The president of ChemTech is trying to decide whether to start a new product line or purchase a small company. It is not financially possible to do both. To make the product for a 3-year period will require an initial investment of $250,000. The expected annual cash flows with probabili­ties in parentheses are $75,000 (0.5), $90,000 (0.4), and $150,000 (0.1). To purchase the small company will cost $450,000 now. Market surveys indicate a 55% chance of increased sales for the company and a 45% chance of severe decreases with an annual cash flow of $25,000. If decreases are experienced in the first year, the company will be sold immediately (during year 1) at a price of $200,000. Increased sales could be $100,000 the first 2 years. If this occurs, a deci­sion to expand after 2 years at an

Question

additional investment of $100,000 will be considered. This expansion could generate cash flows with indi­cated probabilities as follows: $120,000 (0.3), $140,000 (0.3), and $175,000 (0.4). If expansion is not chosen, the current size will be maintained with anticipated sales to continue. Assume there are no salvage values on any investments. Use the description given and a 15% per year return to do the following:

(a) Construct a decision tree including all values and probabilities.
(b) Determine the expected PW values at the “expansion/no expansion” decision node after 2 years provided sales are up.
(c) Determine what decision should be made now to offer the greatest return possible for ChemTech.
(d ) Explain in words what would happen to the expected values at each decision node if the planning horizon were extended beyond 3 years and all cash flow values continued as forecasted in the description.

Answer 1

(a) Construct the decision tree



(b) At D2, compute PW of cash flows and E(PW) using probability values.



Expansion option



(PW for D2, $120,000) = –100,000 + 120,000(P/F,15%,1) = $4352

(PW for D2, $140,000) = –100,000 + 140,000(P/F,15%,1) = $21,744

(PW for D2, $175,000) = $52,180



E(PW) = 0.3(4352 + 21,744) + 0.4(52,180) = $28,700



No expansion option



(PW for D2, $100,000 = $100,000(P/F,15%,1) = $86,960

E(PW) = $86,960

Conclusion at D2: Select no expansion option



(c) Complete rollback to D1 considering 3 year cash flow estimates.



Produce option, D1



E(PW of cash flows) = [0.5(75,000) + 0.4(90,000) + 0.1(150,000](P/A,15%,3)

= $202,063

E(PW or produce) = cost + E(PW of cash flows)

= -250,000 + 202,063

= $-47,937



Buy option, D1



At D2, E(PW) = $86,960

E(PW for buy) = cost + E(PW of sales cash flows)

= -450,000 + 0.55(PW sales up) + 0.45(PW sales down)

PW Sales up = 100,000(P/A,15%,2) + 86,960(P/F,15%,2)

= $228,320

PW sales down = (25,000 + 200,000)(P/F,15%,1)

= $195,660



E(PW for buy) = -450,000 + 0.55 (228,320) + 0.45(195,660)

= $-236,377



Conclusion: E(PW for produce) is larger than E(PW for buy); select

produce option.



Note: Both returns are less than 15%, but the return is larger for

produce option.



(d) The return on the initial investment would increase, but it would increase faster for the produce option.