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No there is definitely something wrong with it. Why would the hire period be fixed at 12 months? If I do the same thing with the Evans calc for 48 months, the monthly cost is a quarter of what the Cyclescheme one is.
https://www.evanscycles.com/b2b/ride-to-work/savings-calculator
Unless you can only pay it off in a year via Cyclescheme?
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The Cyclesheme calculator is only designed for the case where the salary sacrifice (hire) period is 12 months (which is the default period for the scheme). If you hover over the question mark next to "when do you want to own your package?" (where you select "4 years" or "1 year"), it says: "At the end of your Hire Period you will need to select an Ownership Option. We recommend you choose the 4 year ‘Own it Later’ option as this will increase your savings." This option has an effect on the overall cost (the 1 year option is more expensive). There is no option in the Cyclescheme calculator to vary the salary sacrifice period.
It seems to be working fine. Are you multiplying the "monthly cost to you" by 48 months instead of 12? The hire period is 12 months regardless of whether you select "4 years"(own it later) or "1 year" (own it now) in the calculator. Choosing the "own it later" reduces the ownership fee.