The value of a project is $$100$ and the cost at t$=0$ is $$104.$

The project value follows a binomial model. It could go up to

$$180$ or down to $$60.$ The government posts a guarantee of

$$78$ at time $1.$ What is the value of the option? The

required rate of return is $20\%$ and the risk$-$free rate is $8\%$

per period.