Question

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5. M. Rudolph Inc. has an exposure to the price of steel. The price is currently at $50/coil. If the price remains the same one year from now, profits will be $10 million. Profits move linearly with the price of steel: for every $1/coil increase/decrease in price of steel, profits decrease/increase $200,000. Management wants to ensure that profits are not reduced by more than $1,000,000 due to changes in the price of steel. a. Draw a graph that reflects the relationship between the price of steel (horizontal axis) and Rudolph's profit, showing specifically steel prices of $40, $45, $50, $55 and $60. b. To hedge their risk, would Rudolph use a call or a put option? Why? C. If the cost of the option is $100,000, what would be the desired strike price? d. Show the cash flows one year from now for steel prices of $40, $45, $50, $55 and $60. Draw a graph that reflects the relationship between the price of steel (horizontal axis) and Rudolph's profit, assuming the option is purchased, showing specifically steel prices of $40, $45, $50, $55 and $60. f. Contrary to the market, the Rudolph management team believes that the risk of steel price movements is mostly one-sided against them. Therefore, they are considering entering into a forward contract instead of an option. Why would they consider this?

Answer 1

Only first 4 sup parts are being solved here.

a. Graph reflecting the relationship is copied below.

Data used for the graph:

Profit	Price
7800000	61
8000000	60
8200000	59
8400000	58
8600000	57
8800000	56
9000000	55
9200000	54
9400000	53
9600000	52
9800000	51
10,000,000	50
10200000	49
10400000	48
10600000	47
10800000	46
11000000	45
11200000	44
11400000	43
11600000	42
11800000	41
12000000	40

Price 9200000 9400000 0000096 000'000'Or 10600000 11000000 11200000 10200000 10400000 10800000 11400000 11600000 7800000 8000000 8200000 8400000 8600000 8800000 9000000

b. To hedge their risk, Rudolph will buy call option. Because Rudolph would like to lock in the price of steel and call option gives the right to Rudolph to buy steel at the desired price rather than relying on the market price which may rise upwards. Rise in steel price reduces the profits.

c. Management wants to ensure that profits are not reduced by more than 1,000,000. If the cost of the option is 100,000 then Rudolph needs to protect the price drop to avoid reduction by more than 1,000,000 - 100,000 = 900,000. The desired strike price needs to be 54 as the profit reduction is 800,000. It cannot be 55 as the profit reduction will be 1,000,000 and the total reduction will be 1,000,000+100,000 = 1,100,000 which is not desirable by the management.

d. If call option of $100,000 is purchased then the cash flow is as follows:

For price of $40, cash flow will be $12,000,000 - 100,000 = $11,900,000

For price of $45, cash flow will be $11,000,000 - 100,000 = $10,900,000

For price of $50, cash flow will be $10,000,000 - 100,000 = $9,900,000

For price of $55, cash flow will be $9,000,000 - 100,000 = $8,900,000

For price of $60, cash flow will be $8,000,000 - 100,000 = $7,900,000