21 years of age with an obvious v shape hair loss! Can FUE be an option for couple of sessions if donor area is thick?

It's important to have your hair loss evaluated by an experienced doctor.  Then your hair loss needs to be medically managed, stabilized, and then you can discuss surgical options.  Surgery should never be the first choice.

If you have genetic hair loss in a "V" pattern sometime referred to a Norwood 3, you may be a hair transplant candidate.  But you would need to see a doctor for a proper exam.

Considering Propecia at your age is
reasonable as this can help to thicken your current hair and retard/prevent
future hair loss. It is not unusual to
see some shedding after starting this medication, but this is a temporary
phenomenon. I would not advise a
surgical procedure at your age. Your
pattern and rate of hair loss is unpredictable at this time, and it is best to
wait until you are older before considering a surgery.

It's great you've started finasteride (Propecia). It is quite normal to get a bit more loss in the first 6 weeks of using it.Hair comes from mom's side and dad's side. We might resemble on parent more than another but genetics most certainly comes from both sidesMost men at 21 have thick donor areas - even those who go on to be quite bald. At 21 it would simply be a guess as to what your future hair loss patterns will be.Hair transplants are rarely rarely a good option before 25. It is important to understand how you will do on finasteride (Propecia) and also understand what sort of progression you will have (if any). I know it feels like a good idea to consider a transplant, but it's probably not.

It is not a great idea to get a hair transplant at your age and at the very beginning of your hair loss. Hair loss is progressive and a hair transplant is permanent. You may end up with a ring of hair around your head and baldness in the center if you were to get a transplant. It is important to start preventative measures. Propecia is a good step. You could also try vitamins and certain shampoos depending on your specific hair loss. You need to get the hair loss under control before considering a hair transplant. FUE or strip can be an option once these measures are taken. It would be best to visit a doctor that specializes in hair loss so that they can examine your scalp, determine the cause of your hair loss, and then come up with a treatment plan customized to you.  

at age 21 you are too young to consider for hair transplant. Its important to wait till the hair loss stabilizes and can reconsider transplant by mid to late 20's

Yes, it sounds like you are a good candidate for the FUE procedure that I do. I use the back and sides of the hairline which needs to be buzz cut(but rather fashionable). We can usually transplant about 2000-2500 grafts. It takes about 6+ hours in our certified operating room and is done mostly under a local anesthetic. The price is about $6 per graft. The donor area grows in quite quickly but it takes time(months) for the hair to grow in.

You need to see a doctor. The change from a concave hairline to a V shaped hairline is the maturing effect of hairline in most men that occurs between ages 20-29. A doctor specializing in this field will tell you if that is what is happening to you. 

Hair transplant is not recommended until the cause of hair loss is established. At this time it is a good idea to stay on a medical regiment routine to slow down the progression.  However you can visit with a hair restoration specialist to get evaluated and come up with a comprehensive plan if your hair loss continues.