Common Base amp gain problem
At 1.44mA the transistor has a Re of 25/1.44 = about 17 ohms.

To this you must add the 50 ohm of R5, which you forgot ;)

So the gain would be 5000/(50+17) = 74.

Common base amplifiers have very low input impedance, and it depends on bias current, so the gain will depend on the output impedance of the source, which might also not be a perfect 50R resistor, but maybe the output impedance of a semiconductor...

If the RF source is connected by a long coax, then it gets a little bit more subtle. The RF source would have 50R output impedance, and we must terminate the cable on the transistor's side by adding a (50-17)=33R resistor. So the gain would be different, yet again.

Also we have not taken into account the imperfections of this transistor. Its datasheet fT is around 300 MHz... at 10mA, with a rather high Vce, and without a collector load. 

At 1.4mA, and with the very low Vce used here, the figure will be different, the transistor will be slower. Its hFe will be quite low, and it will require a non-negligible base current.

Also, the collector-to-base capacitance is multiplied by Miller effect, which increases base current.

You have connected the base to a perfect simulated capacitor, which has negligible impedance at 27MHz. However, the transistor has an internal base resistance, which combined to base current, reduces your gain.

Also, the real capacitor you used in implementing the circuit will not be perfect. It will have ESL and ESR...

...and the output impedance of your amp is 5k which is very inconvenient  at 27MHz, anything you connect there will have capacitance and suck all of the signal. This is why you need an emitter follower or buffer on the output.

Anyway, 


If you want to convert your 120mVpp sine into a square wave google "clock conversion sine to square" and you will find schematics.
If you want to keep your sine but amplify it, I would suggest using a canned RF amplifier like these , there are many such chips available for low prices (less than 50 cents) and all the complicated design challenges have been handled by the manufacturer... all you have to do is not screw up the supply/biasing/bypassing.
You can also use a highspeed opamp, but they are finicky about layout.
There are also fixed-gain "video amplifiers" which will solve your problem, basically they're opamps with feedback resistors included in the package.
Or you can roll your own, but you will need more gain stages, you can't 
get a gain of 200 at 27 MHz with a single transistor mounted on a PCB.


Also here's a primer on capacitors at HF:

The inductance of the cap is the same as a piece of wire having the shape of the path taken by the current. Thus, a through-hole capacitor with e=5.08mm between the pins, with the internal foils sitting 2mm above the board, can be modeled as a 5mmx2mm square loop if we close the circuit with a trace on the board below. This loop has an inductance of 9nH.

2pi x 9nH x 27MHz = 1.5 ohms inductive

If the cap has low ESR then you get a LC tank circuit which may resonate, and since it drives the base of your BJT, you just built a Colpitts. It is very easy to unintentionally build an oscillator when combining devices with gain (ie, transistors) and layout parasitics... A transistor whose base is driven by a reactive impedance, without enough real (resistive) impedance in series may create some headaches...

This does not depend on capacitor type, chemistry, etc, only its mechanical construction (you will no doubt guess that axial caps are much worse than radials). 

A leaded ceramic will have the same HF behavior as a modern good quality leaded electrolytic. Same inductance. 

Basically, if you want a low-inductance capacitor, it needs to be low-profile, and lay flat against your ground plane to reduce the loop area. And therefore...



This means MLCC (ceramic) of X7R type for bypassing, or C0G type if you need an accurate value. Or SMD Film caps.

Then you add the inductance of the whole loop, traces, vias, ground plane etc.



So when you see audiophiles adding bypass caps...



Ickkkkkkk.