You just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy?

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2 You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each month? Your car dealer is willing to lease you a new car for $299 a month for 60 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 4.9%, what is the current value of the lease? Today is January 1. Starting today, Sam is going to contribute $140 on the first of each month to his retirement account. His employer contributes an additional 50% of the amount contributed by Sam. If both Sam and his employer continue to do this and Sam can earn a monthly rate of ½ of 1 percent, how much will he have in his retirement account 35 years from now? 2

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4 . Winston Enterprises would like to buy some additional land and build a new factory. The anticipated total cost is $136 million. The owner of the firm is quite conservative and will only do this when the company has sufficient funds to pay cash for the entire expansion project. Management has decided to save $450,000 a month for this purpose. The firm earns 6% compounded monthly on the funds it saves. How long does the company have to wait before expanding its operations? Your insurance agent is trying to sell you an annuity that costs $100,000 today. By buying this annuity, your agent promises that you will receive payments of $ a month for the next 40 years. What is the rate of return on this investment? You have some property for sale and have received two offers. The first offer is for $189,000 today in cash. The second offer is the payment of $100,000 today and an additional $100,000 two years from today. If the applicable discount rate is 8.75%, which offer should you accept and why? You just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy? You are paying an effective annual rate of 13.8% on your credit card. The interest is compounded monthly. What is the annual percentage rate on your account? 4

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7 What is the effective annual rate if a bank charges you 7.64% compounded quarterly? The Smart Bank wants to appear competitive based on quoted loan rates and thus must offer a 7.9 annual percentage rate. What is the maximum rate the bank can actually earn based on the quoted rate? You want to have $10,000 saved ten years from now. How much less do you have to deposit today to reach this goal if you can earn 6% rather than 5% on your savings? 7

8 A bond is a legally binding agreement between a borrower and a lender that specifies the: Par (face) value Coupon rate Coupon payment Maturity Date The yield to maturity is the required market interest rate on the bond. Primary Principle: Value of financial securities = PV of expected future cash flows Bond value is, therefore, determined by the present value of the coupon payments and par value. Interest rates are inversely related to present (i.e., bond) values. 8

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11 Make no periodic interest payments (coupon rate = 0%) The entire yield to maturity comes from the difference between the purchase price and the par value. Cannot sell for more than par value Sometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs) Treasury Bills and principal only Treasury strips are good examples of zeroes. Face value (F) Discount rate (r) 11

12 Information needed for valuing pure discount bonds: Time to maturity (T) = Maturity date today s date Face value (F) Discount rate (r) Find the value of a 30 year zero coupon bond with a $1,000 par value and a YTM of 6%. 12

13 Level Coupon Bonds Make periodic coupon payments in addition to the maturity value The payments are equal each period. Therefore, the bond is just a combination of an annuity and a terminal (maturity) value. Coupon payments are typically semiannual. Effective annual rate (EAR) = (1 + R/m) m 1 13

14 Level Coupon Bond: Example Consider a U.S. government bond with a 6 3/8% coupon that expires in December The Par Value of the bond is $1,000. Coupon payments are made semi annually (June 30 and December 31 for this particular bond). Since the coupon rate is 6 3/8%, the payment is $ On January 1, 2010, the required annual yield is 5%. Mention Consols Make sure to discuss the yield to maturity concept - show implicit reinvestment assumption Show relationship between YTM, CR, FV and Market Value 14

15 The Present Value of Common Stocks The value of any asset is the present value of its expected future cash flows. Stock ownership produces cash flows from: Dividends Capital Gains Valuation of Different Types of Stocks Zero Growth Constant Growth Differential Growth A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity. What is the stock worth? The discount rate is 12%. + The value of a firm depends upon its growth rate, g, and its discount rate, R. Where does g come from? g = Retention ratio Return on retained earnings 15

16 Where does R come from? The discount rate can be broken into two parts. The dividend yield The growth rate (in dividends) In practice, there is a great deal of estimation error involved in estimating R. Using the DGM to Find R Growth Opportunities Growth opportunities are opportunities to invest in positive NPV projects. The value of a firm can be conceptualized as the sum of the value of a firm that pays out 100% of its earnings as dividends and the net present value of the growth opportunities. Consider a firm that has EPS of $5 at the end of the first year, a dividend payout ratio of 30%, a discount rate of 16%, and a return on retained earnings of 20%. 16

17 alternatively First, we must calculate the value of the firm as a cash cow. Second, we must calculate the value of the growth opportunities. 17

Finding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26

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