A NON-DIVIDEND-PAYING STOCK IS CURRENTLY TRADING AT USD 40 AND HAS...
11.
A non-dividend-paying stock is currently trading at USD 40 and has an expected return of 12% per year. Using
the Black-Scholes-Merton (BSM) model, a 1-year, European-style call option on the stock is valued at USD 1.78.
The parameters used in the model are:
N(d
1
) = 0.29123
N(d
2
) = 0.20333
The next day, the company announces that it will pay a dividend of USD 0.5 per share to holders of the stock
on an ex-dividend date 1 month from now and has no further dividend payout plans for at least 1 year. This
new information does not affect the current stock price, but the BSM model inputs change, so that:
N(d
1
) = 0.29928
N(d
2
) = 0.20333
If the risk-free rate is 3% per year, what is the new BSM call price?
a.
USD 1.61
b.
USD 1.78
c.
USD 1.95
d.
USD 2.11
Correct Answer: c
Rationale:
The value of a European call is equal to S * N(d
1
) – Ke
-rT
* N(d
2
), where S is the current price of the stock.
In the case that dividends are introduced, S in the formula is reduced by the present value of the dividends.
Furthermore, the announcement would affect the values of S, d
1
and d
2
. However, since we are given the new
values, and d
2
is the same, the change in the price of the call is only dependent on the term S * N(d
1
).
Previous S * N(d
1
) = 40 * 0.29123 = 11.6492
New S * N(d
1
) = (40 – (0.5 * exp(-3%/12)) * 0.29928 = 11.8219
Change = 11.8219 – 11.6492 = 0.1727
So the new BSM call price would increase in value by 0.1727, which when added to the previous price of 1.78 equals