Question

An asset has a first cost of $45,000, a recovery period of 5 years, and a $3000 salvage value. Use the DDB depreciation method (making sure that last book value equals the salvage value), and calculate the present worth of depreciation at i = 18% per year.

Answer 1

DDB (double declinning Balance method) depreciates assets at the rate double than straight line.

It calculates depreciation on declining value of an asset.

DDB rate = 100/useful life *2

=100/5 *2

=40%

Year	Book value at the beginning	Depeciation rate	Depreciation expense	Book value at the end
1	$45,000	40%	$18,000($45,000*40%)	$27,000[$45,000-$18,000]
2	$27,000	40%	$10,800($27,000*40%)	$16,200($27,000-$10,800)
3	$16,200	40%	$6,480($16,200*40%)	$9,720($16,200*$6,480)
4	$9,720	40%	$3,888($9,720*40%)	$5,832($9,720-$3,888)
5	$5,832	40%	$2832	$3,000

Last year's depreciation will be adjusted to get salvage value as ending book value.

Now we will find present value of depreciation at 18%

Year	Depreciation expense	PV factor of $ 1 at 18%	Present worth
1	$18,000($45,000*40%)	0.84746[1/1.18]	$15,254.28[$18,000*0.84746]
2	$10,800($27,000*40%)	0.71818[1/.18]^2	$7,756.34[$10,800*0.71818]
3	$6,480($16,200*40%)	0.60863[1/1.18]^3	$3,943.92[$6,480*0.60863]
4	$3,888($9,720*40%)	0.51579[1/1.18]^4	$2,005.39[$3,888*0.51579]
5	$2832	0.43711[1/1.18]^5	$1,237.90[$2,832*0.43711]
		Total	$30,197.84

Thus, PW of depreciation is $30,197.83