Net Present Value-Unequal Lives Al a Mode, Inc., is considering one of two inves

Question

Net Present Value-Unequal Lives

Al a Mode, Inc., is considering one of two investment options. Option 1 is a $43,000 investment in new blending equipment that is expected to produce equal annual cash flows of $13,000 for each of seven years. Option 2 is a $52,000 investment in a new computer system that is expected to produce equal annual cash flows of $17,000 for each of five years. The residual value of the blending equipment at the end of the fifth year is estimated to be $9,000. The computer system has no expected residual value at the end of the fifth year.

Assume there is sufficient capital to fund only one of the projects. Determine which project should be selected, comparing the (a) net present values and (b) present value indices of the two projects, assuming a minimum rate of return of 10%. Use the present value tables appearing above.

a. Determine the net present values of the two projects.

b. Determine the present value indices of the two projects. If required, round the present value index to two decimal places.

Which project should be selected? (If both present value indices are the same, either project will grade as correct.)
SelectBlending EquipmentComputer SystemItem 9

Present Value of $1 at Compound Interest Year 6% 10% 12% 15% 20% 1 0.943 0.909 0.893 0.870 0.833 2 0.890 0.826 0.797 0.756 0.694 3 0.840 0.751 0.712 0.658 0.579 4 0.792 0.683 0.636 0.572 0.482 5 0.747 0.621 0.567 0.497 0.402 6 0.705 0.564 0.507 0.432 0.335 7 0.665 0.513 0.452 0.376 0.279 8 0.627 0.467 0.404 0.327 0.233 9 0.592 0.424 0.361 0.284 0.194 10 0.558 0.386 0.322 0.247 0.162

Explanation / Answer

a.

For Blending Equipment

Initial Investment = $43,000

Annual Cash flow = $13,000

PV of annuity factor at 10% for 7 year = 4.868

Present value of annuity = $13,000 × 4.868

= $63,284

Present value of annuity is $63,284.

Net present value = $63,284 - $43,000

= $20,284.

Net Present value of Blending Equipment is $20,284.

For Computer System

Initial Investment = $52,000

Annual Cash flow = $17,000

Scrap Value = $9,000

PV of annuity factor at 10% for 5 year = 3.791

PV factor at 10% for 5 year = 0.621

Present value of annuity = ($17,000 × 3.791) + ($9,000 × 0.621)

= $64,447 + $5,589

= $70,036

Present value of annuity and scrap value is $70,036

Net present value = $70,036 - $52,000

= $18,036.

Net Present value of computer system is $18,036.

b.

Present value indices for Blending Equipment = $63,284 / $43,000

= 1.4717

Present value indices for Blending Equipment is 1.4717.

Present value indices for computer system = $70,036 / $52,000

= 1.3468

Present value indices for Computer system is 1.3468.

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