If the book value using flat rate after the first year equals 16% while the book value using reducing-balance depreciation equals 26%: find the difference between the book values after 4 years?

Answer 1

To start, we can calculate the book value using both methods after 4 years:

For flat rate depreciation:
Book value after 4 years = original value - (original value * flat rate * years)
Book value after 4 years = original value - (original value * 0.16 * 4)
Book value after 4 years = original value - (0.64 * original value)
Book value after 4 years = 0.36 * original value

For reducing-balance depreciation:
Book value after 4 years = original value * (1 - reducing-balance rate) ^ years
Book value after 4 years = original value * (1 - 0.26) ^ 4
Book value after 4 years = original value * 0.74 ^ 4
Book value after 4 years = original value * 0.28477

Now, we can find the difference between the book values after 4 years:
Difference = (0.36 * original value) - (original value * 0.28477)
Difference = 0.07523 * original value

Therefore, the difference between the book values after 4 years is 7.523% of the original value.