FIN3403 exam 1 Review Definitions CHPT 5 Future value The amount an investment is worth after 1 or more periods Compounding The process of accumulating interest on an investment over time to earn more interest Present value The amount an investment is worth at the beginning of the investment horizon Formulas CHPT 5 KEY FV future value PV present value r period interest rate expressed as a decimal n number of periods Future value FV PV 1 r n Present value PV FV 1 r n Interest Discount Rate r FV PV 1 t 1 Number Rate n ln FV PV ln 1 r Things to Always Remember CHPT 5 A longer time n equals a lower present value PV A greater discount rate r equals a lower present value PV Cash outflow is negative Cash inflow is positive Annuity A finite series of equal payments that occur at regular intervals Perpetuity An infinite series of equal payments Definitions CHPT 6 EAR is the rate we earn or pay after we account for compounding We should use the EAR to compare alternatives Formulas CHPT 6 APR Period rate x Number of periods per year Period rate APR Number of periods per year EAR 1 m APR m 1 Continuous Compounding EAR eAPR 1 Perpetuity formula PV PMT Things To Know For CHPT 6 When a corporation sells preferred stock the buyer is promised a fixed cash flow dividend every Preferred stock is an important example of perpetuity quarter forever Semi Annually 2 Monthly 12 Quartly 4 EAR NOTES periods you need to compute the EAR and use that for comparison If you want to compare two alternative investments with different compounding You should NEVER divide the effective rate by the number of periods per year it will NOT give you the period rate You ALWAYS need to make sure that the interest rate and the time period match If you are looking at annual periods you need an annual rate If you are looking at monthly periods you need a monthly rate Treasury bills are excellent examples of pure discount loans The principal amount is repaid at some future date without any periodic interest payments Interest only loans require the borrower to pay interest each period and the entire principal at the end Coupon The stated interest payment made on a bond Definitions CHPT 7 Par value face value The principal amount of a bond that is repaid at the end of the term of the bond Coupon rate The annual coupon divided by the face value of the bond Maturity The specified date on which the principal amount of the bond is paid Yield to maturity yield The rate required on a bond Yield to maturity is the relevant interest rate required return Bond Value PV of coupons PV of par value Bond Value PV of annuity PV lump some Interest Rate Risk The risk that arises for bond owners from fluctuating interest rates Price Risk Change in price due to changes in interest rates Long term bonds have more price risk than short term bonds Low coupon rate bonds have more price risk than high coupon rate bonds Reinvestment Rate Risk Uncertainty concerning rates at which cash flows can be reinvested Bond Pricing Theorem Bonds of similar risk and maturity will be priced to yield about the same return regardless of the coupon rate If you know the price of one bond you can calculate its YTM and use that to find the price of the second bond Treasury Securities Federal government debt Government Bonds T bills Pure discount bonds with original maturity of 1 year or less T notes Coupon debt with original maturity between 1 and 10 years T bonds Coupon debt with original maturity greater than ten years Municipal Securities Debt of state and local governments Varying degrees of default risk rated similar to corporate debt Interest received is tax exempt at the federal level Bond Ratings High Grade Moody s Aaa and S P AAA Capacity to pay is extremely strong Moody s Aa and S P AA Capacity to pay is very strong Moody s A and S P A Capacity to pay is strong but more susceptible to changes in Moody s Baa and S P BBB Capacity to pay is adequate adverse conditions will have more impact on the firm s ability to pay Moody s Ba and B and S P BB and B Considered possible that the capacity to pay will Medium Grade circumstances Low Grade degenerate Very Low Grade Moody s C and below and S P C and below income bonds with no interest being paid or in default with principal and interest in arrears Things to know for Chpt 7 If coupon rate YTM then bond price par value If coupon rate is less than YTM then bond price is less than par value Why The coupon rate is less desirable so it sells for a discount which just makes up for the lower coupon When the price is below par value it s called a discount bond If coupon rate is more than YTM then bond price is above par value Why Higher coupon rate causes the value to be above par When the price is above par value it s called a premium bond There are the purely mechanical reasons for these results We know that present values decrease as rates increase Therefore if we increase our yield above the coupon the present value price must decrease below par On the other hand if we decrease our yield below the coupon the present value price must increase above par There are also more intuitive ways to explain this relationship Explain that the yield to maturity is the interest rate on newly issued debt of the same risk and that debt would be issued so that the coupon yield Then suppose that the coupon rate is 8 and the yield is 9 Ask the students which bond they would be willing to pay more for Most will say that they would pay more for the new bond Since it is priced to sell at 1 000 the 8 bond must sell for less than 1 000 The same logic works if the new bond has a yield and coupon less than 8 Another way to look at it is that return dividend yield capital gains yield The dividend yield in this case is just the coupon rate The capital gains yield has to make up the difference to reach the yield to maturity Therefore if the coupon rate is 8 and the YTM is 9 the capital gains yield must equal approximately 1 The only way to have a capital gains yield of 1 is if the bond is selling for less than par value If price par there is no capital gain Technically it is the current yield not the coupon rate capital gains yield but from an intuitive standpoint this helps some students remember the relationship and current yields and coupon rates are normally reasonably close Bonds issued in the U S usually make coupon payments semiannually So if a bond has a …
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