Consider a capital asset consisting of three expensive, important LRUs. The time

Question

Consider a capital asset consisting of three expensive, important LRUs. The time to failure of these LRUs has a constant failure rate , 12.3. Whenever an LRU fails it is replaced by a ready-to-use spare part from stock, if any is available. The time-to-replace the faulty LRU is negligible. The faulty LRU is sent to a repair shop and the time to repair the component has a constant repair rate . Note the repair time includes the order-and-ship time and possible extra waiting at the repair shop. For LRU i, we initially procure s, spare parts. If at a point in time LRU i fails and we do not have an available ready-to-use one on stock, e.g. this happens when all spare parts s, are under repair, the capital asset is considered to be on failure. It will function again whenever the repair of one of these faulty spare parts is completed and replaced in the asset. The objective of the technical department responsible for maintaining the capital asset is to maximize the asset limiting availability by stocking enough spare parts of each type. There is budget limit of S30,000 to be invested in the procurement of spare parts. Find the best target stock levels s, for the following case: LRU LRU Price (S) 1050 4890 15990 0.2 0.13 0.05 3

Explanation / Answer

Expected Return on holding stock = 12%

Interest rate on three-month T-bills = 2%

Calculate the stock with a beta of -0.3, 0.7, and 1.6

Using Capital Asset Pricing Model:

Interest rate on 3 months T-bill = 2%

Interest rate on 12 months T-bill = 2% * 4 = 8%

Calculating Return at beta of -0.3:

Required Rate of Return (R) = Risk-free Rate (Rf) + ß (RM – Rf)

Required Rate of Return (R) = 8% + (-0.3) (12 – 8%)

Required Rate of Return (R) = 0.08 + (-0.3) (0.04)

Required Rate of Return (R) = 0.08 -0.012

Required Rate of Return (R) = 0.068 (or) 6.8%

Calculating Return at beta of 0.7:

Required Rate of Return (R) = Risk-free Rate (Rf) + ß (RM – Rf)

Required Rate of Return (R) = 8% + (0.7) (12 – 8%)

Required Rate of Return (R) = 0.08 + (0.7) (0.04)

Required Rate of Return (R) = 0.08 + 0.028

Required Rate of Return (R) = 0.108 (or) 10.8%

Calculating Return at beta of 1.6:

Required Rate of Return (R) = Risk-free Rate (Rf) + ß (RM – Rf)

Required Rate of Return (R) = 8% + (1.6) (12 – 8%)

Required Rate of Return (R) = 0.08 + (1.6) (0.04)

Required Rate of Return (R) = 0.08 + 0.064

Required Rate of Return (R) = 0.144 (or) 14.4%

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