Question

1. The stock of RUSH Music Enterprises (RUSH) has a current spot price of 100. RUSH stock pays a quarterly dividend of 3.50. The next dividend is payable in 2 months. The continuously compounded risk free interest rate is 5%. Calculate the price of a 9 month Prepaid Forward contract on the stock of RUSH. 2. The R40 Index pays dividends at a continuous rate of 3%. The current price of the R40 Index is 1500. The continuously compounded risk free interest rate is 6%. Calculate the price of a prepaid forward if you receive the Index in eight months. 3. The R30 Index has a current price of 2000. The two year prepaid forward price of the Index is 1900. The risk free interest rate is 8% compounded continuously. Calculate the dividend rate on the Index.

Answer 1

1) With a dividend of $3.5 the dividend yield is 3.5% for the quarter [Dividend/Price]  

Price of prepaid forward contract= Spot rate * E^{(risk free rate-dividend pay out)*9months/12months}

= 100*e^{(5%-3.5%)*0.75}

^{=100*1.0113135 (as per exponential calculator)}

^=$101.131

²⁾

Price of prepaid forward contract= Spot rate * E^{(risk free rate-dividend pay out)*8months/12months}

= 100*e^(6%-3%)*2/3

^=100*e^.02

^{=100*1.02020 (as per exponential calculator)}

^=$102.02

³⁾

Price of prepaid forward contract= Spot rate * E^{(risk free rate-dividend pay out)*time}

1900=2000*e^{(8%-dividend yield)*2years}

1900/2000=e^{(8%-dividend yield)*2years}

Therefore,

ln[1900/2000]=(8%-dividend yield)*2 years

1/2 ln(1900/2000)=8%-dividend yield

8%-1/2 ln(1900/2000)=Dividend yield

8%-1/2 (-0.0512933)=Dividend yield (as per log tables)

8%+2.5647%=Dividend yield

Thus , Dividend yield=10.5647%