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 $60,230 per year and it is estimated that with the new computers net cash flows would grow to $82,515 per year. Updating all of the computers would initially cost $66,012. The estimated remaining life of the old computers is 1 year and the expected lifetime of the new computers is 4 years. The scrap value of the old computers is estimated to be $12,648 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 $11,383.

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 4 years in perpetuity.
• Option 2: Replace the old computers with the new computers now and replace them every 4 years in perpetuity.

The company's required rate of return is 14.2% 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 4 years in perpetuity.
	Option 2:	Replace the old computers with the new computers now and replace them every 4 years in perpetuity.

Answer 1

a). Option 1: Use old computers for one more year and then replace with new computers every 4 years till perpetuity

Cash flow at Time T = 1 (CF1) = scrap value of old computer - investment in new computers + cash flow from old computers

= 12,648 - 66,012 + 60,230 = 6,866

CF2, CF3 and CF4 = cash flow from new computers = 82,515

CF5 cash flow = cash flow from new computers + scrap value of new computers - investment in new computers

= 82,515 + (11,383 - 66,012) = 82,515 + (-54,629)

Cash flows from CF2 to CF5 are repeated every 4 years till perpetuity.

To find the present value (PV) of these cash flows, we need to find the annual worth (AW) of these cash flows over 4 years which can then be used to calculate PV in perpetuity.

Cash flow from new computers of 82,515 remains same every year, so its AW = 82,515

AW of -54,629: FV = 54,629; N 4; rate = 14.20%, solve for PMT. AW = -11,068.54

Total AW = 82,515 -11,068.54 = 71,446.46

So, cash flows become: CF1 = 6,866; CF2 till perpetuity = 71,446.46

PV of cash flows at T = 1 from CF2 till perpetuity = 6,866 + 71,446.46/14.2% = 510,010.07

PV of cash flows at T = 0 is 510,010.07/(1+14.2%) = 446,593.76 or 446,594 (NPV of 1st option)

b). Option 2: Replace old computers now and use new computers with replacement every 4 years till perpetuity

This option has the same cash flows as option 1 except that cash flows are shifted to T = 0, so

CF0 = 6,866 and CF1 to perpetuity are 71,446.46

PV of these cash flows at T = 0 becomes 6,886 + 71,446.46/14.2% = 510,010.07 or 510,010 (NPV of 2nd option)

c). Option 2 has higher NPV than Option 1 so Option 2 should be chosen.