Question

A project is worth $18 million today. One year from today, the project will be worth $22 million with high demand and $14 million with low demand. It will also be possible to sell the project off for $16 million one year from today. Using risk neutral probabilities, which of the following is closest to the value of the abandonment option if the risk-free rate is 4% per year?

1. $0.79 million
2. $1.58 million
3. $2.71 million
4. $3.45 million

Answer 1

Answer - Option A is correct 0.79 million

Workings

Step -1 calculation of risk neutral probabilities

Risk neutal probability (p) = r - d / u - d

where

r = rate of interest = 1.04

d = down factor = 14/18 = 0.777 ............................ (Project worth when demand is low / Project worth today)

u = up factor = 22/18 = 1.222 ....................... (Project worth when demand is high / porject worth today)

p = 1.04 - 0.7777 / 1.2222 - 0.7777 = 0.263 / 0.445 = 0.59 ........................ (probability of up move)

(1-p) = 0.41 ............................. (probability of down move)

Step 2 - Calculation of present value expected profit without abandonment

Scenario	Worth of Project after 1 year (A)	Profit (Worth of project after 1 year - Worth of project today)	Risk neutral Probability	Expected Profit without abandonment	Present Value factor (1/1.04)	Present value of expected profit without abandonment
High Demand	22	4	0.59	2.36	0.96	2.27
Low Demand	14	-4	0.41	-1.64	0.96	-1.58
						0.69

Therefore present value of expected profit without abandonment = 0.69

Step 3 - Calculation of present value expected profit with abandonment

If we have the abandonment option, in the case of low demand scenario we will sell the project at the end of year 1 at $ 16 million

Thereafter we will calculate the present value of expected profit in the same manner as calculated in step 2 above

Scenario	Worth of Project after 1 year (A)	Profit (Worth of project after 1 year - Worth of project today)	Risk neutral Probability	Expected Profit with abandonment	Present Value factor (1/1.04)	Present value of expected profit with abandonment
High Demand	22	4	0.59	2.36	0.96	2.27
Low Demand (Project sold for 16 million)	16	-2	0.41	-0.82	0.96	-0.79
						1.48

Therefore present value of expected profit with abandonment = 1.48

Step 4 - value of abandonment optioin

Value of abandonment option = Step 3 - Step 2

Value of abandonment option = 1.48 - 0.69 = 0.79 million