A jeweler has contracted to sell a silver ornament to a distributor for 22 in on

Question

A jeweler has contracted to sell a silver ornament to a distributor for 22 in one year. The ornament requires one ounce of silver, and has a fixed production cost of 2 per ornament. The possible prices of silver in one year and their probabilities are given below. 3. Silver Price per ounce18 Probability 19 0.3 20 0.4 0.3 The jeweler also has the option of entering a forward contract which will guarantee the purchase of silver for 19 per ounce in one year. What's the difference between the profit obtained using the forward hedge and the expected profit without hedging.

Explanation / Answer

Case 1: If Forward Contract is made, Cost of Silver = 19 per Ounce

Silver Ornament:

Sales Revenue = 22

Fixed Production Cost = 2

Cost of Silver used in Production (One Ounce is needed) = 19

Therefore, Profit to the Jeweler in the Case = 22-2-19 = 1.00

Case 1: If probabilistic Silver Pricing is taken in to account;

Expected Cost of Silver = Probabilistic Weight of Silver = Sum of the product of the Silver Price per Ounce and the probability of that price to occur = (18*0.3)+(19*0.3)+(20*0.4) = 19.9

Silver Ornament:

Sales Revenue = 22

Fixed Production Cost = 2

Cost of Silver used in Production (One Ounce is needed) = 19.1

Therefore, Profit to the Jeweler in the Case = 22-2-19.1 = 0.9

Hence the difference between the profit obtained using the forward hedge and the expected profit without hedging = 1.00 - 0.9 = 0.1

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