Answer to Question #140287 in Financial Math for Janelle Brits

Question

5.2 A machine was purchased for R650 000. The rate of depreciation of the machine is 25% per year on the educing balance and the cost of a new machine increases by 13% per year.

5.2.1 Calculate the value of the old machine after three years. (2)

5.2.2 Calculate the replacement cost of the machine after three years if the old machine is traded in. (2)

5.2.3 An equal amount is deposited monthly into a sinking fund for the replacement of the old machine. Calculate the monthly instalment if interest is earned at a rate of 7,5% per year, compounded monthly.

Answer 1

5.2.1

Depreciation is the transfer of fixed assets in the production process to the cost of products as they wear out (material and moral). In other words, this is a write-off from the balance sheet of funds as objects become obsolete.

These costs are recorded in the accounting report in the form of monthly / quarterly depreciation charges.

This is a certain percentage of the cost of fixed resources that are subject to wear and tear. It is also sometimes said that this is a fraction of the value of an asset included in the cost of goods. It is considered to be the rate of depreciation.

Therefore, we subtract from the original cost the amount of depreciation, which is calculated as a percentage of the original cost at a rate of 25% per year, a residual cost is obtained, which is equal to the original cost minus the amount of accumulated depreciation (percentage of the original)

$650 000-650 000\times0.25-650 000\times0.25-650 000\times0.25=162500$

5.2.2

We will also calculate the cost of a new car in a year as the sum of the original cost and a percentage of the original cost at a rate of 13% per year, depreciation is vice versa, the replacement cost is obtained, which is equal to the original cost, adjusted by a certain percentage (plus):

$650 000+650 000\times0.13+650 000\times0.13+650 000\times0.13=903 500$

if the old car is sold at the residual value, then the replacement cost will be equal to:

903 500-162 500=741 000

5.2.3

this is an annuity, find the formula:

$FV=A\times\frac{(1+r)^n-1}{r}$

$741 000=A\times\frac{(1+0.00625)^{36}-1}{0.00625}$

$741 000=A\times40.2313824$

A=18418.46