1. Compute the Future Worth of the cash flows shown in the diagram below. Use interest rates shown.
2. A capital equipment project is expected to provide positive cash flows of $4,400 the first year, $5,500 the second year, $6,600 the third year, -$4,300 the fourth year, $8,800 the fifth year, and $9,900 the sixth year. It is estimated the initial project cost would be about $25,000. What is the internal rate of return for the project? Use spreadsheet to solve the problem (draw the NPW plot (NPW vs interest rate) and IRR function).
3. For the cash flows tabulated below, compute the rate of return to the nearest 0.10%.
|
Year
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Cash Flow, $
|
-300
|
400
|
250
|
100
|
-50
|
-200
|
-350
|
4. Using Rate of Return Analysis, determine the most economical alternative below. Assume a minimum attractive rate of return of 6%, and a 5-year life with no salvage value for each. The alternatives are mutually exclusive.
|
Data
|
|
Alternative
|
|
|
|
|
A
|
B
|
C
|
D
|
|
Intial Cost
|
$400,000
|
$100,000
|
$500,000
|
$200,000
|
|
Annual Cost
|
$900
|
$120,000
|
$23,000
|
$9,000
|
|
Annual Benefits
|
$101,800
|
$39,700
|
$148,200
|
$55,200
|
5. The cash flows for three different alternatives are given in the table below. Assume that alternatives are replaced at the end of their useful lives. Life = 8 years. Use "EXCEL" to solve this problem (graph the NPW of each alternative versus the interest rate).
i. Develop a choice table from 0-10%.
ii. Choose the best alternative for a MARR of 7%.
|
|
A
|
B
|
C
|
|
First cost
|
2,000
|
6,000
|
5,000
|
|
EUAB
|
275
|
400
|
750
|
|
Salvage Value
|
750
|
5,000
|
0
|
6. A machine costs $5,240 and generates an annual end-of-year benefit of $1,000 for 8 years. If a nominal annual interest rate of 9.532% with continuous compounding is assumed, calculate the breakeven point in years, at which the purchase price equals the present value of the benefits received.
7. The following data is available for three different alternatives. MARR =12%
|
Data
|
Alt. A
|
Alt. B
|
Alt. C
|
|
Intial Cost
|
$6,000
|
$900
|
$1,500
|
|
Uniform Annual Benefit
|
$525
|
$300
|
$450
|
|
Useful Life, Years
|
20
|
5
|
10
|
Alternatives B and C are replaced at the end of their useful lives with identical replacements. Using the above data, find the best alternative using benefit cost ratio analysis.
8. Find the rate of return for the following cash flow. (i) determine how many roots are possible and (ii) graph the PW versus the interest rate to see whether multiple roots occur. (iii) use MIRR as the project's ROR if it is necessary. (external investing rate is 12% and external borrowing rate is 6%)
|
Year
|
Cash Flow
|
|
0
|
-$5,000
|
|
1
|
$20,000
|
|
2
|
-$12,000
|
|
3
|
-$3,000
|