1. **State the problem:** We need to find the equivalent uniform annual cost (EUAC) of maintenance for a Volvo Backhoe given different maintenance costs over 10 years and overhaul costs at years 5 and 8, with an interest rate of 6% compounded annually. 2. **Given data:** - Maintenance cost for first 5 years: P40,000 per year - Maintenance cost for next 5 years: P60,000 per year - Overhaul cost at end of 5th and 8th year: P140,000 each - Interest rate: 6% per year compounded annually 3. **Formula used:** The EUAC is calculated by converting all costs to their present worth (PW) and then converting that PW to an equivalent uniform annual cost using the capital recovery factor (CRF). - Present Worth of uniform series: $$PW = A \times \frac{1 - (1+i)^{-n}}{i}$$ - Capital Recovery Factor: $$CRF = \frac{i(1+i)^n}{(1+i)^n - 1}$$ - Equivalent Uniform Annual Cost: $$EUAC = PW \times CRF$$ 4. **Calculate present worth of maintenance costs:** - For first 5 years at P40,000/year: $$PW_1 = 40000 \times \frac{1 - (1+0.06)^{-5}}{0.06}$$ Calculate: $$PW_1 = 40000 \times \frac{1 - (1.06)^{-5}}{0.06} = 40000 \times 4.21236 = 168494.4$$ - For next 5 years at P60,000/year (years 6 to 10), present worth at year 5: $$PW_{2,5} = 60000 \times \frac{1 - (1+0.06)^{-5}}{0.06} = 60000 \times 4.21236 = 252741.6$$ - Present worth at year 0 for these 5 years: $$PW_2 = \frac{PW_{2,5}}{(1+0.06)^5} = \frac{252741.6}{(1.06)^5} = \frac{252741.6}{1.338225} = 188823.3$$ 5. **Calculate present worth of overhaul costs:** - Overhaul at year 5: $$PW_{OH5} = \frac{140000}{(1.06)^5} = \frac{140000}{1.338225} = 104600.3$$ - Overhaul at year 8: $$PW_{OH8} = \frac{140000}{(1.06)^8} = \frac{140000}{1.593848} = 87798.3$$ 6. **Total present worth:** $$PW_{total} = PW_1 + PW_2 + PW_{OH5} + PW_{OH8} = 168494.4 + 188823.3 + 104600.3 + 87798.3 = 549716.3$$ 7. **Calculate capital recovery factor for 10 years:** $$CRF = \frac{0.06(1.06)^{10}}{(1.06)^{10} - 1} = \frac{0.06 \times 1.790847}{1.790847 - 1} = \frac{0.107451}{0.790847} = 0.1359$$ 8. **Calculate equivalent uniform annual cost:** $$EUAC = PW_{total} \times CRF = 549716.3 \times 0.1359 = 74669.3$$ **Final answer:** The equivalent uniform annual cost of maintenance is approximately P74669.3 per year.