Question

A single stock futures contract on a nondividend-paying stock with current price $140 has a maturity of one year.

a. If the T-bill rate is 4.4%, what should the futures price be? (Round your answer to 2 decimal places.)

Futures price            $

b. What should the futures price be if the T-bill rate is still 4.4% and the maturity of the contract is three years? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Futures price            $

c. What if the interest rate is 5.7% and the maturity of the contract is three years? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Futures price            $

Explanation:

a.

F₀ = S₀(1 + r_f) = $140 × 1.044 = $146.16

b.

F₀ = S₀(1 + r_f)^T = $140 × (1.044)³ = $159.31

c.

F₀ = S₀(1 + r_f)^T = $140 × (1.057)³ = $165.33

Answer 1

(a)

Future price formula = Spot rate * (1 + Risk free rate)^n

maturity (n)= 1 year

Spot rate = 140

risk free rate= 4.40%

So, future price = 140*(1+4.4%)^1

146.16

So, future price of contract should be $146.16

(b)

maturity (n)= 3 year

Spot rate = 140

risk free rate= 4.40%

So, future price = 140*(1+4.4%)^3

159.3050458

So, future price of contract should be $159.31

(b)

maturity (n)= 3 year

Spot rate = 140

risk free rate= 5.70%

So, future price = 140*(1+5.7%)^3

165.330507

So, future price of contract should be $165.33