How much is a shower?

December 29, 2011
By

(This article was first published on factbased, and kindly contributed to R-bloggers)

After looking at my heating expenses, I turned to the costs for water heating. For some time, I looked at my water meter before and after taking a shower or a bath. Quite often, I forgot one or the other measurement, but I collected about 40 observations. Here is what they look like:

The data suggest that for a shower, it takes between 17 and 26.5 liters hot water and between 11 and 16.5 liters cold water. For a bath, it is 60 to 77 liters hot water and 24 to 32.5 liters cold water. (The numbers refer to the 25% and 75% percentiles, respectively.) The larger share of cold water for a shower makes sense, since I use cold water at the end of the shower for its “invigorating effect”.

Multiplied with the average costs, as charged by my landlord the last three years, a bath takes 0.94 to 1.22 EUR and a shower costs 0.29 to 0.45 EUR (again, first and third quartiles). So taking a shower for 0.50 EUR at the fitness club is not optimal, but also not very expensive.

There are water saving shower heads for 30 EUR. It is advertised that such a shower head uses 6.5 liter per minute instead the usual 15 to 16 liters per minute. I believe 15 liters per minute is too much. So let’s assume I save 3.5 liters per minute or (using the median water use of the data) 12 liters per shower. Is it cost-efficient?

Twelve liters less per shower at 10.5 EUR/cbm means a saving of 0.126 EUR per shower. I assume 20 showers a month. This is tentative, since with this assumption the costs sum up to 70 EUR a year for hot water while my bills amount in average to 110 EUR total costs for hot water. So the new shower head saves 20*0.126=2.52 EUR per month.

Let’s calculate the payback period. With an interest rate of 4% p.a. and 5 years expected serviceable life the monthly gain calculates to

2. 52 - 30 * 0. 04 / 12 - 30 / (5 * 12) = 1. 92

so after 30 / 1. 92 = 16 months, the investment is repaid. This seems acceptable. But just to be sure, let’s calculate the internal rate of return, too. In excel, there is a function IRR for this procedure, which is implemented in three lines in R. For convenience, the irr function is stored in the pft package. The result is 8.3% which seems decent.

Just for reference, here comes the R code for the plot and the irr function:

Read more »

To leave a comment for the author, please follow the link and comment on his blog: factbased.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...



If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Comments are closed.