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The incandescent bulb is costing her (14 kWh/month)($0.12 per kWh) $1.68 per month.
The new bulb uses one-fourth the electricity, so its running cost would be $1.68/4 $0.42
per month. So her return on this investment would be $1.68 $0.42 $1.26 per month.So the payback period would be $3.03/$1.26 2.40 months. In other words, the more
expensive bulb pays for itself in a bit less than 2½ months.A strength of the payback period method is that it is easier to explain to other people who
are not so familiar with the concept of present value. Another is that it does not require any
consideration of rate of return. It allows us to quickly see just how long (whether measured
in elapsed time or in use) an investment needs to get in order to justify the investment. The
downside, of course, is that it gives no indication of what sort of rate of return actually is
being earned, nor does it take into account how much is to be gained beyond the payback
period. We know how long Jenny needs to use the CF lightbulb for it to be financially
advantageous, and know that it is a fairly short period of time. We did not, however, take
any measurement of just how much she will save overall. We might be able to calculate this
if we want to, but calculating the overall savings goes beyond simple payback analysis.
Still, knowing the overall potential savings can be a useful addition to payback analysis.Example 14.2.4 The CF lightbulb Jenny bought is rated to last 5 years. If it lasts
that long, what will her total savings be by using it instead of an incandescent?We saw that Jenny is saving $1.26 per month with the CF bulb. Five years is 60 months, so
she would save a total of (60)($1.26) $75.60 worth of electricity. Since the CF bulb cost
an extra $3.03, her total savings would be $75.60 $3.03 $72.57.Using Payback Periods for Comparisons
Payback periods can also be an especially useful tool for comparing a choice of invest-
ments opportunities, especially when the long term is hard to predict.Example 14.2.5 Harold and Olivia are taking out a mortgage to buy a house.
They will be borrowing $145,000. For a 30-year fi xed-rate mortgage, the interest rate
would be 8¼%. If they pay 0.5 points, the rate would be reduced to 8%. If they pay
2.5 points, the rate would be 7 ¾%. (One point equals 1% of the amount borrowed.)^3
Find the payback period for each option.0.5-point option: The point would cost (0.5%)($145,000) $725. They would save ¼%
on their rate, or roughly (¼%)($145,000) $362.50 per year. (This is not exactly correct,
because it applies the interest savings to the full original principal. With each payment on the
loan, the principal is slightly reduced, and so the savings will actually be a bit less than this.
However, since the progress made on paying down the principal of a 30-year mortgage is
slow in the early years, this should not be far from the actual savings.)The payback period would be approximately $725/$362.50 2 years.2.5-point option: The point would cost (2.5%)($145,000) $3,625. They would save ½% on
their rate, or roughly (½%)($145,000) $725 per year. The payback period is $3,625/$725
5 years.Harold and Olivia may want to take the payback period into account when choosing
between these options. As it happens, over the full term of the mortgage, they would actu-
ally save much more money with the 2.5-point option (you can verify this by calculating
the payments at each rate and then comparing the totals paid over 30 years). However, very
few 30-year mortgages actually last 30 years. It is likely that they will refinance their loan,
sell the house, or pay off the loan early, even if they are not thinking about doing any of
those things right now. The payback period can help them evaluate just how long they need
to stay put with the loan to break even on paying the points. They may choose the 0.5-point
option over the 2.5-point one, or even forego paying points and accept the higher 8^1 ⁄ 4 %, if
they are concerned that things may change in less than the 5-year payback period.(^3) For more information on points, see Chapter 10, Section 10.2.
14.2 The Payback Period Method 575