Here is the problem:Q$19.$ We solve the problem backwards using the replicating portfolio technique from class.

At date two. The NPV of investment in the up$-$up state is $7\mathrm{.}75-4\mathrm{.}6=3\mathrm{.}15,$ in the

up$-$down state it is $6\mathrm{.}5-4\mathrm{.}6=1\mathrm{.}9,$ in the down$-$up state it is $4-4\mathrm{.}6<mn\; id="EditorElement\_2430779">0</mn>$ so you wont

execute the option, and in the down$-$down state it is $8-4\mathrm{.}6=3\mathrm{.}4.$ Therefore, we invest

at date two as long as we aren't in the down$-$up state.

At date one. The value at date one of delaying investment until date two is given in

the tree below. The value of delay in the upstate at date $1$ is $2\mathrm{.}612,$ which exceeds the

value from investing $7-4\mathrm{.}8=2\mathrm{.}2.$ Therefore, we delay investment at date one in the

up state.In the down state, the value of delaying is $1\mathrm{.}264$ while the value from direct execution

is $7-4\mathrm{.}8=2\mathrm{.}2.$ As a result, it is optimal to invest in the down state at date one.

At date zero. The value from direct investment is $7\mathrm{.}4-5=2\mathrm{.}4$ while the value of

delaying is $2\mathrm{.}36.$ Therefore, it is optimal to invest at date zero.

To conclude, at date zero we investment. The NPV of this investment opportunity is

$2\mathrm{.}4.$

The problem and solution is attached. I understand how to calculate the NPV$$s but not the value of delaying investment at date $1($up$-$state: $2\mathrm{.}612,$ down$-$state: $1\mathrm{.}264)$ and date $0(2\mathrm{.}36)$