Question

2. Henry has an assignment from his boss at Czech Glass and Wood Sculpting to evaluate depreciation methods for writing off the $200,000 first cost of a newly acquired Trotec CO2 laser system for engraving and cutting. Productive life is 8 years and the salvage value is zero. Calculate the total PW of depreciation at 10% per year if the depreciation can be switched between DDB and SL, maximizing the PW of total depreciation. Fill in the table provided and state the year of the switch. Use the general rules of switching for DDB to SL. (P/F,10%,t) Factor SPresent Worth of D. DDB Model SL Model Yeart SDP $BV, $D L Larger $D, 0 Totals -- -- --

Answer 1

The above question completely based on Depreciation method ( SLM - Straight Line Method , DDB - Double Declining Method - 2/n year = 2/8 =0.25 = 25% depreciation rate .

We need to calculate year to shift depreciation between DDB to SLM with help of VDB( Variable Declining Method) - detail formula updated in Excel  

Complete Analysis on Depreciation
Cost of a newly acquired Trotec($)	2,00,000
Productive Life( Yrs)	8
Salvage value	-
Depreciation calculation @ DDB Method
Depreciation calculation @SL Method
Depreciation Rate	10%
Depreciation Straight Line Method
Cost of a newly acquired Trotec($)(a)	2,00,000
Salvage value(b)	-
Balance Value(a-b)- (c)-$	2,00,000
Productive Life( Yrs) (d)	8
Depreciation Per Year ( c/d)-$	25,000
Normally Double Declining Method
of Depreciation ( 2times of Straight Line depreciation)-2/N ( N = No of Year)' so rate of depreciation	25%

					Double Declining Method)					DDB to SL
Year	SLM ( Straight Line Method)$(f)	Book Value ($)(e)	Formula		Opening Balance($)(a)	Depreciation($)(b)	Closing Balance($)(c)	Formula		Book Value($)(g)	Depreciation($)(h)	Depreciation(VDB)	Depreciaton in $	Book Value
0		2,00,000	Depreciation	Book Value	2,00,000			Depreciation(25%) ( as above)	Book Value	2,00,000
1	25,000	1,75,000	As per above	(e-f)		50,000	1,50,000	(a*b)= c	(a-c)	1,50,000	50,000	VDB(Cost of the asset,Salavage Value,Number of years,Year 0, Year1,2)	VDB(200,000,0,8Year,year 0,Year 1,2)	(g-h)
2	25,000	1,50,000		(e-f)	1,50,000	37,500	1,12,500	(a*b)= c	(a-c)	1,12,500	37,500		VDB(200,000,0,8Year,year 1,Year 2,2)	(g-h)
3	25,000	1,25,000		(e-f)	1,12,500	28,125	84,375	(a*b)= c	(a-c)	84,375	28,125		VDB(200,000,0,8Year,year 2,Year 3,2)	(g-h)
4	25,000	1,00,000		(e-f)	84,375	21,094	63,281	(a*b)= c	(a-c)	63,281	21,094		VDB(200,000,0,8Year,year 3,Year 4,2)	(g-h)
5	25,000	75,000		(e-f)	63,281	15,820	47,461	(a*b)= c	(a-c)	47,461	15,820		VDB(200,000,0,8Year,year 4,Year 5,2)	(g-h)
6	25,000	50,000		(e-f)	47,461	11,865	35,596	(a*b)= c	(a-c)	31,641	15,820		VDB(200,000,0,8Year,year 5,Year 6,2)	(g-h)
7	25,000	25,000		(e-f)	35,596	8,899	26,697	(a*b)= c	(a-c)	15,820	15,820		VDB(200,000,0,8Year,year 6,Year 7,2)	(g-h)
8	25,000	-		(e-f)	26,697	6,674	20,023	(a*b)= c	(a-c)	-	15,820		VDB(200,000,0,8Year,year 7,Year 8,2)	(g-h)

Derived PV on the basis of depreciation calculate above ( VDB basis) and we noticed that Present value after switch is $ 537637 which is higher by SLM ( without Switch ) - $ 2,00,000

So Switch is Acceptable

					DDB to SL					Present Value	Present Value - Formula use	PV in $ term
Year	SLM ( Straight Line Method)$(f)	Book Value ($)(e)	Formula		Book Value($)(g)	Depreciation($)(h)	Depreciation(VDB)	Depreciaton in $	Book Value	Depreciation on VDB Basis
0		2,00,000	Depreciation	Book Value	2,00,000
1	25,000	1,75,000	As per above	(e-f)	1,50,000	50,000	VDB(Cost of the asset,Salavage Value,Number of years,Year 0, Year1,2)	VDB(200,000,0,8Year,year 0,Year 1,2)	(g-h)	$45,455	PV(10%,Year1,-VDB base depreciation)	PV(10%,1,-50000)
2	25,000	1,50,000		(e-f)	1,12,500	37,500		VDB(200,000,0,8Year,year 1,Year 2,2)	(g-h)	$65,083	PV(10%,Year2,-VDB base depreciation)	PV(10%,2,-37500)
3	25,000	1,25,000		(e-f)	84,375	28,125		VDB(200,000,0,8Year,year 2,Year 3,2)	(g-h)	$69,943	PV(10%,Year2,-VDB base depreciation)	PV(10%,3,-28125)
4	25,000	1,00,000		(e-f)	63,281	21,094		VDB(200,000,0,8Year,year 3,Year 4,2)	(g-h)	$66,864	PV(10%,Year3,-VDB base depreciation)	PV(10%,4,-21094)
5	25,000	75,000		(e-f)	47,461	15,820		VDB(200,000,0,8Year,year 4,Year 5,2)	(g-h)	$59,971	PV(10%,Year4,-VDB base depreciation)	PV(10%,5,-15820)
6	25,000	50,000		(e-f)	31,641	15,820		VDB(200,000,0,8Year,year 5,Year 6,2)	(g-h)	$68,902	PV(10%,Year5,-VDB base depreciation)	PV(10%,6,-15820)
7	25,000	25,000		(e-f)	15,820	15,820		VDB(200,000,0,8Year,year 6,Year 7,2)	(g-h)	$77,020	PV(10%,Year6,-VDB base depreciation)	PV(10%,7,-15820)
8	25,000	-		(e-f)	-	15,820		VDB(200,000,0,8Year,year 7,Year 8,2)	(g-h)	$84,400	PV(10%,Year7,-VDB base depreciation)	PV(10%,8,-15820)
Total	2,00,000									$5,37,637