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.