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

B2c. Option to delay or defer 5 / 7

Syllabus B2c)

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

Option to delay or defer

The key here is to be able to delay investment without losing the opportunity, creating a call option on the future investment.

Illustration

MMC is considering whether to undertake the development of a new computer game based on an adventure film due to be released in 24 months. 

However, at present, there is considerable uncertainty about whether the film, and therefore the game, is likely to be successful. 

MMC has forecast the following PV of cash flows:

Year Current 1 2 3 4 5 6
PV (11%)($) -7m -6.31m -28.42m 18.28m 11.86m 5.93m 2.68m

The company will require $35 million for production, distribution and marketing costs at the start.

The relevant cost of capital for this project is 11% and the risk free rate is 3•5%.

MMC has estimated the likely volatility of the cash flows at a standard deviation of 30%.

Required:

Estimate the financial impact of the directors’ decision to delay the production and marketing of the game.

Solution

  1. Calculate NPV

    Net Present Value = $(2•98 million) 

    On this basis the project would be rejected.

  2. Present value of project’s positive cash flows discounted to current day:

    $18•28m + $11•86m + $5•93m + $2•68m = $38•75m

  3. Identify variables:

    Current price (Pa) = $38•75m
    Exercise price (Pe) = $35m
    Exercise date = 2 years
    Risk free rate = 3•5%
    Volatility = 30%

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

    d1 = [ln(38•75/35) + (0•035 + 0•5 x 0•30^2) x 2]/(0•30 x √2) = 

    d1 = (0.10178 + 0.16) / 0.42426 = 

    d1 = 0•6170

  5. Calculate d2 = d1 - s√t

    d2 = 0•6170 – (0•30 x √2) = 0•1927

  6. Using the Normal Distribution Table provided

    N(d1) = 0•5 + 0•2291 + 0•7 x (0•2324 – 0•2291) = 0•7314
    N(d2) = 0•5 + 0•0753 + 0•3 x (0•0793 – 0•0753) = 0•5765

  7. Value of option to delay the decision 

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

    = 38•75 x 0•7314 – 35 x 0•5765 x e^(–0•035 x 2) 
    = 28•34 – 18•81 = $9•53m

  8. Overall value of the project = $9•53m – $2•98m = $6•55m

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