1. **Stating the Problem**: A firm must decide between buying or leasing motor vehicles priced at 500 million K. The vehicles have a 5-year usage, residual value is 10% of cost (resale value), and straight-line depreciation is used. The firm’s tax rate is 30%. Leasing involves 24% annual interest, 50% down payment, equal monthly payments over 5 years, and a final payment of 1% of loan amount. 2. **Calculate Depreciation for Buy Option**: Cost = 500m Residual Value = 10% of 500m = 50m Depreciable amount = 500m - 50m = 450m Annual depreciation = 450m / 5 = 90m per year 3. **Calculate Tax Shield from Depreciation**: Tax shield = Depreciation * tax rate = 90m * 0.3 = 27m per year 4. **Calculate Net Cost of Buying (Ignoring financing for now)**: Net cost per year after tax shield = Annual depreciation - Tax shield = 90m - 27m = 63m Over 5 years = 63m * 5 = 315m But we must consider the initial cost and the salvage value after 5 years: Initial cost = 500m Less salvage (resale) value (after tax effect) = 50m * (1 - 0.3) = 35m Net cost of buying = Initial cost - After tax salvage value - Tax shield total = 500m - 35m - (27m * 5) = 500m - 35m - 135m = 330m 5. **Lease Option Calculations:** Loan amount = 500m Down payment (50%) = 250m Loan balance to amortize = 250m Interest rate = 24% annual Duration = 5 years = 60 months Monthly interest rate = 24% / 12 = 2% = 0.02 Use amortization formula for monthly payment $P$: $$P = L \times \frac{r(1+r)^n}{(1+r)^n - 1}$$ Where $L$ = loan amount 250m, $r$=0.02, $n$=60 Calculate numerator: $$0.02 \times (1.02)^{60}$$ Calculate denominator: $$(1.02)^{60} - 1$$ Using $$ (1.02)^{60} \approx 3.28103 $$ Numerator = $$0.02 \times 3.28103 = 0.0656206$$ Denominator = $$3.28103 - 1 = 2.28103$$ Monthly payment $$P = 250m \times \frac{0.0656206}{2.28103} = 250m \times 0.02877 = 7.1925m$$ Total payments over 60 months = $$7.1925m \times 60 = 431.55m$$ Add down payment = 250m Add final payment (1% of loan) = $$250m \times 0.01 = 2.5m$$ Total lease payments = $$250m + 431.55m + 2.5m = 684.05m$$ 6. **Calculate Tax Benefit on Lease Payments**: All lease payments are typically tax deductible. Tax benefit = 30% of lease payments Tax benefit = $$0.3 \times 684.05m = 205.215m$$ 7. **Net cost of lease after tax**: Net lease cost = Total lease payments - Tax benefit Net lease cost = $$684.05m - 205.215m = 478.835m$$ 8. **Comparison and Advice**: Net cost buy option = 330m Net cost lease option = 478.835m Since 330m < 478.835m, buying the vehicles is financially better for the firm. **Final conclusion:** The firm should buy the motor vehicles rather than lease them as it results in a significantly lower net cost over 5 years.