A company needs to decide between buying a factory and machinery or leasing it. Analyze the financial implications of each option.

The "Buy" option involves purchasing the following assets:

• Factory building: $\text{Ksh } 10,000,000$
• Installation of plant and machinery: $\text{Ksh } 30,000,000$
• Trailer: $\text{Ksh } 2,000,000$
• 3 Phase Power supply: $\text{Ksh } 4,000,000$

The total initial capital outlay for the "Buy" option is:

$$10,000,000 + 30,000,000 + 2,000,000 + 4,000,000 = \text{Ksh } 46,000,000$$

The "Lease" option involves annual lease payments of $\text{Ksh } 4,000,000$ for 10 years, with a cost of capital of 18% p.a.

First, calculate the Present Value Annuity Factor (PVAF) for 10 years at 18%:

$$\text{PVAF} = \frac{1 - (1 + r)^{-n}}{r}$$

Where $r = 0.18$ and $n = 10$.

$$\text{PVAF} = \frac{1 - (1 + 0.18)^{-10}}{0.18}$$ $$\text{PVAF} = \frac{1 - (1.18)^{-10}}{0.18}$$ $$\text{PVAF} = \frac{1 - 0.191105}{0.18}$$ $$\text{PVAF} = \frac{0.808895}{0.18} \approx 4.49386$$

Next, calculate the Present Value of Lease Payments:

$$\text{PV of Lease} = \text{Annual Lease Payment} \times \text{PVAF}$$ $$\text{PV of Lease} = 4,000,000 \times 4.49386$$ $$\text{PV of Lease} \approx \text{Ksh } 17,975,440$$