The announcement of the HAC cement factory states that the $200 million (M) inve

Question

The announcement of the HAC cement factory states that the $200 million (M) investment is planned for 2012. Most large investment commitments are actually spread out over several years as the plant is constructed and production is initiated. Further investigation may determine, for example, that the $200 M is a present worth in the year 2012 of anticipated investments during the next 4 years (2013 through 2016). Assume the amount planned for 2013 is $100 M with constant decreases of $25 M each year thereafter. As before, assume the time value of money for investment capital is 10% per year to answer the following questions using tabulated factors and spreadsheet functions, as requested below.

In equivalent present worth values, does the planned decreasing investment series equal the announced $200 M in 2012? Use both tabulated factors and spreadsheet functions.

Given the planned investment series, what is the equivalent annual amount that will be invested from 2013 to 2016? Use both tabulated factors and spreadsheet functions.

Explanation / Answer

The decreasing investment series has Cash flows at Year 2013 = $100 M, at Year 2014 = 100-25=$75 M, at Year 2015= 75-25 = $50 M & ar Year 2016 = 50-25 = $25 M

The discount factor of each year for discounting the cash flows to Year 2012 = 1/((1+r)Year-2012) where r=10%

Present Value of each cash flow at Year 2012(= Cash Flow at each year * discount Factor)

NPV at 2012 = 90.91+61.98+37.57+17.08 = $207.53 Million

No, the decreasing investment series net worth is not equal to the announced $ 200 M in 2012. Infact it is $7.53 M more than that announced in 2012

Now, lets find the equivalnet annual amount that makes the NPV of series equal to $ 200 M

Let the amount be P, then the CF'S at 2014 = P-25, at 2015=P-25-25 = P-50, at 2016 = P-50-25 = P-75

Present Value of each cash flow at Year 2012(= Cash Flow at each year * discount Factor)

NPV at 2012 = 0.9091P+0.8264P-20.66+0.7513P-37.567+0.6830P-51.225 = 3.1698P-109.452

This NPV should be equal to $ 200 Million

-> 3.1698P-109.452 = 200

->3.1698P = 309.452

->P= $97.62 M

Hence an amount of $97.62 M for 2013 with a constant decrease of $25 M each year till 2016 is equivalent to the announced $ 200 M in 2012.

Year 2013 2014 2015 2016 Cash Flows at each year(in $ Million) 100 75 50 25 Discount Factor for each year 1/1.1 = 0.9091 1/(1.12) = 0.8264 1/(1.13) =0.7513 1/(1.14) = 0.6830

Present Value of each cash flow at Year 2012(= Cash Flow at each year * discount Factor)

90.91 61.98 37.57 17.08

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