##
## Here we duplicate Figures 12.10 (gold price lattice) and 12.11 (Simplico gold mine) that consider the simplico gold mine.
## okular ../EBook/Investment_Science.djvu -p 353 & 
##
source('../Chapter12/utils.R')

r = 0.1 ## the original example
r = 0.04 ## setting for exercise 8

R = 1 + r ## one-year discount factor

u = 1.2 ## the original example
##u = 1.3 ## setting for exercise 12
p_up = 0.75

d = 0.9
p_down = 0.27

##q = 2/3
q = (R - d)/(u - d)

er = 10000 ## extraction rate (ounces per year)
ec = 200 ## extraction cost (per ounce)

print( ( er*(1719.9 - ec) + q*16.9*1.e6 + (1-q)*12.3*1.e6 ) / R )

S0 = 400 ## current spot price

## Get the grid of gold spot prices:
##
n_years = 10
SSpot = make_spot_table(S0, u, d, n_years)
print('Spot gold price=')
print(round(SSpot, 1))

## Solve for the_value of the mine:
##
n_steps = n_years+1 ## = number of columns = number of years + the initial spot_value
n_rows = n_steps

V = matrix(NA, nrow=n_rows, ncol=n_steps)
for( jj in seq(n_rows, 1, -1) ){
    for( ii in 1:jj ){
        if( jj == n_steps ){ ## the final column/timestep
            V[ii, jj] = 0
        }else{
            pv_profit_from_mining = max( c(er * (SSpot[ii, jj] - ec)/R, 0) )
            if( jj == n_steps-1 ){
                V[ii, jj] = pv_profit_from_mining
            }else{
                V[ii, jj] = pv_profit_from_mining + ( q*V[ii, jj+1] + (1-q)*V[ii+1, jj+1] )/R
            }
        }
    }
}
print(round(V/1.e6, 1))