### First-Year Deductions for Decline in Value

#### (a) Prime Cost Method
* **Working:** $\text{Cost} \times \left(\frac{1}{\text{Effective Life}}\right) = \$30,000 \times \left(\frac{1}{5}\right) = \$30,000 \times 0.2$
* **First-year deduction:** **$6,000**

#### (b) Diminishing Value Method
* **Working:** $\text{Cost} \times \left(\frac{2}{\text{Effective Life}}\right) = \$30,000 \times \left(\frac{2}{5}\right) = \$30,000 \times 0.4$
* **First-year deduction:** **$12,000**

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### Controlling Authority
The controlling authority for these capital allowance rules is the **Australian Taxation Office (ATO)**, administering the rules enacted under the ***Income Tax Assessment Act 1997* (Cth)** (specifically Division 40).