$3.$ Use the information below to answer the questions that follow concerning the use of decision trees to value a project and real options. Hi Tech Inc. is considering producing a new line of printers designed to produce professional quality digital photographs. It decision process consists of three separate stages.

Stage $1$: At time $0$ conduct an $$80,000$ study of the market potential for the new printer.

Stage $2$: If it appears that a sizable market exist for the machine it will spend $$100,000$ developing prototypes of the printer.

Stage $3$: Depending on the tests of the prototype the firm will either build a high volume machine for a cost of $$50,000$ or not produce any machine. If it does produce a machine there are three possible sets of cash flows generated for each machine. Each set of cash flows is expected to continue in perpetuity. The project is represented in the decision tree below.

t$=0$ t$=1$ t$=2$ t$=3$ to infinity NPV@$10\%$ Prob

$100,000$

$0\mathrm{.}2$

$-50,00040,000$

$0\mathrm{.}80\mathrm{.}6$

$0\mathrm{.}2-7,000$ Use the information below to answer the questions that follow concerning the use of decision trees to value

a project and real options. Hi Tech Inc. is considering producing a new line of printers designed to produce

professional quality digital photographs. It decision process consists of three separate stages.

Stage $1$: At time $0$ conduct an $$80,000$ study of the market potential for the new printer.

Stage $2$: If it appears that a sizable market exist for the machine it will spend $$100,000$ developing prototypes of

the printer.

Stage $3$: Depending on the tests of the prototype the firm will either build a high volume machine for a cost of

$$50,000$ or not produce any machine. If it does produce a machine there are three possible sets of cash flows

generated for each machine. Each set of cash flows is expected to continue in perpetuity. The project is

represented in the decision tree below.

$00$

a$.$ Calculate the expected NPV for the project assuming the correct weighted average cost of capital is $10\%.$

Include the probabilities you use $($show how you set up the problem$)(10$ points$)$

b$.$ How much would the firm be willing to pay for an option to abandon the project if the firm realizes that

the outcome with negative $7,000$ cash flow each year after time $t=3$ is correct? Assume that it must take

the first $-7,000$ then can abandon the project and eliminate any future losses. The firm will also be able to

sell the machine for $$40,000$ tax free $($the $40,000$ would also be received at time $t=3$ points$)$

$-100,000$

$0\mathrm{.}8$

$-80,000$

$0\mathrm{.}2$

$0$

$0\mathrm{.}20$

a$.$ Calculate the expected NPV for the project assuming the correct weighted average cost of capital is $10\%.$ Include the probabilities you use $($show how you set up the problem$)(10$ points$)$

b$.$ How much would the firm be willing to pay for an option to abandon the project if the firm realizes that the outcome with negative $7,000$ cash flow each year after time t $=3$ is correct? Assume that it must take the first $-7,000$ then can abandon the project and eliminate any future losses. The firm will also be able to sell the machine for $$40,000$ tax free $($the $40,000$ would also be received at time t$=3)(10$ points$)$