AFMP4
Syllabus B. Advanced Investment Appraisal B2. Application of option pricing theory in investment decisions

# B2c. Option to abandon 6 / 7

### Syllabus B2c)

Assess, calculate and advise on the value of options to delay, expand, redeploy and withdraw using the BSOP model.

### Option to abandon

An abandonment options is the ability to abandon the project at a certain stage in the life of the project.

Whereas traditional investment appraisal assumes that a project will operate in each year of its lifetime, the firm may have the option to cease a project during its life.

Abandon options gives the company the right to sell the cash flows over the remaining life of the project for a salvage/scrape value therefore like American put options.

Where the salvage value is more than the present value of future cash flows over the remaining life, the option will be exercised.

#### Illustration

Bulud Co offered Chmura Co the option to sell the entire project to Bulud Co for \$28 million at the start of year three. Chmura Co will make the decision of whether or not to sell the project at the end of year two.

A standard deviation is 35%
The return on short-dated \$ treasury bills of 4%.

PV of the cash flow:

 (all amounts in \$, 000s) year 1 2 3 4 5 present values (\$ 000s) 1496.9 4938.8 9946.5 7604.2 13,062.9

NPV of project = \$(451,000)

Required

An estimate of the value of the project taking into account Bulud Co’s offer.

#### Solution

1. Calculate NPV

NPV of project = \$(451,000)

On this basis the project would be rejected.

2. Present value of underlying asset (Pa) = \$30,613,600 (approximately)

(This is the sum of the present values of the cash flows foregone in years 3, 4 and 5)

3. Identify variables:

Current price (Pa) = \$30,613,600
Exercise price (Pe) = \$28,000,000

Exercise date = 2 years
Risk free rate = 4%
Volatility = 35%

4. Calculate d1 = (ln (Pa/Pe) + r + 0.5^2) t) / s√t

d1 = [ln(30,613•6/28,000) + (0•04 + 0•5 x 0•35^2) x 2]/[0•35 x 21/2] = 0•589

5. Calculate d2 = d1 - s√t

d2 = 0•589 – 0•35 x √2 = 0•094

6. Using the Normal Distribution Table provided

N(d1) = 0•5 + 0•2220 = 0•7220
N(d2) = 0•5 + 0•0375 = 0•5375

7. Call value

= Pa N(d1) - Pe N(d2) e^(-rt)

= \$30,613,600 x 0•7220 – \$28,000,000 x 0•5375 x e^(–0•04 x 2) = approx. \$8,210,000

8. Put value = c - Pa + Pe e^(-rt)

= \$8,210,000 – \$30,613,600 + \$28,000,000 x e^(–0•04 x 2) = approx. \$3,444,000

9. Net present value of the project with put option = \$3,444,000 – \$451,000 = approx. \$2,993,000

Since the project yields a positive net present value it would be accepted.