source('utils.R')

## rent is in millions:
rent_cost = 2
##rent_cost = 0 # building the grid with this value you will see that you will never harvest

u = 1.2
d = 0.9

r = 0.10

S0 = 5 ## the inital value of the trees (in millions)

R = 1 + r # total return over the next year

q = (R - d)/(u - d)
print(c(u, d, R, q))

n_years = 10

delta_t = 1 ## yearly steps

growth_factor = c(1, 1.6, 1.5, 1.4, 1.3, 1.2, 1.15, 1.1, 1.05, 1.02, 1.01)
sum_growth_factor = cumprod(growth_factor)
print(round(growth_factor, 2))
print(round(sum_growth_factor, 2))

## Build the value lattice:
##
SSpot = make_spot_table(S0, u, d, n_years)
print('Spot (number value) lattice=')
print(round(SSpot, 2))

## Price the "as you like it" option by working backwards:
##
n_years = length(growth_factor)-1
n_steps = n_years+1

LV = matrix(NA, nrow=n_steps, ncol=n_steps) ## the value of the number
Harvest = matrix(NA, nrow=n_steps, ncol=n_steps) ## whether to harvest the number at this node
for( jj in seq(n_years+1, 1, -1) ){
    for( ii in 1:jj ){
	if( jj == (n_years+1) ){ ## the final column/timestep
	    LV[ii, jj] = SSpot[ii, jj] * sum_growth_factor[jj] ## you must cut at the end of the 10th year
	    Harvest[ii, jj] = 1
	}else{
	    cut_trees = SSpot[ii, jj] * sum_growth_factor[jj]
	    rent = -rent_cost + (q*LV[ii, jj+1] + (1-q) *LV[ii+1, jj+1])/R
	    LV[ii, jj] = max(c(cut_trees, rent))
	    if( cut_trees > rent ){
		Harvest[ii, jj] = 1
	    }else{
		Harvest[ii, jj] = 0
	    }
	}
    }
}

print('Lumber value lattice=')
print(round(LV, 2))
print('Cut trees at this node or not')
print(round(Harvest, 2))