A young graduate is trying to decide whether to lease or buy a car for the next three years. The cash flows for each choice are shown below. (We will ignore gas, insurance, and tag fees.)

YEAR	0	1	2	3
LEASE	-$4,429.00	-$3,500.00	-$3,500.00	-$3,500.00
PURCHASE	-$36,510.00	0	0	$24,579.00

The graduate has a personal discount rate of 6.00%.

What is the NPV of leasing the car for three years? (HINT: Answer will be a NEGATIVE number)

The Net Present Value (NPV) calculation takes the sum of cash flows discounted to their present value. The formula for NPV is:

\[
NPV = \sum \frac{C_t}{(1 + r)^t}
\]

Where:
- $C_t$ is the cash flow at time $t$,
- $r$ is the discount rate (in this case, 6%, or 0.06),
- $t$ is the year (starting from 0 for year 0, 1 for year 1, etc.).

Given the cash flows for leasing:
- Year 0: $-4,429.00$
- Year 1: $-3,500.00$
- Year 2: $-3,500.00$
- Year 3: $-3,500.00$

Let's calculate the NPV of leasing using the discount rate of 6%.

### Step 1: Apply the formula for each year
\[
NPV_{\text{leasing}} = \frac{-4429}{(1+0.06)^0} + \frac{-3500}{(1+0.06)^1} + \frac{-3500}{(1+0.06)^2} + \frac{-3500}{(1+0.06)^3}
\]

Now, we compute each term individually.

\[
NPV_{\text{leasing}} = -4429 + \frac{-3500}{1.06} + \frac{-3500}{1.06^2} + \frac{-3500}{1.06^3}
\]

\[
NPV_{\text{leasing}} = -4429 + \frac{-3500}{1.06} + \frac{-3500}{1.1236} + \frac{-3500}{1.1910}
\]

\[
NPV_{\text{leasing}} = -4429 - 3301.89 - 3115.97 - 2939.69
\]

### Step 2: Sum the discounted cash flows
\[
NPV_{\text{leasing}} = -4429 - 3301.89 - 3115.97 - 2939.69 = -13,786.55
\]

Thus, the **NPV of leasing the car** for three years is approximately **$-13,786.55$**.

Would you like further details or clarification?

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Here are five related questions for expanding your understanding:

1. What is the NPV of purchasing the car using the same discount rate?
2. How would the NPV change if the personal discount rate were 8% instead of 6%?
3. What other factors should a graduate consider when deciding between leasing and purchasing, aside from NPV?
4. How does the length of time impact the NPV for leasing versus purchasing?
5. Can the residual value of the purchased car at the end of year 3 affect the NPV calculation?

**Tip**: When comparing financial options like leasing vs. purchasing, always ensure you're comparing costs over the same time period and accounting for factors like resale value or residual value!

A young graduate is trying to decide whether to lease or buy a car for the next three years. The cash flows for each choice are shown below. (We will ignore gas, insurance, and tag fees.) YEAR 0 1 2 3 LEASE -$4,429.00 -$3,500.00 -$3,500.00 -$3,500.00 PURCHASE -$36,510.00 0 0 $24,579.00 The graduate has a personal discount rate of 6.00%. What is the NPV of leasing the car for three years? (HINT: Answer will be a NEGATIVE number)

Learn how to calculate the Net Present Value (NPV) of leasing a car for three years with a 6% discount rate. This example provides cash flow details for both leasing and purchasing, demonstrating the NPV formula and discounting method. Ideal for finance students or young graduates making financial decisions.

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