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FINANCE 460 Problem Set #1 Solutions 1. As discussed in class the YTM and the IRR of an investment are analogous concepts. The IRR is the rate of return that results in the NPV = 0. Looking at the bond pricing equation, the price of the bond in the same as the initial investment, and the PV of the annuity coupon payments and the PV of the face value to be received at maturity is the same as the PV of the bond's future cash flows. The YTM is the rate of return that result in the Price of the bond = PV of the future cash flows. If you subtract Pb from both sides you have 0 = -Pb(initial investment) + PV of future cash flows. So, the YTM is the same as the IRR. 2. Suppose that r = 10% and the coupon rate =12%, Face Value = 1000 and N=30. Then I/Y =10 N=30 PMT =120 and FV =1000, then Pb = 1188.54 Suppose that r=10% and the coupon rate = 8%, Face Value = 1000 and N=30. Then I/Y =10 N=30 PMT =80 and FV = 1000, then Pb = 811.46 3.For the first bond in #2, the bond sells at a premium = 188.54 = PV of the additional $20 coupons over and above bonds that are currently issued at par. This already issued bond's price will be bid upwards in the market to reflect the PV of these extra coupons.Check this! For the second bond in #2, the bond sells at a discount of 188.54 which is the PV of the fewer $20 coupons (relative to a bond newly issued at par). Chapter 2 problems 1. d 2. c 3. a you would have to pay the asked price of 107:27 =107.84375% of par = 1078.4375 b. the coupon rate = 5 5/8% implying coupon payments of $56.25 annually, or $28.125 semi-annually. c. current yield = Annual coupon/price = 56.25/1078.4375 = 5.22% 4. Preferred stock is like long term debt in that it typically promises a fixed payment each year.In this way, it is a perpetuity. Preferred stock is also like long-term debt in that it does not give the holder voting rights in the firm. Also, some issues are callable just like many issues of debt. Preferred stock is like equity in that the firm is under no contractual obligation to make the preferred stock dividend payments. Failure to make payments does not set off corporate bankruptcy, preferred stock has a higher priority than common stock but lower priority than bonds. THE REMAINING QUESTIONS WILL BE MORE RELEVANT LATER IN THE COURSE WHEN WE COVER INDIVIDUAL CHAPTERS ON THIS MATERIAL. 6. Taxable income = .3*$4 =1.20 Taxes = .3(1.20) = $.36 After tax income = (4-.36) =3.64 After tax rate of return = 3.64/40 = 9.1% 7. a. The closing price =$80.36 which is $3.39 lower than yesterday's price. Therefore yesterday's close -= $83.75 b. you could buy: 5000/80.36 = 62.22 shares c. Your annual dividend income = 1.4% of $5000 = $70 d. Price/Earnings = 18 and Price = 80.36 so that EPS = 80.36/18=4.46 11. a. the taxable bond-with a zero tax bracket the after tax-yield for the taxable bond is the same as the before tax yield, which is greater than the yield on the municipal bond. b. the taxable bond -the after tax yield for the taxable bond = .05*(1-.10)=4.5% c. you are indifferent. The after-tax yield for the taxable bond = .05*(1-.2)=4.0% d.the municipal bond offers the higher after-tax return for investors in tax brackets above 20%. 14.a . The December maturity futures price is $278.30 per ounce. If the contract closes at $283 in December, your profit on each contract (for delivery of 100 ounces of gold) will be $283-278.30*100 = 470 b. there are 77,991 contracts outstanding calling for delivery of 7,799,100 ounces of gold. 15. a. yes. As long as the stock price> expiration price, exercise the call. The gross payoff =107-105=2. Your net profit = 2-2.60 =-$.60 b. the rate of return =-.60/2.60 = -23.08% c. a put with exercise price 105 would expire worthless for any stock price equal or greater than 105. An investor in such a put would have a rate of return over the holding period return of -100% 16. there is always a chance that the option will expire in the money. Investors will pay something for this chance of a positive payoff.