Homework 2

Suppose short-term municipal bonds pay a yield of 4%, while comparable taxable bonds pay 5%. Which gives you the higher after-tax yield for the following tax brackets: A. Zero? B. 10%? C. 20%? D. 30%?

Remember: After-tax yield = Rate on the taxable bond * (1 － Tax rate) A. Taxable bond (duh) B. Taxable. After tax yield = 4.5% C. Neither; both have 4% after-tax yield. D. Municipal; the after tax yield on the taxable bond is 3.5%. Basically, for any tax bracket above 20%, the municipal bond offers a better after-tax return.

Consider the three stocks in the following table. Pt represents the price at time t, and Qt represents shares outstanding at time t. Stock C splits two-for-one in the last period. P0 Q0 P1 Q1 P2 Q2 A 90 100 95 100 95 100 B 50 200 45 200 45 200 C 100 200 110 200 55 400 A. Calculate the rate of return on a price-weighted index of the three stocks for the first period (t = 0 to t = 1). B. What must happen to the divisor for the price-weighted index in year 2? C. What is the first period rate of return for a market value-weighted index? D. What is the first period rate of return for an equally weighted index?

A. At t = 0, the value of the index is: ($90 + $50 + $100)/3 = 80 At t = 1, the value of the index is: ($95 + $45 + $110)/3 = 83.33 Therefore: the rate of return is: V1/ V0 － 1 = (83.33/80) - 1 = 0.0417 or 4.17% B. Without the split, stock C would sell for $110, and the value of the index would be the average price of the individual stocks included in the index: ($95 + $45 + $110)/3 = $83.33. After the split, stock C sells at $55; however, the value of the index should not be affected by the split. We need to set the divisor (d) such that: 83.33 = ($95 + $45 + $55) / d Therefore: d = 2.34 C. Total market value at t = 0 is: ($90 x 100) + ($50 x 200) + ($200 x 100) = $39,000 Total market value at t = 1 is: ($95 x 100) + ($45 x 200) + ($110 x 100) = $40,500 Rate of return = V1 / V0 － 1 = ($40,500 / $39,000) - 1 = 0.0385 or 3.85% D. The return on each stock is as follows: RA = V1 / V0 － 1 = ($95/$90) - 1 = 0.0556 or 5.56% RB = V1 / V0 － 1 = ($45/$50) - 1 = -0.10 or -10.00% RC = V1 / V0 － 1 = ($110/$100) - 1 = 0.10 or 10.00% So, the equally-weighted average = [5.56% + (-10.00%) + 10.00%] / 3 = 1.85%

Look at the Apple options in the table (this is Figure 2.9 in the book). Suppose you buy an August expiration call option with exercise price $355. A. If the stock price in August is $377, will you exercise your call? What are the profit and rate of return on your position B. What if the stock price in August is $367? C. What if the August price is $355?

A. Yes, exercise the call. Gross profit is: ($377 - $355) x 100 shares = $2,200 Net profit = ($22 - $13.70) x 100 shares = $830 Rate of return = $8.30 / $13.70 = 0.6058 or 60.59% gain B. Yes. As long as the stock price at expiration exceeds the exercise price, it makes sense to exercise the call. Gross profit is: ($367 - $355) x 100 shares = $1,200 Net profit = ($12 - $13.70) x 100 shares = $170 loss Rate of return = -$1.70/$13.70 = -0.1241 or 12.41% loss C. The call option with an exercise price of $355 would expire worthless for any stock price equal to or less than $355. An investor in such a put would have a rate of return over the holding period of -100% because they would lose what they paid for the option ($13.70 per share).

Use the information from the bond listing below; answer the following questions for the bond maturing in 2040 (it's Figure 2.3 in your book): A. How much would you have to pay to purchase one of the bonds (assume each bond costs $1,000)? B. What is the coupon rate? What would be the amount paid semiannually? C. What is the current yield (the actual return you would receive) of the bond? HINT: The actual return would be the coupon income as a fraction of the amount you paid for the bond.

A. You would have to pay the asked price of 98. So: 98 = 98% of par = $980.00 B. The coupon rate is 4.25%, implying coupon payments of $42.5 annually or $21.25 semiannually. C. Given the asked price and coupon rate, we can calculate current yield with the formula: Current yield = Annual Coupon Income/ Price = 4.25 / 98 = 0.0434 = 4.34%

A T-bill with a face value of $10,000 and 87 days to maturity is selling at a bank discount ask yield of 3.4%. What is the price of the bill? What is its bond equivalent yield?

Bank discount of 87 days: 0.034 x (87 days/360 days) = 0.008217 Price: $10,000 x (1 - 0.008217) = $9,917.83 Bond equivalent yield = (Face value - Purchase Price) / (Purchase price x T) or: ($10,000 - $9,917.83) / ($9,917.83 x (87 days/ 360 days)) So, Bond equivalent yield = .0348 or 3.48%

Both a call and a put are currently traded on a stock; both have strike prices of $50 and six month maturities. What will be the profit to an investor who buys the call for $4 in the following scenarios for stock prices in six months? A. $40 B. $45 C. $50 D. $55 E. $60 Do the same for an investor who buys the put for $6.

Call for $4: Value of call at expiration Initial Cost. Profit P = $40 0 4 -4 P = $45 0 4 -4 P = $50 0 4 -4 P = $55 5 4 1 P = $60 10 4 6 Put for $6: Value of put at expiration Initial Cost Profit P = $40 10 6 4 P = $45 5 6 -1 P = $50 0 6 -6 P = $55 0 6 -6 P = $60 0 6 -6

8. What would you expect to happen to the spread between yields on commercial paper and Treasury bills if the economy were to enter a recession?

The spread will widen. Deterioration of the economy increases credit risk, that is, the likelihood of default. Investors will demand a greater premium on debt securities subject to default risk.

Find the equivalent taxable yield of the municipal bond in #1 for tax brackets of zero, 10%, 20% and 30%.

Using the formula of equivalent taxable yield (r) = rm / (1－ t), we get: A. r = 0.04 / (1 － 0) = 0.04 or 4.00% B. r = 0.04 / (1 － 0.10) = 0.0444 or 4.44% C. r = 0.04 / (1 － 0.20) = 0.05 or 5.00% D. r = 0.04 / (1 － 0.30) = 0.0571 or 5.71%