The formula for Black-Scholes is: C = SN (d1) -- X (e-rt) N (d2)

In this case, S = 432, X = 235, r = 3.7%, t = 43 days.

D1 = 2.23, so N (d1) = .9871; D2 = 1.95, so N (d2) = .974. Therefore C =

432(.9871) -- 235 (.99559)(.974) = 189p

ii) a) The annualized volatility of Tate & Lyle is calculated by the square root of time rule. Thus = .8177(?250) = 12.92%

The continuously generated risk free rate is the logarithm of the nominal risk free rate. In this case, the continuously generated risk free rate is R= ln (1+3.7) = 3.6332%

b) There are two main reasons for the differences between the firm's observed equity volatility and the volatility of its underlying revenue generation. One is that stock prices are forward looking, while revenue generation is backward looking. Market sentiment towards the company can be impacted by its past performance, but the correlation between the two will always be imperfect.

Another key difference is that revenue generation does not translate evenly into equity for shareholders. The firm's capital structure, its operating costs, its taxation rates and a number of other variables all impact on the degree to which revenues flow through to shareholders. The market only measures the value of the equity, not the value of the entire firm.

c) To account for the effects of the dividend, the current share price must be reduced by the amount of the expected dividend. In this case, the expected dividend is 2.268p, so the price should be set to 420.73.

Thus, we have 420.73(.584683) - 423 (177.106)

The price of a call option therefore is 68.83p.

Using put-call parity,...

To calculate the credit score, we tabulate the following inputs:
F equals 3999 * 1.7607 = 7041. .0011F = 7.745

= total income / total assets; therefore 3553/3999 = 0.888, so 5.13 ? equals 4.55.

The debt status for Tate & Lyle is 0, because the debt is unsubordinated, according to the 2008 Annual Report. This value therefore is 0.

Gearing is 0.28, to 2.85*L = 0.804

Interest cover is 328 / 86 = 3.81, so .007 * 3.81 = 0.026

The firm's beta is .8177, so .87B = .711

Unsystematic risk is assumed to be .0705. Thus, 2.9 (0.0705) = .20445

The score for Lyle & Tate therefore is

5.67+ 7.745 + 4.55 -- 0 - .804 - .026 + .711 - .20445 = 16.64

This gives the company a AAA score.

ii. The additional debt capacity would impact the gearing ratio. The gearing ratio that would bring this company down below 5.19 would be 4.017, all other things being average. Of course, such a rate of gearing would have an impact on the interest cover ratio as well.

iii. The main limitation of this type of modeling for considering risk is that it is heavily oriented towards firm size. Tate & Lyle is a large company with low debt and as such, receives a high credit score based on this model. While this seems reasonable, it is unreasonable that the company could have four times the long-term debt to assets and still have a AAA rating. Such a firm would likely be insolvent. This model is useful for reasonably small companies, but places far too much emphasis on firm size.