LOS b: Calculate and interpret the price and the value of an equity forward contract, assuming dividends are paid either discretely or continuously.

Q1. Calculate the no-arbitrage forward price for a 90-day forward on a stock that is currently priced at $50.00 and is expected to pay a dividend of $0.50 in 30 days and a $0.60 in 75 days.  The annual risk free rate is 5% and the yield curve is flat.

A)   $50.31.

B)   $49.49.

C)   $48.51.

Q2. An index is currently 965 and the continuously compounded dividend yield on the index is 2.3%. What is the no-arbitrage price on a one-year index forward contract if the continuously compounded risk-free rate is 5%.

A)   991.4.

B)   991.1.

C)   987.2.

Q3. Jim Trent, CFA has been asked to price a three month forward contract on 10,000 shares of Global Industries stock. The stock is currently trading at $58 and will pay a dividend of $2 today. If the effective annual risk-free rate is 6%, what price should the forward contract have? Assume the stock price will change value after the dividend is paid.

A)   $56.85.

B)   $56.82.

C)   $58.85.

Q4. The value of the S& 500 Index is 1,260.  The continuously compounded risk-free rate is 5.4% and the continuous dividend yield is 3.5%.  Calculate the no-arbitrage price of a 160-day forward contract on the index.

A)   $562.91.

B)   $1,310.13.

C)   $1,270.54.

Q5. A stock is currently priced at $110 and will pay a $2 dividend in 85 days and is expected to pay a $2.20 dividend in 176 days. The no arbitrage price of a six-month (182-day) forward contract when the effective annual interest rate is 8% is closest to:

A)   $110.00.

B)   $110.06.

C)   $110.20.

LOS b: Calculate and interpret the price and the value of an equity forward contract, assuming dividends are paid either discretely or continuously. fficeffice" />

Q1. Calculate the no-arbitrage forward price for a 90-day forward on a stock that is currently priced at $50.00 and is expected to pay a dividend of $ffice:smarttags" />0.50 in 30 days and a $0.60 in 75 days.  The annual risk free rate is 5% and the yield curve is flat.

A)   $50.31.

B)   $49.49.

C)   $48.51.

Correct answer is B)

The present value of expected dividends is: $0.50 / (1.05^{30 / 365}) + $0.60 / (1.05^{75 / 365}) = $1.092

Future price = ($50.00 ? 1.092) × 1.05^{90 / 365} = $49.49

Q2. An index is currently 965 and the continuously compounded dividend yield on the index is 2.3%. What is the no-arbitrage price on a one-year index forward contract if the continuously compounded risk-free rate is 5%.

A)   991.4.

B)   991.1.

C)   987.2.

Correct answer is A)

FP = S₀ e^-δT (e^RT) = S₀ e^(R-δ)T = 965e^(.05-.023) = 991.4

Q3. Jim Trent, CFA has been asked to price a three month forward contract on 10,000 shares of Global Industries stock. The stock is currently trading at $58 and will pay a dividend of $2 today. If the effective annual risk-free rate is 6%, what price should the forward contract have? Assume the stock price will change value after the dividend is paid.

A)   $56.85.

B)   $56.82.

C)   $58.85.

Correct answer is B)

One method is to subtract the future value of the dividend from the future value of the asset calculated at the risk free rate (i.e. the no-arbitrage forward price with no dividend).

FP = 58(1.06)^1/4 – 2(1.06)^1/4 = $56.82

This is equivalent to subtracting the present value of the dividend from the current price of the asset and then calculating the no-arbitrage forward price based on that value.

Q4. The value of the S& 500 Index is 1,260.  The continuously compounded risk-free rate is 5.4% and the continuous dividend yield is 3.5%.  Calculate the no-arbitrage price of a 160-day forward contract on the index.

A)   $562.91.

B)   $1,310.13.

C)   $1,270.54.

Correct answer is C)

FP = 1,260 × e^{(0.054 ? 0.035) × (160 / 365)} = 1,270.54

Q5. A stock is currently priced at $110 and will pay a $2 dividend in 85 days and is expected to pay a $2.20 dividend in 176 days. The no arbitrage price of a six-month (182-day) forward contract when the effective annual interest rate is 8% is closest to:

A)   $110.00.

B)   $110.06.

C)   $110.20.

Correct answer is B)

In the formulation below, the present value of the dividends is subtracted from the spot price, and then the future value of this amount at the expiration date is calculated.

(110 – 2/1.08^85/365 – 2.20/1.08^176/365) 1.08^182/365 = $110.06

Alternatively, the future value of the dividends could be subtracted from the future value of the stock price based on the risk-free rate over the contract term.

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