Question

During the COVID-19 outbreak, toilet paper (TP) became a commodity. To hedge their price risk, large corporations started trading forward contract on it. As senior analyst at your financial institution, you are asked to price a forward for a client. The client wants to secure the purchase of 5,000 rolls of TP for delivery in 6 months. The current price of TP $2.50 per roll. Your cost of risk-free borrowing and lending is 0.75% (continuous time).

You could sign a contract with a TP producer for a future delivery, but you are afraid that, in the extreme circumstances, the producer might pick a client willing to pay more for the TP and "default" on delivery of the TP. To avoid this situation, you will buy the TP right now, at the spot price of $2.50 per roll, and store it. Storing the TP will require renting a small office space at $91 per month, payable at the beginning of each month.

You need to pay a one time delivery fee of $100, immediately. You will also need to pay $100 for delivery at the maturity of the 6 months.

Storing the TP for the client is convenient to you. If you are ever in shortage of TP, you can use some from the storage, and then buy some on the market to replace what you bought. You estimate the convenience as a continuous time yield of 0.50% (continuous time).

Including all costs and convenience, what is the fair price of TP in 6 months?

Answer 1

total FV of TP considering Risk free cost@ 0.75%( continues time) = $18278.50

plus Storage cost of TP for 6 month of office = $546

plus one time Delivery fee = $ 100

plus at the time delievery Fee    = $ 100

Total cost        = $ 19024.50

Fair value per TP assuming Yield @ 0.50%( continues Time ) = $24428

thus per TP = 24428 /5000 = $4.8856

working note

1. FV of TP considering Rist Fre cost @ .75% ( continiues Time)

FV = PV x e to the power ( iXt)

FV = 12500 x e to the power 0.375

using exponental table find e to the power 0.375 value

= 12500x 1.46228 = $18278.50

2. Fair Value of total TP assumming Yield @ 0.50( continues Time)

FV = 19024.50 x e to the power 0.25

using exponental table e to the power 0.25 value.

FV = 19024.50 x 1.28403 = $24428