\end{array}$

DDB Rate =

$0.1\times 2=0.2$

DDB
Year	Depreciation Base ($)	Depreciation Rate	Annual Depreciation ($)	Year-end Book Value ($)
1	2,00,000	0.2	40,000	1,60,000
2	1,60,000	0.2	32,000	1,28,000
3	1,28,000	0.2	25,600	1,02,400
TOTAL			97,600

Conclusion:

Double declining balance depreciation is $ 97600

(e).

v.

150% Declining balance depreciation.

150% Declining balance depreciation is $77175.

Given:

Cost of machine = $200000

Useful Life = 10 years.

Calculation:

150% Declining balance depreciation rate = 0.1 x 1.5 = 0.15

150% DECLINING BALANCE METHOD
Year	Depreciation Base ($)	Depreciation Rate	Annual Depreciation ($)	Year-end Book Value ($)
1	2,00,000	0.15	30,000	1,70,000
2	1,70,000	0.15	25,500	1,44,500
3	1,44,500	0.15	21,675	1,22,825
TOTAL			77,175

Conclusion:

150% Declining balance depreciation is $77175.

To determine

iii.

Sum-of-years-digit depreciation.

Answer to Problem 43P

Sum-of-years-digit depreciation is $98182.

Explanation of Solution

Given:

Cost of machine = $200000

Useful Life = 10 years.

Calculation:

Sum-of-years-digit depreciation (SOYD)

$\begin{array}{l}=1+2+3+4+5+6+7+8+9+10\\ =55\end{array}$

Depreciation base = $200,000

Annual depreciation in year N = $\text{Depreciation base×}\frac{\left(\text{Number of years remaining at beginning of year N}\right)}{\text{SOYD}}$

SOYD
Year	Depreciation Base ($)	Depreciation Rate	Annual Depreciation ($)	Year-end Book Value ($)
1	2,00,000	10/55	36,364	1,63,636
2	2,00,000	9/55	32,727	1,30,909
3	2,00,000	8/55	29,091	1,01,818
TOTAL			98,182

Conclusion:

Sum-of-years-digit depreciation is $98182.

iv.

Double declining balance depreciation.

Double declining balance depreciation is $ 97600.

Given:

Cost of machine = $200000

Useful Life = 10 years.

Calculation:

SLM Depreciation rate =

$\begin{array}{l}\frac{1}{UsefulLife}\\ =\frac{1}{10}\\ =0.1\end{array}$

DDB Rate =

$0.1\times 2=0.2$

DDB
Year	Depreciation Base ($)	Depreciation Rate	Annual Depreciation ($)	Year-end Book Value ($)
1	2,00,000	0.2	40,000	1,60,000
2	1,60,000	0.2	32,000	1,28,000
3	1,28,000	0.2	25,600	1,02,400
TOTAL			97,600

Conclusion:

Double declining balance depreciation is $ 97600

(e).

v.

150% Declining balance depreciation.

150% Declining balance depreciation is $77175.

Given:

Cost of machine = $200000

Useful Life = 10 years.

Calculation:

150% Declining balance depreciation rate = 0.1 x 1.5 = 0.15

150% DECLINING BALANCE METHOD
Year	Depreciation Base ($)	Depreciation Rate	Annual Depreciation ($)	Year-end Book Value ($)
1	2,00,000	0.15	30,000	1,70,000
2	1,70,000	0.15	25,500	1,44,500
3	1,44,500	0.15	21,675	1,22,825
TOTAL			77,175

Conclusion:

150% Declining balance depreciation is $77175.

To determine

iv.

Double declining balance depreciation.

Answer to Problem 43P

Double declining balance depreciation is $ 97600.

Explanation of Solution

Given:

Cost of machine = $200000

Useful Life = 10 years.

Calculation:

SLM Depreciation rate =

$\begin{array}{l}\frac{1}{UsefulLife}\\ =\frac{1}{10}\\ =0.1\end{array}$

DDB Rate =

$0.1\times 2=0.2$

DDB
Year	Depreciation Base ($)	Depreciation Rate	Annual Depreciation ($)	Year-end Book Value ($)
1	2,00,000	0.2	40,000	1,60,000
2	1,60,000	0.2	32,000	1,28,000
3	1,28,000	0.2	25,600	1,02,400
TOTAL			97,600

Conclusion:

Double declining balance depreciation is $ 97600

(e).

To determine

v.

150% Declining balance depreciation.

Answer to Problem 43P

150% Declining balance depreciation is $77175.

Explanation of Solution

Given:

Cost of machine = $200000

Useful Life = 10 years.

Calculation:

150% Declining balance depreciation rate = 0.1 x 1.5 = 0.15

150% DECLINING BALANCE METHOD
Year	Depreciation Base ($)	Depreciation Rate	Annual Depreciation ($)	Year-end Book Value ($)
1	2,00,000	0.15	30,000	1,70,000
2	1,70,000	0.15	25,500	1,44,500
3	1,44,500	0.15	21,675	1,22,825
TOTAL			77,175

Conclusion:

150% Declining balance depreciation is $77175.