Suppose you are studying two hardware lease proposals. Lease Option 1 costs only $4,000 but requires that the entire amount be paid in advance. Option 2 costs $5,000, but the payments can be $1,000 per year for the next four years. If you do NPV analysis assuming a 14% discount rate, which proposal is less expensive? What happens if you use an 8% rate?

Question

Suppose you are studying two hardware lease proposals. Lease Option 1 costs only $4,000 but requires that the entire amount be paid in advance. Option 2 costs $5,000, but the payments can be $1,000 per year for the next four years. If you do NPV analysis assuming a 14% discount rate, which proposal is less expensive? What happens if you use an 8% rate?

Answer 1

To determine which proposal is less expensive using NPV (Net Present Value) analysis, we need to calculate the present value of the cash flows for each option and then compare them.

Let's start with the first proposal, Lease Option 1.

1. Calculate the present value for Lease Option 1:

Since the entire amount needs to be paid upfront, the cash flow is -$4,000 at time 0 (today's time).

To calculate the present value, we use the formula:
PV = CF / (1 + r)^n

Where:
PV = Present Value
CF = Cash Flow
r = Discount Rate
n = Time period

Using a discount rate of 14% and n = 0, we have:
PV1 = -$4,000 / (1 + 0.14)^0 = -$4,000

Now let's move on to the second proposal, Lease Option 2.

2. Calculate the present value for Lease Option 2:

In this case, the cash flows are $1,000 per year for four years:

Year 1: $1,000
Year 2: $1,000
Year 3: $1,000
Year 4: $1,000

Using the same formula as before, we calculate the present value of each cash flow and sum them up.

PV2 = $1,000 / (1 + 0.14)^1 + $1,000 / (1 + 0.14)^2 + $1,000 / (1 + 0.14)^3 + $1,000 / (1 + 0.14)^4

Simplifying the equation gives us:
PV2 ≈ $870.41 + $761.58 + $667.69 + $586.51 ≈ $2,885.19

Now, let's compare the present values for both proposals at a discount rate of 14%.

For Lease Option 1, PV1 = -$4,000
For Lease Option 2, PV2 ≈ $2,885.19

Since the NPV represents the cost of the investment, a smaller NPV indicates a less expensive option. In this case, Lease Option 1 has a lower NPV (-$4,000), making it less expensive than Lease Option 2 ($2,885.19).

Now, let's see what happens if we use an 8% discount rate.

Repeating the same process with a discount rate of 8%:

For Lease Option 1, PV1 = -$4,000
For Lease Option 2, PV2 ≈ $3,042.44

In this scenario, Lease Option 2 has a higher present value ($3,042.44) than Lease Option 1 (-$4,000), making Lease Option 1 less expensive at an 8% discount rate as well.

Therefore, regardless of the discount rate used, Lease Option 1 is consistently less expensive than Lease Option 2.