smc-813-10-Find $S$

A company purchases a machine for $50 000. The two methods of depreciation being considered are the declining-balance method and the straight-line method.

For the declining-balance method, the salvage value of the machine after `n` years is given by the formula
`S=V_(0)xx(0.80)^(n),`
where `S` is the salvage value and `V_(0)` is the initial value of the asset.
i. What is the annual rate of depreciation used in this formula? (1 mark)
ii. Calculate the salvage value of the machine after 3 years, based on the given formula. (1 mark)
For the straight-line method, the value of the machine is depreciated at a rate of 12.2% of the purchase price each year.
When will the value of the machine, using this method, be equal to the salvage value found in part (a) (ii)? (2 marks)

Show Answers Only

i. `20text{%}`
ii. `$25\ 600`
`text{4 years}`

Show Worked Solution

a.i. `text{Depreciation rate}\ = 1-0.8=0.2=20text{%}`

a.ii. `text{Find}\ \ S\ \ text{when}\ \ n=3:`

`S`	`=V_0 xx (0.80)^n`
	`=50\ 000 xx (0.80)^3`
	`=$25\ 600`

b. `text{Using the SL method}`

`S_n`	`= 50\ 000-(0.122 xx 50\ 000)xxn`
	`=50\ 000-6100n`

`text{Find}\ \ n\ \ text{when}\ \ S_n=$25\ 600`

`25\ 600`	`=50\ 000-6100n`
`6100n`	`=24\ 400`
`n`	`=(24\ 400)/6100`
	`=4\ text{years}`

♦♦ Mean mark (a.i.) 24%.
COMMENT: A poor State result in part (a.i.) that warrants attention.

♦ Mean mark part (b) 38%.

`S`	`= V_0 (1-r)^n`
	`= 2467 (1-0.15)^3`
	`= 2467 (0.85)^3`
	`= $1515`

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Financial Maths, STD2 F4 2021 HSC 4 MC