91Ó°ÊÓ

The NPV for buying a car is calculated below:

$$\begin{gathered} \text{r =}\frac{\text{4}}{\text{100}}\text{= 0.04} \\ \text{NPV = - 20,000 +}\frac{\text{12,000}}{{\left(\text{1 + 0.04}\right)}^{\text{6}}} \\ \text{= - \$ 10,516.23} \end{gathered}$$

The NPV for leasing the car is calculated below:

The payment needs to be made at the beginning of each year.

$$\begin{gathered} \text{NPV = - 3600 -}\frac{\text{3600}}{\text{1.04}}\text{-}\frac{\text{3600}}{{\left(\text{1.04}\right)}^{\text{2}}} \\ \text{= - 3600 - 3461.54 - 3328.40} \\ \text{= - \$ 10,389.94} \end{gathered}$$

Leasing the car is better than buying the car, as the NPV is higher, i.e., lower negative value.

The NPV for buying a car is calculated below:

$$\begin{gathered} \text{r =}\frac{\text{12}}{\text{100}}\text{= 0.12} \\ \text{NPV = - 20,000 +}\frac{\text{12,000}}{{\left(\text{1 + 0.12}\right)}^{\text{6}}} \\ \text{= - \$ 13,920.43} \end{gathered}$$

The NPV for leasing the car is calculated below:

The payment needs to be made at the beginning of each year.

$$\begin{gathered} \text{NPV = - 3600 -}\frac{\text{3600}}{\text{1.12}}\text{-}\frac{\text{3600}}{{\left(\text{1.12}\right)}^{\text{2}}} \\ \text{= - 3600 - 3214.29 - 2869.90} \\ \text{= - \$ 9,684.18} \end{gathered}$$

Leasing the car is better than buying the car, as the NPV is higher. i.e., lower negative value.

An investor will be indifferent between two options when the NPVs are equal. Thus, to be indifferent between buying and leasing the car, the NPVs must be equal. Hence, the NPVs are $\text{- 20,000 +}\frac{\text{12,000}}{{\left(\text{1 + r}\right)}^{\text{6}}}\text{= - 3600 -}\frac{\text{3600}}{\left(\text{1 + r}\right)}\text{-}\frac{\text{3600}}{{\left(\text{1 + r}\right)}^{\text{2}}}$.

The interest rate increases from 4% to 12%; thus lease become a better option. The NPVs are calculated below:

The interest rate will be 3.8%, where the NPVs are almost equal.