I would suggest that you do not charge anything at all to the potential client because the instant you take money for a shoot, the relationship between you and your friend changes. They become your client proper and their expectation is that you will deliver everything they request. The pressure on you is to deliver and that may cause you to make an error. The strain on your relationship may damage it and you may lose a friend and end up involved in a legal dispute. Taking money for a service implies you are a fit and proper person to provide the service you have charged for and the legal profession will crush you on that ground alone.
As for your fiscal investment... in truth, you have not made any. Your equipment was purchased as an integral part of your leisure time interest in photography. You cannot make any of your clients pay for it. You purchased it for a purpose and you have derived the intended use from it. The potential client owes you no fee on that basis.
You say that you are learning and one of your posting tags clearly states 'beginner'. We are all still learning. It is likely that my own four decades of professional work experience probably trumps your photographic work experience.
You say that you are comfortable in Photoshop CS6. Really? Is compositing your thing? Can you rescue poorly captured images. Could you create automatic actions to extract the best processing out of your images. Are you comfortable with ACR and its RAW file processing quirks? What number of images will you shoot and how long would you expect to take to process say... 100 images?
Will you provide printable images on DVD or will you just sell the images as computer files? What about the copyright in them... Will you keep it or sell it? What sort of colour space will you use to process the images? Have you any idea which printing house will be used to print the images?
Do you know how to arrange the images to print in a specific colour space. Will your pictures be processed in Pantone CMYK or Hexachrome? How much will it cost you to hire a backup camera system and the other possible lenses which you require and don't have... such as a good portrait focal length for example?
What will regulate the agreement between you and your client? Generally, a contract of work to be delivered and the manner it which it will be completed, is the only safe way professionals regulate the manner in which clients receive their work. Delivery time spans and the use of make-up artists and art directors form an important part of many shooting contracts because of the additional costs which they incur.
Can you get an insurance policy which will compensate the client for any messed up images in a one off event? What is one possible solution to you being ill-prepared to undertake a professional shoot is this: you explain to the client that you are an amateur photographer. You are therefore able to reduce the client's expectation by doing this...
You offer to assist by taking a few 'snaps' so your client's expectations remain low. You offer to GIVE the client any images you shoot and which they like. It will give you experience of the professional arena. You do not irritate local professionals by undercutting the going rates. You can ask the client to recommend you if your work turns out to be brilliant. Your client would possibly give you permission to use some of the images on your website.
Alternatively, you could just tell the client that you have insufficient experience to handle such a commission but you can recommend a local photographer, with whom you are friends, and see if you can tag along and shoot a few images. There is a world of difference between shooting a few images because you just want to try something new to see what it produces and shooting images for a person who is providing their dollars to enable you to shoot what they want.
Turning your leisure interest into a business is fraught with peril. Your description of the situation suggests to me that you would be making a mistake on this occasion. Not for nothing do professionals look at a basic minimum kit for professional work... And then duplicate it! So you would need at least two professional quality camera bodies, lenses in all focal lengths from wide-angle through to at least medium telephoto. Filters including polarising and neutral density and speed lights or studio lights and light shaping tools.
The sundries box should have remote controls, screwdrivers, duck tape, background materials and spare batteries. What you would be paid for is the guarantee that you would not fail to deliver the client's requested images. Over a period of one or two years, a professional photographer is able to amortise the cost of carrying so much equipment. It cannot be done by adding the cost of your kit to a single job of work.
If a person fell over and bumped their head on your kit bag, you would need to be covered by some sort of public liability insurance. In the UK, I always carried £5 million worth of public liability insurance. If setting up a portable studio at an event, I was required to do a health and safety risk assessment and then implement measures to mitigate any perceived risks.
I hope this helps. You cannot be an occasional professional and it is entirely wrong, in my view, to take money for a professional job of work; when you have not taken any of the essential steps to guarantee that the outcome of your involvement will guarantee the results for the paying client.