Let’s break down the decision as a **replacement project**: should you **replace** the old machine with the new one? We need to compare the **Net Present Value (NPV)** of keeping the old machine versus replacing it. ### **Step 1: Initial Outlay** If you replace: - **Cost of new machine:** $160,000 - **Sale of old machine:** +$50,000 (market value) - **Net initial outlay:** $160,000 - $50,000 = **$110,000** ### **Step 2: Incremental Annual EBITDA** - **New machine EBITDA:** $35,000/year - **Old machine EBITDA:** $24,000/year - **Incremental EBITDA:** $11,000/year ### **Step 3: Depreciation (CCA)** Both machines have a **CCA rate of 40%** (declining balance), and **no salvage value** at the end of 10 years. - **Old machine UCC:** Purchased for $105,000 one year ago. - **CCA claimed last year:** $105,000 × 40% = $42,000 - **UCC at start of this year:** $105,000 - $42,000 = $63,000 - **Sale of old machine:** $50,000 - **Recaptured CCA:** Since $50,000 < $63,000, there is **no recapture**. Instead, the UCC is reduced by sale amount. - New UCC after sale: $63,000 - $50,000 = $13,000 (this will be written off as a **terminal loss** if you don’t buy a new machine, but if you do buy the new one, the new machine's UCC is $160,000). - **CCA on new machine:** - **First year:** Half-year rule applies, so CCA base = $160,000 × 0.5 = $80,000 - CCA claimed: $80,000 × 40% = $32,000 ### **Step 4: Incremental Depreciation (CCA) and Tax Savings** - CCA tax shield each year = CCA × Tax rate (0.4) We'll need to calculate the **incremental CCA tax shield**. #### **If Keep Old Machine:** - UCC = $63,000 (after 1 year), continues to depreciate at 40% per year. #### **If Buy New Machine:** - UCC = $160,000 (half-year rule in year 1), depreciates at 40%. #### **Incremental CCA:** Let’s calculate the CCA schedule for both machines for 10 years and find the present value of the **incremental CCA tax shield**. But to simplify, let’s **approximate** the present value of the CCA tax shield. **PV of CCA tax shield:** For an asset with no salvage value and declining balance depreciation: \[ PV_{CCA} = \text{UCC}_0 \times \frac{d \times t_c}{r + d} \] Where: - \( d \) = CCA rate = 0.4 - \( t_c \) = tax rate = 0.4 - \( r \) = discount rate = 0.11 For the **new machine** (UCC = $160,000, half-year rule): - Effective UCC for PV calculation: $160,000 × 0.5 = $80,000 (in year 1) - PV of CCA tax shield = $160,000 × 0.5 × (0.4 × 0.4) / (0.11 + 0.4) - = $80,000 × 0.16 / 0.51 - = $12,800 / 0.51 ≈ **$25,098** For the **old machine** (UCC = $63,000): - PV = $63,000 × 0.16 / 0.51 ≈ $9,882 **Incremental CCA tax shield PV = $25,098 - $9,882 = $15,216** ### **Step 5: Terminal Loss (If old machine is scrapped)** If you sell the old machine now, you have a UCC left of $13,000 (see above). At the end of the new machine’s life, if there is no salvage, this UCC can be claimed as a terminal loss. But since both machines have no salvage, the terminal loss will occur either way (either on $13,000—if you sell the old machine now—or on the remaining UCC after 10 years if you keep the old machine). The **incremental effect is minimal** and can be ignored for this analysis. ### **Step 6: Calculate NPV of Replacement** **Incremental annual after-tax cash flow:** - Incremental EBITDA: $11,000/year - Incremental CCA tax shield per year: Already included in PV above. - Tax on incremental EBITDA: $11,000 × (1 - 0.4) = $6,600/year **PV of incremental after-tax EBITDA:** - 10-year annuity at 11%: \( PV = 6,600 \times \frac{1 - (1+0.11)^{-10}}{0.11} \) - \( = 6,600 \times 5.8892 = \$38,870 \) **Total NPV:** - PV of incremental after-tax EBITDA: $38,870 - PV of incremental CCA tax shield: $15,216 - Less: Initial net outlay: $110,000 \[ \text{NPV} = 38,870 + 15,216 - 110,000 = \boxed{-\$55,914} \] ### **Conclusion** **The NPV of replacing the machine is negative (\$55,914).** **You should **NOT** replace your current machine.** --- **If you have access to Excel, you can verify this with a more detailed cash flow table, but the above analysis covers all major items.** --- #### **Summary Table** | Item | Amount | |-----------------------------|---------------| | Initial Outlay | -$110,000 | | PV Incremental EBITDA | +$38,870 | | PV Incremental CCA Shield | +$15,216 | | **NPV** | **-$55,914** | --- **Recommendation:** **Do not replace the old machine.**