5.9 Consider the following investment project: An $2,000 $2,400 $3,400 $2,500 $2

Question

5.9 Consider the following investment project: An $2,000 $2,400 $3,400 $2,500 $2,500 $3,000 10% 12% 14% 15% 13% 10% 0 2 4 Suppose, as shown in the foregoing tables, that the company's reinvestment opportunities change over the life of the project (i.e., the firm's MARR changes over the life of the proj- ect). For example, the company can invest funds available now at 10% for the first year, 12% for the second year, and so forth. Calculate the net present worth of this investment, and determine the acceptability of the investment.

Explanation / Answer

The reinvestment opportunities change every year, so the returns will be discounted at different rates for every year.

Year 1 return will be discounted at 10%

Year 2 return will be discounted at 12% to find the value at the end of year 1; this value be further discounted at 10% to find the value at year 0.

Year 3 return will be discounted at 14% to find the value at the end of year 2; this value be further discounted at 12% to find the value at year 1 and then at 10% to find the value at year 0.

Year 4 return will be discounted at 15% to find the value at the end of year 3; this value be further discounted at 14% to find the value at year 2, then at 12% to find the value at the end of year 1 and then at 10% to find the value at year 0.

Year 5 return will be discounted at 13% to find the value at the end of year 4, this value will be discounted at 15% to find the value at the end of year 3; this value be further discounted at 14% to find the value at year 2, then at 12% to find the value at the end of year 1 and then at 10% to find the value at year 0.

Net Present Value = 9913.14-2000 = 7913.14

Since NPV is positive, project should be accepted.

Years 0 1 2 3 4 Discount Rate 10% 12% 14% 15% 13% 0 -2000 1 2400 =2400/1.10 = 2181.82 2 3400 = 3035.71/1.10 = 2759.54 = 3400/1.12 = 3035.71 3 2500 = 1958.02/1.10 = 1780.02 = 2192.98/1.12 = 1958.02 = 2500/1.14 = 2192.98 4 2500 = 1702.63/1.10 = 1547.84 =1906.94/1.12 = 1702.63 = 2173.91/1.14 = 1906.94 = 2500/1.15= 2173.91 5 3000 = 1808.10/1.10= 1643.73 = 2025.07/1.12 = 1808.10 = 2308.58/1.14 = 2025.07 = 2654.87/1.15 = 2308.58 =3000/1.13= 2654,87 =9913.14

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