1. 1 Valuation Concepts Part 1: Bond Valuation

2. Besley: Chapter 7 2 Basic Valuation The value of any asset is based on the present value of the future cash flows the asset is expected to produce. 0n-112n CF 1 › CF 2 › CF n-1 › CF n › PV of CF n › PV of CF 1 › PV of CF 2 › PV of CF n-1 › Value

3. Besley: Chapter 7 3 Basic Valuation Asset Value= V = CF 1 /(1+k) 1 + CF 2 /(1+k) 2 +... + CF n /(1+k) n Where: CF t = Anticipated cash flow (CF) in period t k = required rate of return for an asset in this class A larger asset value (V) will result from: A larger expected CF A lower required return rate

4. Besley: Chapter 7 4 Bond Valuation - Terminology Bond: Long term debt instrument Principal Amount: the amount that the debtor borrows and promises to repay at some future date. Also know as Maturity Value; Par Value and Face Value Bonds typically have a face value of $1,000 or some multiple thereof.

5. Besley: Chapter 7 5 Bond Valuation - Terminology Coupon Payment: the fixed dollar payment per period (usually each six months) Coupon Interest Rate: the annual interest rate paid on the bond (=Coupon Payment/Face Value) Maturity Date: the date on which the maturity value must be repaid to the bondholder Original Maturity: the number of years to maturity as of the bonds issue date

6. Besley: Chapter 7 6 Bond Valuation - Terminology Call Provision: a provision within the bond terms that allows the bond issuer to “call back” the bonds and repay them at a date prior to the maturity date (a call provision usually calls for the issuer to pay the par vale plus one year’s interest when the bonds are called A Call Provision allows the debtor to take advantage of lowering interest rates by issuing new debt at the lower rate and using the proceeds of the sale to retire the older (more expensive) debt.

7. Besley: Chapter 7 7 Basic Bond Valuation Model 0n-112n INT PVA of INT PV of M Bond Value = V d M k d = rate of return on a debt instrument Bond Value = V d = INT/(1+k d ) 1 + INT/(1+k d ) 2 +... + INT/(1+k d ) n + M/(1+k d ) n =  t=1 n INT (1 + k d ) t M (1 + k d ) n = INT(PVIFA k d,n) + M(PVIF k d,n)

8. Besley: Chapter 7 8 Bond Valuation M = 1,000 N= 10 years K d = 10% INT= 100 0128 5 4 367 9 10 100 1,000 -90.91 -82.64 -75.13 -68.30 -62.09 -56.45 -51.32 -46.65 -42.41 -38.55 -385.54 -1,000.00

9. Besley: Chapter 7 9 Numerical Solutions M = 1,000 N= 10 years K d = 10% INT= 100 V d = INT{ [1-(1/(1+k d ) N ]/k d } + M[1/(1+k d ) N ] = 100{ [1-(1/(1.10) 10 ]/0.10} + 1,000[1/(1.10) 10 ] = 100{6.1446} + 1,000[0.3855] = 614.4567 + 385.5433 = 1,000.00

10. Besley: Chapter 7 10 Tabular Solutions M = 1,000 N= 10 years K d = 10% INT= 100 V d = INT(PVIFA k d,N ) + M(PVIF k d,N ) = INT(PVIFA 10%,10 ) + M(PVIF 10%,10 ) = 100(6.1446) + 1,000(0.3855 = 614.46 + 385.5 = 999.96 = 1,000.00

11. Besley: Chapter 7 11 Tabular Solutions M = 1,000 N= 10 years K d = 10% INT= 100 Input: Output: NI/YPV PMT FV 10 1,000 100 1,000

12. Besley: Chapter 7 12 Bond Valuation The price of a bond being purchased between interest payments must be adjusted for the earned interest being purchased. 1,000+(180/360)(100) = 1,050 Basic Price Coupon Payment Total Time Time Interest Earned Bond Price

13. Besley: Chapter 7 13 Bond Valuation Suppose that 1-year after the bond is issued, interest rates have fallen to 5% k d drops below the Coupon Rate (5% vs. 10%) Coupon Payments and Maturity Value remain constant V d increases to $1,355.38 V d = INT(PVIFA 5%,9 )+M(PVIF 5%,9 ) V d = 100(7.1078)+1,000(0.6446)

14. Besley: Chapter 7 14 Bond Valuation Suppose you decide to sell the bond after 1-year after rates have fallen (the new price is the $1,355.38). Sell Price:$1,355.38 Coupons:$100 Total Inflows:$1,455.38 Price Paid:$1,000.00 Net Profit:$455.38 Yield:$455.38/$1,000.00 = 45.538%

15. Besley: Chapter 7 15 Yields The yield (total rate of return) is comprised of two components: Current Yield (Interest Yield): Annual Coupon Payment divided by its current market value Capital Gains Yield: Capital Gain on the bond divided by the current market value

16. Besley: Chapter 7 16 Yields Current Yield Current Yield = INT/V d = 100/1,000 = 10% Capital Gains Yield Capital Gains Yield= (V d,End – V d,Begin )/V d,Begin = (1,355.38 – 1,000)/1,000 = 35.54%

17. Besley: Chapter 7 17 Yields Current Yield:10.00% Capital Gains Yield:35.54% Total Yield:45.54%

18. Besley: Chapter 7 18 Yields This assumes that rates do not change after year one, if interest rates do fluctuate, so will the price.

19. Besley: Chapter 7 19 Bond Movement Bond prices are inversely related to interest rates: When interest rates increase bond prices will fall and the bond will trade at a discount (bond price is less than maturity value) When interest rates decrease bond prices will rise and the bond will trade at a premium (bond price is greater than maturity value) Market Value will always approach par, the closer it gets to maturity.

20. Besley: Chapter 7 20 Yield to Maturity (YTM) Yield to Maturity (YTM): The average rate of return earned on a bond if held to maturity. Approximate YTM = (Annual Interest+Accrued Capital Gains)/Avg. Value of Bond = INT+[(M-V d )/N] [(2(V d )+M)/3] This is an approximation and does not include the TVM.

21. Besley: Chapter 7 21 Bond Values with Semiannual Compounding

22. Besley: Chapter 7 22 Bond Values with Semiannual Compounding V d = (INT/2)(PVIFA k d /2,2N ) + M(PVIF k d /2,2N ) NOTE: The maturity value must be discounted at the same percentage and time period as the annuity.

23. Besley: Chapter 7 23 Interest Rate Risk Two types of interest rate risks: Interest Rate Price Risk: The risk that changing interest rates will adversely affect bond prices. Increasing interest rates will force the bond prices down exposing the bond holder to a loss on the bond price. Interest Rate Reinvestment Risk: The risk that changing interest rates will cause the cash flows generated by the bond to be invested at a rate other than the original bond rate..

24. Besley: Chapter 7 24 Interest Rate Risk Decrease in Bond Price Due to 5% Increase in Rate

25. Besley: Chapter 7 25 Interest Rate Risk

26. Besley: Chapter 7 26 Interest Rate Risk Effect of Reinvestment Rate Risk Effect of Interest Rate Risk

27. Besley: Chapter 7 27 Interest Rate Risk Reinvestment Risk

28. Besley: Chapter 7 28 Interest Rate Risk Reinvestment Risk 2,000 1,500 1,000 500 0 5 10 15 20 25 14-Year Bond 1-Year Bond