a) Both Directors are correct to a point but are failing to see the whole picture.

The Marketing Director is correct in her interpretation of the calculated NPV. The NPV can normally be interpreted as showing the impact of a project on shareholder wealth, so a negative NPV would indicate that the investment would erode shareholder value and should thus be rejected.

The Finance Director (FD) is correct to point out a weakness of conventional NPV analysis. High uncertainty is usually reflected in a higher discount rate and hence a lower NPV. However, greater uncertainty will usually result in higher option values, so the FD is correct to suggest that option values must be incorporated and that TK has an option to delay investment, giving a call option.

The FD is wrong to suggest that ignoring options is the only weakness of NPV. A more complete analysis would also try to incorporate non-financial factors such as the possible implications for TK‟s image with alcoholic research laboratories (targeting the younger generation). Some investors and customers may object to this link and hence future sales would be compromised.

b) Using the Black-Scholes model for European call options (₦million)

 Time, t = 1  S0 = PV of future cash flows = 4,500  E = the exercise price = cost of investment = 250 + 4,500 = 4,750  Interest rate = 0.05  Volatility = 0.35

d1 =

In S0

E + (r + 0.5σ2)T

σ T

= In 4500/4750 + 0.05 + 0.5 × 0.352 1

0.35 × 1

= 0.1634

d2 = d1 − σ T = 0.1634 −0.35 × 1 = −0.1866

N d1 = 0.5 + 0.0636 + 0.34 0.0675 −0.0636 = 0.5649

N d2 = N −0.1866 = 1 −N 0.1866

= 1 − 0.5 + [0.0714 + 0.66 0.0753 −0.0714 ]

= 1 −0.5740 = 0.4260

Inputting data into call formula:

C0 = S0 N d1 −Ee−rtN d2

= 4,500 0.5649 − 4750e−0.05 1 × 0.426 = 617.24

Recommendation The high value of the call option would suggest that the offer of a license should be accepted.                                                                                                                                                                                                                                                                                  c)

The Black – Scholes model was developed for European options. As production could commence at any time during the 1 year period the option is an American option rather than a European option.

It can be argued that, where there is no dividend payable and where time value still exists, it is worthwhile holding an American option to expiry and thus the valuation as a European call is valid.

In this case, however, it is likely that investment would be commenced (i.e. the call option exercised) as soon as the forecast NPV became positive due to revised forecasts. The valuation as a European call would thus give a lower limit on the value of the option to delay.