Gladstone Corporation has a plant that can generate a cash flow of $3 million annually. Due to the change of the business environment, the cash flow next year will either increase by 20% or decrease by 20%, with probabilities of 30% and 70%, respectively. Gladstone’s CEO expects the above change to be permanent. The expense to run this plant is $2.5 million per year. The cost of capital for this plant is estimated to be 8% per annum. Gladstone can shut down the plant at a cost of $0.5 million at any time. The value of the option to abandon the plant will be closest to:[Fill in the blank]单项选择题
A
a. $0.8 million.
B
b. $0.5 million.
C
c. $0.1 million.
D
d. $0.2 million.

Question

Gladstone Corporation has a plant that can generate a cash flow of $3 million annually. Due to the change of the business environment, the cash flow next year will either increase by 20% or decrease by 20%, with probabilities of 30% and 70%, respectively. Gladstone’s CEO expects the above change to be permanent. The expense to run this plant is $2.5 million per year. The cost of capital for this plant is estimated to be 8% per annum. Gladstone can shut down the plant at a cost of $0.5 million at any time. The value of the option to abandon the plant will be closest to:[Fill in the blank]单项选择题

A

a. $0.8 million.

B

b. $0.5 million.

C

c. $0.1 million.

D

d. $0.2 million.

BlackTom AI · Accepted Answer

Immediate net cash flow today = $3.0m − $2.5m = $0.5m. The abandonment option lets Gladstone avoid future negative perpetual cash flows (at a cost) after the one-year random permanent shift.

1) Relevant concepts
- Net cash flow = revenue − operating expense.
- Perpetuity value = cash flow / cost of capital.
- Option value = value when firm can optimally abandon − value when it cannot.
- Probabilistic expectation and one-period discounting (cost of capital 8%).

2) Step-by-step reasoning
- Today (year 0) the net cash flow = 0.5m.
- From year 1 onward the gross revenue changes permanently: up 20% (prob 0.3) or down 20% (prob 0.7). So year-1 net flows:
  - Up state: revenue 3×1.2 = 3.6 ⇒ net = 3.6 − 2.5 = 1.1m.
  - Down state: revenue 3×0.8 = 2.4 ⇒ net = 2.4 − 2.5 = −0.1m.

3) Calculations (all intermediate steps)
- Perpetuity values from year 1 in each state:
  - Up: 1.1 / 0.08 = 13.75m.
  - Down: −0.1 / 0.08 = −1.25m.
- Value without abandonment (cannot stop): expected perpetuity at t=1 = 0.3×13.75 + 0.7×(−1.25) = 4.125 − 0.875 = 3.25m. Discount to t=0: 3.25 / 1.08 = 3.009259m. Add year-0 cash 0.5 ⇒ V_no_option = 3.509259m.
- Value with abandonment (can choose at t=1):
  - If up: continue, value at t=1 = 13.75m.
  - If down: abandon immediately, pay 0.5m (better than staying and incurring −1.25m perpetuity).
  - Expected value at t=1 = 0.3×13.75 + 0.7×(−0.5) = 4.125 − 0.35 = 3.775m. Discount to t=0: 3.775 / 1.08 = 3.494444m. Add year-0 cash 0.5 ⇒ V_with_option = 3.994444m.
- Option value = V_with_option − V_no_option = 3.994444 − 3.509259 = 0.485185m ≈ 0.5m.

4) Why the correct answer is correct
Allowing abandonment increases project value by roughly $0.485m because abandonment avoids larger expected losses in the down state; rounding yields $0.5m.

5) Why other choices are wrong
- (a) $0.8m is too large compared with the computed ≈$0.485m.
- (c) $0.1m and (d) $0.2m are too small; they understate the benefit of avoiding the −0.1m perpetual in the down state and the saved expected loss after discounting.