Question

A company has the opportunity to take over a redevelopment project in an industrial area of a city. No immediate investment is required, but it must raze the existing buildings over a four-year period and, at the end of the fourth year, invest $2,400,000 for new construction. It will collect all revenues and pay all costs for a period of 10 years, at which time the entire project, and properties thereon, will revert to the city. The net cash flows are estimated to be as follows:
Year End Net Cash Flow

1 $500,000
2 $300,000
3 $100,000
4 $2,400,000
5 $150,000
6 $200,000
7 $250,000
8 $300,000
9 $350,000
10 $400,000

Tabulate the PW versus the interest rate and determine whether multiple IRRs exist. If so, use the ERR method when e 8% per year to determine a rate of return. A new municipal refuse-collection truck can be purchased for $84,000. Its expected useful life is six years, at which time its market value will be zero. Annual receipts less expenses will be approximately $18,000 per year over the six-year study period. Use the PW method and a MARR of 18% to determine whether this is a good investment.

Answer 1

Answer:

1-a. The are multiple IRRs stated as follows:

The first IRR value = 4.09%

Second IRR value = 31.82%

1-b. Rate of return = 7.58%

2. This is NOT a good investment because the NPV is negative.

Explanation:

Note: The estimated Net Cash Flow for the 4th year in the data is erroneously stated in the question as a positive value instead as a negative value since it is a cost.

The estimated net cash flows correctly before answering the question as follows:

Year End             Net Cash Flow

1                             $500,000

2                            $300,000

3                            $100,000

4                          –$2,400,000

5                            $150,000

6                            $200,000

7                            $250,000

8                            $300,000

9                            $350,000

10                           $400,000

The explanation of the answers is now given as follows:

1-a. Tabulate the PW versus the interest rate and determine whether multiple IRRs exist.

Note: See Part 1-a of the attached excel file for the tabulation of the PW versus the interest rate.

From Part 1-a of the attached excel file, it can be observed that multiple IRRs exist. This is because there two IRRs stated as follows:

The first IRR value = 4.09%

Second IRR value = 31.82%

1-b. If so, use the ERR method when e 8% per year to determine a rate of return.

Note: See Part 1-a of the attached excel file for the calculation of total future value of income when e = 8% per year.

In the attached excel file, note that year 4 has a cost not income. Therefore,

From attached excel, we have:

Total Future Value of Income = $3,661,508.81

In the attached excel file, note that year 4 has a cost (not income) of $2,400,000. Therefore, it future value is not calculated. However, the present of the cost can be calculated as follows:

Present value of cost in year 4 = $2,400,000 / (100% + e)^4 = $2,400,000 / (100% + 8%)^4 = $1,764,071.65

The rate of return can now be calculated as follows:

Rate of return = ((Total Future Value of Income / Present value of cost in year 4)^(1/Number of period)) - 1 = (($3,661,508.81 / $1,764,071.65)^(1/10)) - 1 = 0.0758, or 7.58%

2. Use the PW method and a MARR of 18% to determine whether this is a good investment.

Note: See Part 2 of the attached excel file for the calculation of net present value (NPV).

From part 2 of the attached excel file, we have:

Net present value = –$21,043.15

Since the net present value is negative, this implies that this is NOT a good investment.

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