Suppose you are studying two hardware lease proposals. Lease Option 1 costs $4,000, but requires that the entire amount be paid in advance. Option 2 costs $5,000, but the payments can be $1,000 now and $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 $4,000, but requires that the entire amount be paid in advance. Option 2 costs $5,000, but the payments can be $1,000 now and $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 analysis, we need to calculate the Net Present Value for each option and compare the values. The NPV formula is:

NPV = Cash Flows / (1 + Discount Rate)^n

Let's calculate the NPV for each option using a 14% discount rate:

Option 1:
Cash Flow = -$4,000 (paid in advance)
Discount Rate = 14%
n = 0 (since it's a one-time payment)

NPV = -$4,000 / (1 + 0.14)^0
NPV = -$4,000 / 1
NPV = -$4,000

Option 2:
Cash Flows = -$1,000 now and -$1,000 per year for the next four years
Discount Rate = 14%
n = 0 (for the initial payment), n = 1 (for the first payment), n = 2 (for the second payment), n = 3 (for the third payment), n = 4 (for the fourth payment)

NPV = (-$1,000 / (1 + 0.14)^0) + (-$1,000 / (1 + 0.14)^1) + (-$1,000 / (1 + 0.14)^2) + (-$1,000 / (1 + 0.14)^3) + (-$1,000 / (1 + 0.14)^4)
NPV = (-$1,000 / 1) + (-$1,000 / 1.14) + (-$1,000 / 1.2996) + (-$1,000 / 1.4802) + (-$1,000 / 1.6785)
NPV = -$1,000 - $877.19 - $769.61 - $675.41 - $592.84
NPV = -$4,914.05

Therefore, using a 14% discount rate, Option 1 has an NPV of -$4,000 and Option 2 has an NPV of -$4,914.05. Thus, Option 1 is less expensive.

Now, let's calculate the NPV for each option using an 8% discount rate:

Option 1:
NPV = -$4,000 / (1 + 0.08)^0
NPV = -$4,000 / 1
NPV = -$4,000

Option 2:
NPV = (-$1,000 / (1 + 0.08)^0) + (-$1,000 / (1 + 0.08)^1) + (-$1,000 / (1 + 0.08)^2) + (-$1,000 / (1 + 0.08)^3) + (-$1,000 / (1 + 0.08)^4)
NPV = (-$1,000 / 1) + (-$1,000 / 1.08) + (-$1,000 / 1.1664) + (-$1,000 / 1.2597) + (-$1,000 / 1.36)
NPV = -$1,000 - $925.93 - $857.34 - $792.09 - $730.83
NPV = -$4,305.19

Therefore, using an 8% discount rate, Option 1 has an NPV of -$4,000, and Option 2 has an NPV of -$4,305.19. Again, Option 1 is less expensive.

In both cases, Option 1 is less expensive than Option 2.