Bear in mind that if joining a tour is your option, travel in pair is highly recommended, else single supplement fee required when you travel solo. So for fair comparison, except for hotel room, you need to multiply all by 2 because tour package is based on 2 persons sharing a room.
Using the tour package itinerary you shall check the price of all component following its level / class declared in a package. Eg., if the tour package offers you a room in Hyatt Hotel, try to find the cheapest rate in Hyatt Hotel. Then sum up all the rates (tickets, hotel, places of interest, entry tickets, and add also the local transport expenses). If you found that your calculation is roughly similar with the price offered by tour operator, it means that you are able to save some. If you found that your calculations is lower, it means that you should be able to save even much more.
In most cases you can arrange your own trip and customize it to suit you preferences and budget. But Not all things can be self-arranged by traveler. For some special cases, you have no option other than joining a tour group due to access issue or transportation matters.
In Chiang Mai you need to join a tour group to visit the Long Neck Village, because they only allow visitations with local / permitted guide. In San Fransisco, you need to join a group tour since only authorized boat may dock to Alcatraz island. In some destination, special transportation mode is required (eg. 4 wheel drive car, boat, etc) then it’s wiser to share the transfer with a group of people, a.k.a. join a tour group. In case of small boat for small group of people you may rent the boat for your own (eg. a small boat in Varanasi or Bako National Park).
Despite in very rare situations, finding cheaper tour package (comparing with self arrangements) is possible because tour company works incorporated with many other related business partner.
However your (calculations) effort shall not be in vain. It’s a bit about stretching your dollar, but above all this method grant you a position of a confident buyer — you know what and why you buy. You confidently know what to do: to purchase a package or stick with your own.
