Question

You’ve been hired as an analyst by Abigail’s Trees to do a feasibility study of starting a Chestnut tree farm. Marketing research suggests Abigail’s Trees can sell 25,600 units per year at $62.50 net cash flow per unit for the next 5 years. The appropriate discount rate is 10% and the required initial investment is $5 million.

a. What is the base-case NPV?

b. Assume there is a 50% probability that the project will be very successful and produce net cash flows of $4.2 million per year and a 50% probability it will produce net cash flows of $-1 million per year. If the project generates $-1 million in cash flows, it will be abandoned after year 1. What is the revised NPV? Hint: use a decision tree.

c. What is the value of the option to abandon?

Answer 1

(a)

Annual cash flow = 25600 $62.50 = $1,600,000

Initial investment = $5,000,000

NPV = Present value of cash inflow - initial investment

=[1,600,000/(1+0.10) +1,600,000/(1+0.10)² +1,600,000/(1+0.10)³ +1,600,000/(1+0.10)⁴ +1,600,000/(1+0.10)⁵] - 5,000,000

= 6,065,258.83 - 5,000,000

= $1,065,258.83

(b)

Revised NPV

= 0.5 [4,200,000/(1+0.10) +4,200,000/(1+0.10)² +4,200,000/(1+0.10)³ +4,200,000/(1+0.10)⁴ +4,200,000/(1+0.10)⁵] +

0.5 [-1,000,000/(1+0.10)] - 5,000,000

= 0.5 15,921,304.43 + 0.5 (-909090.91) - 5,000,000

= 7,960,652.22 - 454,545.46 - 5,000,000

= $2,506,106.76

(c) Value of Abandonment Option = Revised NPV - Original NPV

= $2,506,106.76 - $1,065,258.83

= $1,440,847.93