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v1 Financial Maths, STD2 F4 2022 HSC 27

A business buys a delivery van for $60 000. The two depreciation methods under consideration are the declining-balance method and the straight-line method.

  1. For the declining-balance method, the salvage value of the van after `n` years is given by the formula
  2. `S=V_(0)xx(0.75)^(n),`
  3. where `S` is the salvage value and `V_(0)` is the initial cost of the asset.
    1. What is the annual rate of depreciation used in this formula?  (1 mark)

    2. Calculate the salvage value of the van after 2 years, based on the given formula.  (1 mark)

  4. Using the straight-line method, the van depreciates by 13.75% of its purchase price each year.
  5. After how many full years will the value of the van be equal to or less than the value found in part (a) (ii)?  (2 marks)

Show Answers Only
  1.  i. `25text{%}`
  2. ii. `$33\ 750`
  3. `3\ text{years}`
Show Worked Solution

a.i.  `text{Depreciation rate}\ = 1-0.75 = 0.25 = 25text{%}`

a.ii.  `text{Find}\ \ S\ \ text{when}\ \ n=2:`

`S` `= V_0 xx (0.75)^2`
  `= 60\ 000 xx 0.5625`
  `= $33\ 750`

b.  `text{Using the SL method}`

`S_n` `= 60\ 000-(0.1375 xx 60\ 000) xx n`
  `= 60\ 000-8250n`

`text{Set}\ \ S_n \leq 33\ 750`

`33\ 750` `= 60\ 000-8250n`
`8250n` `= 26\ 250`
`n` `= 26\ 250 / 8250 = 3.18`
  `⇒ 3\ text{years (to nearest full year)}`
♦♦ Solid performance expected if depreciation concepts are understood.
HINT: Watch out for rounding when comparing values in part (b).