Question

Investment Timing Option: Decision-Tree Analysis

Wansley Lumber is considering the purchase of a paper company which would require an initial investment of $300 million. Wansley estimates that the paper company would provide net cash flows of $40 million at the end of each of the next 20 years. The cost of capital for the paper company is 13%.

Should Wansley purchase the paper company? (Answers: Yes or No)

Wansley realizes that the cash flows in Years 1 to 20 might be $31 million per year or $49 million per year, with a 50% probability of each outcome. Because of the nature of the purchase contract, Wansley can sell the company 2 years after purchase (at Year 2 in this case) for $285 million if it no longer wants to own it. Given this additional information, does decision-tree analysis indicate that it makes sense to purchase the paper company? Again, assume that all cash flows are discounted at 13%. (Answers: Yes or No)

Wansley can wait for 1 year and find out whether the cash flows will be $31 million per year or $49 million per year before deciding to purchase the company. If so, when? Because of the nature of the purchase contract, if it waits and purchases, Wansley can no longer sell the company 2 years after purchase. Given this additional information, does decision-tree analysis indicate that it makes sense to purchase the paper company? Again, assume that all cash flows are discounted at 13%. (Answers: It doesn't make sense to purchase the paper company; Yes, it makes sense to purchase the paper company today; No, it makes sense to wait one year before deciding whether to make the acquisition)

Answer 1

First part

Cash flows involved are C0 = $ 300 million and an annual cashflow, C = $ 40 million as annuity over n = 20 years and interest rate = cost of capital = r = 13%

Hence, NPV = - C0 + C/r x [1 - (1 + r)^-n] = -300 + 40/13% x [1 - (1 + 13%)^-20] = -19.01 = - $ 19.01 million

Since, NPV is negative, Wansley should not purchase the paper company. Answer: No; It doesn't make sense to purchase the paper company.

Second part

Case 1: Cash flows involved are C0 = $ 300 million and an annual cashflow, C = $ 31 million as annuity over n = 20 years and interest rate = cost of capital = r = 13%

Hence, NPV = - C0 + C/r x [1 - (1 + r)^-n] = -300 + 31/13% x [1 - (1 + 13%)^-20] = -82.23

Since, NPV is negative, hence there will be no point in conitnuing it after year 2, and hence, Wansley can sell the company 2 years after purchase (at Year 2 in this case) for $285 million

Hence, NPV in this case = NPV1 = -C0 + C/(1 + r) + C/(1 + r)² + Sale value / (1 + r)² = - 300 + 31/(1 + 13%) + 31/(1 + 13%)² + 285 = -25.09

Case 2: Cash flows involved are C0 = $ 300 million and an annual cashflow, C = $ 49 million as annuity over n = 20 years and interest rate = cost of capital = r = 13%

Hence, NPV2 = - C0 + C/r x [1 - (1 + r)^-n] = -300 + 49/13% x [1 - (1 + 13%)^-20] = 44.21

Hence, the decision tree should be:

And hence the expected NPV = p1 x NPV1 + p2 x NPV2 = 50% x (-25.09) + 50% x 44.21 = 9.56 = $ 9.56 million

Since, expected NPV is positive, Wansley should purchase the paper company. Answer: YES;  it makes sense to purchase the paper company today

Third Part

Note that NPV under case 1 was still negative even if the company was sold after year 2. Hence, after waiting for 1 year, if the cash flow turns out to be $ 31 million; Wansley should not purchase the paper company.

However, if the annual cash flo turns out to be $ 49 million, the NPV was positive (case 2) and hence Wansley should purchase the paper company then.

hence, the ideal path will be to wait for a year and then decide depending upon the cashflow.

Hence, the answer should be: No, it makes sense to wait one year before deciding whether to make the acquisition)