Question

In: Finance

given: (1)The current price of a stock is 30. (2)A dividend of 1 will be paid...

given:

(1)The current price of a stock is 30.

(2)A dividend of 1 will be paid 6 months from now.

(3)The one-year forward price is 30.9.

Calculate the continuously compounded risk-free annual rate of interest.

Solutions

Expert Solution

Spot Price = 30 | Forward Price = 30.9 | Dividend to be paid 6 months from now = 1

Forward Price formula = Spot rate * ert - Dividend * ert

Let annual risk-free rate be r

Putting values in the formula

=> 30.9 = 30 * er*1 - 1 * er*0.5

Since the equation cannot be solved using Natural log. Hence, trial & error method can be used.

However, I have used Excel's Goal seek to solve the equation, where I change the cell for r and want to set the forward price formula to 30.9

I first set the value for R as 1% to start with the formula, below is how it looked:

Next I used Goal seek for the calculation and below is the screenshot of Goal seek:

Solving the equation, below is the answer I got:

Hence, the annual risk-free rate is 6.24%

jeff jeffy answered 1 year ago
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