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.
