Forward Question..Help

[kin28]

Consider an eight-month forward contract on a stock with a price of $98/share. The delivery date is eight months hence. The firm is expected to pay a $1.8/share dividend in four months time. Riskless zero coupon interest rates(continuously compounded) for different maturities are as follows: 6 months 4%, 8 months 4.5%. The theoretical forward price (to the nearest cent) is:

The answer is
e^rt = 98*e^(8/12*4.5%) - 1.83

I could not firgure out 1.83..could some help and explain plz
Thanks

 

[David Harper CFA FRM]

Forward(6,8) = (4.5%*8-4%*6)/(8-6) = 6.0%, such that FV (+8 months) = $1.80*exp(6%*4/12) = $1.836; i.e., growing the $1.80 at the implied forward rate of 6% for the remaining four months.

fwiw, I first tried $1.80*exp(-4%*4/12)*exp(4.5%*8/12) = $1.8303; i.e., 1.80 in four months, discounted to T0, then FV to T+8 months. But realized that assumes the 4 month rate is 4%, but we don't know that ... so growing forward is maybe the only way

 

[kin28]

Another Question..i wonder the answer is wrong..

Assume the spot rate for EUR/USD is 1.05. A US bank pays 5.5% compounded annually for one year for a dollar deposit and a German pays 2.5% compounded annually for one year for a Euro deposit. What is the forward rate for EUR/USD one year from now?

The answer is: 1.05*1.055/1.025 = 1.0807
But why the calculation is not 1.05*1.025/1.055??
is my calculation is wrong..or i get wrong concept