On this question i know the answer is D but I do not know how they got to that answer can anyone help?

Texas Wildcatters Inc. (TWI) is in the business of finding and

developing oil properties, and then selling the successful ones to

major oil refining companies. TWI is now considering a new potential

field, and its geologists have developed the following data, in

thousands of dollars.

t = 0

. A $400 feasibility study would be conducted at t = 0. The results

of this study would determine if the company should commence drilling

operations or make no further investment and abandon the project.

t = 1

. If the feasibility study indicates good potential, the firm

would spend $1,000 at t = 1 to drill exploratory wells. The best

estimate is that there is an 80% probability that the exploratory wells

would indicate good potential and thus that further work would be done,

and a 20% probability that the outlook would look bad and the project

would be abandoned.

t = 2

. If the exploratory wells test positive, TWI would go ahead and

spend $10,000 to obtain an accurate estimate of the amount of oil in

the field at t = 2. The best estimate now is that there is a 60%

probability that the results would be very good and a 40% probability

that results would be poor and the field would be abandoned.

t = 3

. If the full drilling program is carried out, there is a 50%

probability of finding a lot of oil and receiving a $25,000 cash inflow

at t = 3, and a 50% probability of finding less oil and then only

receiving a $10,000 inflow.

Since the project is considered to be quite risky, a 20% cost of capital

is used. What is the project's expected NPV, in thousands of dollars?

a.

$336.15

b.

$373.50

c.

$415.00

d.

$461.11

e.

$507.22