Al a Mode, Inc., is considering one of two investment options. Option 1 is a $28

Question

Al a Mode, Inc., is considering one of two investment options. Option 1 is a $28,000 investment in new blending equipment that is expected to produce equal annual cash flows of $10,000 for each of seven years. Option 2 is a $32,000 investment in a new computer system that is expected to produce equal annual cash flows of $13,000 for each of five years. The residual value of the blending equipment at the end of the fifth year is estimated to be $7,000. 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 15%. 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.

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

Option 1

Blending equipment:

Cash flow = $10000 per year for seven year

initial investment = $28000

salavage value = nil (assumed as no information is given)

discounting rate = 15%

NPV = -$28000 + $10000 * PVIFA (15%, 7) = -$28000 + $10000 * 4.160 = $13600

PV index = PV of cash inflow / initial investment = $10000 * PVIFA (15%, 7) / 28000 = $41600 / $28000 = 1.49

Option 2

Computer System:

Cash flow = $13000 per year for 5 years

initial investment = $32000

salavage value = $7000

discounting rate = 15%

NPV

= -$32000 + $13000 * PVIFA (15%, 5) + $7000 * PVIF (15%, 5)

= -$32000 + $13000 * 3.352 + $7000 * 0.497 = $15055

PV index

= PV of cash inflow / initial investment

= [ $13000 * PVIFA (15%, 5) + $7000 * PVIF (15%, 5) ] / $32000

= ($13000 * 3.352 + $7000 * 0.497) / $32000

= $47055 / $32000 = 1.47

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