4-1 Introduction Credit is one of the critical mechanisms we have for allocating resources. Although interest has historically been unpopular, this comes from the failure to appreciate the opportunity cost of lending. Interest rates Link the present to the future. Tell the future reward for lending today. Tell the cost of borrowing now and repaying later.

4-2 Future Value and Compound Interest Future value is the value on some future date of an investment made today.

4-3 Future Value and Compound Interest $100 + $100(0.05) = $105 In general: FV = PV + PV(i) = PV(1 + i)

4-4 Future Value and Compound Interest What if you leave your $100 in the bank for two years at 5% yearly interest rate? The future value is: $100 + $100(0.05) + $100(0.05) + $5(0.05) = $ $100(1.05)(1.05) = $100(1.05) 2 In general FV n = PV(1 + i) n

4-5 Future Value and Compound Interest Converting n from years to months is easy, but converting the interest rate is harder. If the annual interest rate is 5%, what is the monthly rate? Assume i m is the one-month interest rate and n is the number of months, then a deposit made for one year will have a future value of $100(1 + i m ) 12.

4-6 Future Value and Compound Interest A basis point is one one-hundredth of a percentage point, 0.01 percent.

4-7 Present Value Financial instruments promise future cash payments so we need to know how to value those payments. Present value is the value today (in the present) of a payment that is promised to be made in the future.

4-8 Present Value Solve the Future Value Formula for PV: FV = PV x (1+i) so This is just the future value calculation inverted.

4-9 Present Value We can generalize the process as we did for future value. Present Value of payment received n years in the future:

4-10 Yield to Maturity Yield to Maturity: the interest rate that equates the present value of an investment with its cost. Note—some texts will have a both a yield to maturity and an internal rate of return

4-11 Coupon Bond Coupons Called a coupon bond as buyer would receive a certificate with a number of dated coupons attached.

4-12 Bond Pricing The relationship between the bond price and interest rates is very important. Bonds promise fixed payments on future dates, so the higher the interest rate, the lower their present value. The value of a bond varies inversely with the interest rate used to calculate the present value of the promised payment.

Bond Prices and Yields to Maturity Move in Opposite Directions If interest rates on newly issued bonds rise, the prices of existing bonds will fall. If interest rates on newly issued bonds fall, the prices of existing bonds will rise. In other words, yields to maturity and bond prices move in opposite directions. The reason, as noted earlier, is that if interest rates rise, existing bonds issued when interest rates were lower become less desirable to investors, and their prices fall. If interest rates fall, existing bonds become more desirable, and their prices rise. This relationship should also hold for other debt instruments. The Inverse Relationship between Bond Prices and Bond Yields

Making the Connection Reading the Bond Tables in the Wall Street Journal Bond A matures on August 15, 2015, and has a coupon rate of 4.250%, so it pays $42.50 each year on its $1,000 face value. Prices are reported per $100 of face value. For Bond A, 112:08 means “112 and 08/32,” or a price of $1, for this $1,000 face value bond. The bid price is the sell price; the asked price is the price to buy the bond. For Bond A, the bid price rose by 8/32 from the previous day. Treasury Bonds and Notes The Inverse Relationship between Bond Prices and Bond Yields

The current yield equals the coupon divided by the price: $42.50/$1,122.50, or 3.79% for Bond A. The current yield of Bond A is well above the yield to maturity of %. This illustrates that the current yield is not a good substitute for the yield to maturity for instruments with a short time to maturity because it ignores the effect of expected capital gains or losses. Making the Connection Reading the Bond Tables in the Wall Street Journal Treasury Bonds and Notes

Making the Connection Reading the Bond Tables in the Wall Street Journal Treasury bills are discount bonds, not coupon bonds. Treasury notes and bonds quote prices, while Treasury bills quote yields. The bid yield is the discount yield for sellers. The asked yield is for buyers. The dealers’ profit margin is the difference between the asked bid yields. The yield to maturity, in the last column, is useful for comparing investments. Treasury Bills

A bond’s rating shows the likelihood that the firm will default on the bond. Prices are quoted in decimals. The last time this Goldman Sachs bond was traded that day, it sold for a price of $1, New York Stock Exchange Corporation Bonds Making the Connection Reading the Bond Tables in the Wall Street Journal

A general equation for the rate of return on a bond for a holding period of one year is: A General Equation for the Rate of Return Three important points to note: 1. For the current yield, the calculation uses the initial price. 2. If you sell the bond, you have a realized capital gain or loss. If you do not sell the bond, your gain or loss is unrealized. 3. Neither the current yield nor the yield to maturity may be a good indicator of the rate of return because they ignore your capital gain or capital loss.

4-19 Real and Nominal Interest Rates Borrowers care about the resources required to repay. Lenders care about the purchasing power of the payments they received. Neither cares solely about the number of dollars, they care about what the dollars buy.

4-20 Real and Nominal Interest Rates Nominal Interest Rates (i) The interest rate expressed in current-dollar terms. Real Interest Rates (r) The inflation adjusted interest rate.

4-21 Real and Nominal Interest Rates The nominal interest rate you agree on (i) must be based on expected inflation (  e ) over the term of the loan plus the real interest rate you agree on (r). i = r +  e This is called the Fisher Equation. The higher expected inflation, the higher the nominal interest rate.

4-22 Real and Nominal Interest Rates Financial markets quote nominal interest rates. When people use the term interest rate, they are referring to the nominal rate. We cannot directly observe the real interest rate; we have to estimate it. r = i -  e