Please present the answer neatly. Thanks Question #2 (25 points) A 2-year old as

Question

Please present the answer neatly. Thanks

Question #2 (25 points) A 2-year old asset is being considered for replacement. Its current market value is $13,000. The estimated market values during the next 3 years are given in the following table (the asset has a useful life of 5 year:s but a similar asset is needed indefinitely). The effective MARR is 10% per year. a) What is the economic life of the asset? (20 points) b) What should be done if the AW of the best alternative is S6,200? (5 points) EOYMarket ValueAnnual Expenses $9,000 $8,000 $6,000 $2,500 $2,700 $3,000

Explanation / Answer

a) Let us calculate the net present value of the asset at the end of 1, 2 & 3 years from now,

If the asset is sold today, there would be a net inflow of $ 13,000

If the asset is sold after 1 year, net inflow = market value - annual cost = (9000-2500) = $ 6500.

Present value of inflow of $ 6500 received after 1 year = Future value / (1+r)n

Present value of inflow of $ 6500 received after 1 year = 6500/1.10^1 = $ 5909.10

If the asset is sold after 2 years, NPV = P.V. of outflow of $ 2700 for each of the 2 years - Present value of $ 9000 received at the end of Year 2 @ 10% discounting factor.

Accordingly, NPV if the asset is sold at the end of Year 2 = $ 2,752.07

If the asset is sold after 3 years, NPV = P.V. of outflow of $ 3000 for each of the 3 years - Present value of $ 6000 received at the end of Year 3 @ 10% discounting factor

Accordingly, NPV if the asset is sold at the end of Year 3 = Negative $ 2952.66

This clearly implies that upto the end of 2 years from today, the project shall have a positive NPV, after which holding the asset for even 1 more year makes it negative. So the economic life of the asset is more than 2 years but less than 3 years.

In order to find the exact economic life, we find the period at which NPV=0, we use interpolation for that purpose,

The 2nd year NPV = 2,752.07, 3rd yr NPV = -2952.66, difference between the NPV = 5704.73

So it means that in 1 year, NPV goes down by 5704.73, so in order to make the NPV zero i.e. for it to decrease by 2752.07, time required will be (2752.07/5704.73) = 0.4824 years beyond year 2

Thus economic life of the asset = 2.4824 years.

b) The annual worth of this asset if we sell it at the end of Year 2 = -2700+8000 * (A / F, i, n)

Annual Worth of this asset = -2700+(8000*0.4762) = 1109.6

If the AW of the best alternative is $ 6200, then the company must go with the best alternative and not with this asset.

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