# What does Descartes’ rule of signs tells us

1. Consider the following cash flow profile and assume MARR is 10 % per year.

EOY NCF

0 -$100.00

1 $25.00

2 $25.00

3 $25.00

4 $25.00

5 $25.00

6 $25.00

a. What does Descartes’ rule of signs tells us about the IRR(s) of this project?

b. What does Norstrom’s criterion tell us about the IRR(s) of this project?

c. Determine the IRR(s) for this project?

d. Is this project economically attractive?

2. What do you know about the mathematical value of a project’s Internal Rate of Return

under each of the following conditions?

a. The Present Worth of a project is greater than 0?

b. The PW of a project is equal to 0?

c. The PW of a project is less than 0?

d. The Future Worth of project is greater than 0?

e. The FW of a project is equal to 0?

f. The FW of a project is less than 0?

g. The Annual Worth of a project is greater than 0?

h. The AW of a project is equal to 0?

i. The AQ of a project is less than 0?

3. A specialty concerete mixer used in construction is purchased for $300,000 seven (7) years ago.

Its annual O&M costs are $105,000. At the end of 8 year planning horizon, the mixer has a salvage

value fo $5,000. If the mixer is replaced the new mixer will require initial investment of $375,000.

At the end of 8 year planning horizon, it will have a salvage value of $45,000. Its annual O&M costs

will be only $40,000 due to newer technology.

Analayze using EUAC measure and MARR of 15% to see if the mixer should be replaced if the older

mixer is sold for market value of $65,000.

a. Use cash flow approach (insider’s viewpoint approach)

4. Logan Public Library is planning a renovation. Cost including cabling will be $33,000, new equipment will

cost $21,000 and e-volume access initiation will be $17,500. Maintenance is expected to run another

$3,500 per year plus $4,000 for renewed e-volume access. The interest rate is 8%, planning horizon is 10 years,

and renovation is expected to have a salvage value of 30% with no salvage value for equipment or e-access.

It’s estimates that visits will increase by 2,500 in the first year and 500 per year thereafter.

If it’s estimated that the average benefits due to new facilities and equipment, access will be $2.00 per person per visit.

a. Should the city approve the plans? Use PW and calculate B-C.

b. What is the smallest benefit per person that will make this project desirable?

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