Please focus on question c Please show all work Consider a 1

Please focus on question c. Please show all work.

Consider a 1-year futures contract on an investment asset that provides no income. It costs $2 per unit to store the asset, with the payment being made at the beginning of the year. Assume that the spot price is $400 per unit and the risk free rate is 10% per annum for all maturitiesb) If currently the bid and ask on this 1-year futures contract are $444.5 and S445 respectively, what will you do? Please be specific and describe what this would imply? c) If this asset provides a lump sunm income distribution mid year that was S50, what would happen. (This is the important queston, please focus on this question. S 1S

Solution

We need to calculate the present value of the income distribution of $ 50

This is 50* e^0.1*6/12 = 50 *e^0.05 = 50 * 0.951 = 47.55

This is deducted from the spot price

400+2-47.55 = 354.45 (S₀)                                             storage costs are added

The price of the future

F₀₌ S₀*e^rt

F₀= S₀ e^0.1

F₀₌ 354.45*1.105 = $ 391.67

Since 391.67 is less than the selling price of the futures contract . He should short the futures contract

and buy the asset . At expiry he will make a profit of 445-391.67 = $ 53.33