Question

1.

a. You see the current 3-month T-bill quoted on a discount basis at 1.9425-1.9350. The T-bill has a $10,000 face value. The T-bill has 86 days until maturity. What price would you pay for one of these T-bills (disregarding transaction charges)? Enter the price you would pay rounded to the nearest cent.

b. You see the current 3-month T-bill quoted on a discount basis at 1.9325-1.9250. The T-bill has a $10,000 face value. The T-bill has 86 days until maturity. What is the bond equivalent ask yield? Enter the yield rounded to two digits in this format, 4.56%

c. You are an investor in the 34% marginal tax bracket. You are looking to invest some of your funds in a fixed income security. You see a Mecklenburg County municipal bond with a yield of 2.75%. The other bond you are considering is a Ford Motor Company corporate bond yielding 4.00%. On the basis of taxable equivalent yield, which bond would you choose?

d. You open a brokerage account and purchase 500 shares of MMM at $150.39 by borrowing half of the required funds (you pay for 250 shares and borrow enough to buy another 250 shares). You pay 6% annual interest on the borrowed money. At the end of one year, what price would trigger a margin call if the maintenance margin were set at 35% by the brokerage firm? Enter the margin call price by rounding to the nearest cent in this format, $123.45

Answer 1

a]

1.9425-1.9350 is the annualized yield discount quote

Price of bond = face value - discount

discount = annualized yield * face value * days remaining to maturity / 360

Here, the annualized discount to use is 1.9425, since the ask price is always higher than the bid price

discount = (1.9425 / 100) * $10,000 * (86 / 360) = $46.40

Price of bond = $10,000 - $46.40 = $9,953.60

b]

BEY = [(face value - price of bond) / price of bond] * (360 / days to maturity)

First, we calculate the price of bond

Price of bond = face value - discount

discount = annualized yield * face value * days remaining to maturity / 360

Here, the annualized discount to use is 1.9325, since the ask price is always higher than the bid price

discount = (1.9325 / 100) * $10,000 * (86 / 360) = $46.17

Price of bond = $10,000 - $46.17 = $9,953.83

BEY = [($10,000 - $9,953.83) / $9,953.83] * (360 / 86) = 0.0194, or 1.94%

c]

After-tax yield of municipal bond = pretax yield = 2.75%. (since municipal bond is tax free)

After-tax yield of corporate bond = pretax yield * (1 - tax rate) = 4.00% * (1 - 34%) = 2.64%

As the the after-tax yield of municipal bond is higher, I would choose the municipal bond

d]

Level of margin at which call will be made = 35% of margin = 35% of (250 * $150.39) = $37,597.50

Interest on borrowed money = 6% * (250 * $150.39) = $2,255.85

Let the price at which margin call will be made be X. Then,

($150.39 - X)*500] - $2,255.85 = $37,597.50

X = $70.68