Question

You are the director of a company and you are considering updating all of your computers to new models. Using the old computers you have net cash flows of $65,209 per year and it is estimated that with the new computers net cash flows would grow to $88,684 per year. Updating all of the computers would initially cost $97,552. The estimated remaining life of the old computers is 1 year and the expected lifetime of the new computers is 3 years. The scrap value of the old computers is estimated to be $17,606 irrespective of whether they are scrapped today or in 1 year. The new computers have an estimated scrap value at the end of their life of $15,845.

Management is considering two different options:

• Option 1: Use the old computers for 1 more year and then replace them with the new computers that will then be replaced every 3 years in perpetuity.
• Option 2: Replace the old computers with the new computers now and replace them every 3 years in perpetuity.

The company's required rate of return is 14.1% pa. Assume that the cost of the computers, the cash flows that they generate and their scrap value remain constant over time.

a)What is the net present value of option 1? Give your answer in dollars to the nearest dollar.

NPV = $

b)What is the net present value of option 2? Give your answer in dollars to the nearest dollar.

NPV = $

c)Which option will you undertake?

	Option 1:	Use the old computers for 1 more year and then replace them with the new computers that will then be replaced every 3 years in perpetuity.
	Option 2:	Replace the old computers with the new computers now and replace them every 3 years in perpetuity.

Answer 1

NPV of one cycle of new computers = (Initial cost) + PV of annual cash flows + PV of salvage value at year end 3

= - 97,552 + 88,684 * PVAF(14.1%, 3 years) + 15,845 * PVF(14.1%, 3rd year)

= -97,552 + 88,684 * 2.3177 + 15,845 * 0.6732

= $118,661

NPV of remaining life of old computers = PV of annual cash flows + PV of salvage value

= 65,209 * PVF(14.1%, 1 year) + 17,606 * PVF(14.1%, 1 year)

= 65,209 * 0.8764 + 17,606 * 0.8764

= $72,581

Discount rate for 3 years period = R = (1 + r)^3 - 1 = (1 + 14.1%)^3 - 1 = 48.54%

(a) Calculation of NPV of Option 1

NPV of Option 1 = NPV of old computers + PV of (NPV of one cycle of new computers) as perpetuity

= 72,581 + PV of (NPV of one cycle of new computers) as perpetuity

PV of (NPV of one cycle of new computers) as perpetuity at the end of year 1 = PV of a perpetuity due = NPV of one cycle of new computers x (1 + R) / R = 118,661 x (1 + 48.54%) / 48.54% = 363,098

Hence, PV today = 363,098 *PVF(14.1%, 1 year) = $318,228

Therefore, NPV of option 1 = 72,581 + 318,228 = $ 390,809

(b) Calculation of NPV of Option 2

NPV of Option 2 = Sale value of old computers today + PV of a perpetuity due

= 17,606 + 363,098

= $ 380,704

(c) Since NPV of Option 1 ($390,809) is higher than NPV of Option 2 ($380,704), hence Option 1 should be selected.