1. Suppose Einar Ace buys 100 shares of Nordic Power Corp. at $20 each. The clea
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Question
1. Suppose Einar Ace buys 100 shares of Nordic Power Corp. at $20 each. The clear inghouse NASDUCK sets a margin requirement of 50% and charges an interest rate of 5% on the loan for purchasing the shares. (a) How much cash does Einar need to invest? (b) Calculate the margin call of NASDUCK if the price falls to $19. (c) What is the return for Einar on the transaction after the price decline? (d) How is the return on equity influenced by a change in the interest rate r? Does your answer depend on the size of the margin requirment? Hint: For this sensitivity analysis use a derivative with respect to r and, then, m.] Suppose that instead Einar short sells 100 shares of German Power Weak Inc. at $15 each. NASD UCK now sets a margin requirement of 20%. (e) How much cash does Einar need to invest? (f) Calculate the margincll of NASDUCK if the price increases to S16 (g) Suppose the price falls to $10. How much cash can Einar take out from his margin account? (h) Suppose he takes out 50% of the amount in part (g). At what price threshold will Einar face a margin call by NASDUCK?Explanation / Answer
1. a. Since the margin requirement is 50%, Einar Ace needs to invest 50% of the initial market value. Initial market value is $2,000 (100 * $20). Of $2,000, Einar Ace will put in $1,000 and NASDUCK will put in $1,000.
So, Einar Ace needs a cash of $1,000 to invest.
b. When price falls to $19, market value declines to $1,900 (100 * $19). Margin balance falls to $900 ($1,000 - $100). Assuming 50% is the Maintenance margin as well, Margin value should be $950 ($1,900 * 50%).
Hence, Margin Call of NASDUCK is $50 ($1,950 - $1,900).
c. As per b., we need to put in extra $50 to our initial investment. To calculate the return on our investment, we need the return amount/total investment.
Return is -$150 ($1,900 - $2,000 -$50 as interest). ($1,000 * 5%)
Investment is $1,000 (initial investment) + $50 (Margin Call) = $1,050
Return after the price decline = -$150/$1,050
= -14.286%
d. Our total return is dependent on the interest rate as if the interest costs go up, our return will decline. Hence, total return and interest rate are inversely related. Similarly, if the margin requirement is high, out total investment goes up keeping the $ return constant which makes the overall return on equity reduce.
e. Investment required = Price of share * No. of shares * Margin %
= $15 * 100 * 20%
= $300
f. Value of investment when price increased to $16 = $1,600. Loss is $100 ($1,500-$1,600). Margin Account falls from $300 to $200. As we need to maintain 20% margin of Market value, Margin amount should be $320. Hence, we need to put in $120 extra as the Margin Call.
g. When price falls to $10, value of investment is now $1,000 and we need to maintain 20%, so margin requirement is $200. We earlier had a balance of $300 and we made an additional profit of $500 (100*($15-$10)). So our total balance is now $800 while we need to maintain only $200. Hence, we can withdraw $600 from our Margin Account.
h. Einar withdraws 50% of the amount in g. meaning they withdraw $300 making the Margin Account Balance as $500.
Suppose the price at which we'll receive a margin call is p. Margin Call will arise when the $500 balance isn't sufficient to support our loss with price increase and the margin maintenance of 20% of the market value. Following equation holds true:
500 = 100*p*20% + 100* (p-15)
where the first part represents the margin maintenance of 20% of the market value and the second part represents the loss on price increase.
500 = 0.2p + 100p - 1500
2000 = 120p
p= 16.67
Hence, if the price increase more than $16.667, Einar will face a margin call.
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