A cost analysis is to be made to determine what, if anything, should be done in

Question

A cost analysis is to be made to determine what, if anything, should be done in a situation offering three "do-something" and one "do-nothing" alternatives. Estimates of the cost and benefits are as follows:

Alternatives            1       2        3          4

Cost                    500     600    700        0

UAB                    120     100    100        0

Salvage                0       200     100       0

Life(yrs)                5         5        10        0

Use a 10-year analysis period for the four mutually exclusive alternatives. At the end of Year 5, Alternatives 1 and 2 may be replaced with identical alternatives( with the same cost, benefits, salvage value, and useful life). (a) If a 6% interest rate is used, which alternative should be selected? (b) If a 10% interest rate is used, which alternative should be selected? Thanks in advance, seems so simple but having some trouble.

Explanation / Answer

Working notes:

1. Alternative 2:

Salvage value will be added to UAB in year 5. So, the UAB in year 5 = 100 + 200 = 300

Since the project will be duplicated, Salvage value will be added to UAB in year 10. So, the UAB in year 10 = 100 + 200 = 300

2. Alternative 3: Salavage value will be added to UAB in year 10. So, the UAB in year 10 = 700 + 100 = 800

As we see from above:

(a) When 6% discount rate is used, only Alternative 1 provides a NPV = 9.35 > 0. So, this alternative should be chosen.

(b) When 10% discount rate is used, all the alternatives 1, 2 & 3 yield negative NPV. So, alternative 4 (with 0 NPV) should be chosen, that is, do nothing.

ALTERNATIVE 1 Year Cost UAB Discount Factor @6% CF: Discounted @6% Discount Factor @10% CF: Discounted @10% 0 -500 1.0000 -500.00 1.0000 -500.00 1 120 0.9434 113.21 0.9091 109.09 2 120 0.8900 106.80 0.8264 99.17 3 120 0.8396 100.75 0.7513 90.16 4 120 0.7921 95.05 0.6830 81.96 5 120 0.7473 89.67 0.6209 74.51 6 -500 0.7050 -352.48 0.5645 -282.24 7 120 0.6651 79.81 0.5132 61.58 8 120 0.6274 75.29 0.4665 55.98 9 120 0.5919 71.03 0.4241 50.89 10 120 0.5584 67.01 0.3855 46.27 120 0.5268 63.21 0.3505 42.06 NPV = 9.35 NPV = -70.57 ALTERNATIVE 2 Year Cost UAB Discount Factor @6% CF: Discounted @6% Discount Factor @10% CF: Discounted @10% 0 -600 1.0000 -600.00 1.0000 -600.00 1 100 0.9434 94.34 0.9091 90.91 2 100 0.8900 89.00 0.8264 82.64 3 100 0.8396 83.96 0.7513 75.13 4 100 0.7921 79.21 0.6830 68.30 5 300 0.7473 224.18 0.6209 186.28 6 -600 0.7050 -422.98 0.5645 -338.68 7 100 0.6651 66.51 0.5132 51.32 8 100 0.6274 62.74 0.4665 46.65 9 100 0.5919 59.19 0.4241 42.41 10 100 0.5584 55.84 0.3855 38.55 300 0.5268 158.04 0.3505 105.15 NPV = -49.98 NPV = -151.34 ALTERNATIVE 3 Year Cost UAB Discount Factor @6% CF: Discounted @6% Discount Factor @10% CF: Discounted @10% 0 -700 1.0000 -700.00 1.0000 -700.00 1 100 0.9434 94.34 0.9091 90.91 2 100 0.8900 89.00 0.8264 82.64 3 100 0.8396 83.96 0.7513 75.13 4 100 0.7921 79.21 0.6830 68.30 5 200 0.7473 149.45 0.6209 124.18 6 -700 0.7050 -493.47 0.5645 -395.13 7 100 0.6651 66.51 0.5132 51.32 8 100 0.6274 62.74 0.4665 46.65 9 100 0.5919 59.19 0.4241 42.41 10 100 0.5584 55.84 0.3855 38.55 200 0.5268 105.36 0.3505 70.10 NPV = -347.88 NPV = -404.93

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