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- By investing in an improved telecommunications system, a call center believes it can save $350,000 per year in costs
each year for the foreseeable future. If the company requires a 7.25% rate of return, what is the present value of this
cost savings? If the new system would cost $2,500,000, is it fi nancially justifi ed by this savings?
C. Projections with Increasing Payments- Find the present value of a perpetuity of $5,000 per year, increasing by 4% annually, assuming the required rate of return is 12%.
- Find the present value of a perpetuity of $7,250 per year, increasing by 5% annually, assuming the required rate of
ret urn is 8%. - A company is considering building a small hydroelectric plant. The plant would produce a profi t of $72,500 in the fi rst
year, and the company believes that electric prices will rise in the future, so this profi t will grow 5% per year. The company
requires an 8% rate of return. The plant can be expected to continue producing power for the foreseeable future. What is
the largest cost to build this facility that these projections would justify? - According to a guidance counselor, someone with a college degree can be expected to earn $15,000 per year more in
her fi rst year after graduation than someone who does not have a degree, and this difference grows by 7% each year.
Suppose that you require an 8% rate of return on your investments.
a. Use a perpetuity to estimate the present value of the projected additional earnings from having a college degree.
According to this, is graduating from college fi nancially worth the effort and expense?
b. Instead of using a perpetuity, suppose that you assume a 40-year working career. Calculate the present value of
$15,000 per year for 40 years, assuming the same rate you used in part a. How does this affect your conclusion?D. Grab Bag- Suppose you have the choice of two investments:
- Part ownership of a landscape company. You project your share of the profi ts will be $12,000 in the fi rst year, and will
increase by 2% annually. - Part ownership of a property management company. You project your share of profi ts will be $12,000 in the fi rst year
and will increase by 5% annually.
You would require a 12% return from either of these investments. The landscape company would require a $125,000
investment; the property management company would require a $150,000 investment. Calculate the net present value
of each of these opportunities. On the basis of their net present values, which opportunity is the more attractive?- Mohan is considering investing in a business that he projects would earn him profi t of $35,000 in the fi rst year. He requires an
11% rate of return. Using perpetuities, calculate the present value of these profi ts, assuming they are growing at a rate of:
a. 1%
b. 3%
c. 5%
d. 8%
e. Does the trend in these values agree with common sense?Exercises 14.1 571