Bond valuation2 nd

CORPORATE DEBT CORPORATE DEBT INSTRUMENTSINSTRUMENTS

Straight Bond Zero Coupon Bond Floating Rate Bond Bonds with Embedded Options Commodity-Linked Bonds

EXAMPLEYear Cash flow 1 20 2 30 3 220

Discount rate = 16 percent

V0 = 20 x PV16%,1 + 30 x PV16%,2 + 220 x PV16%,3

V0 = 20 x 0.862 + 30 x 0.763 + 220 x 0.641

= 180.55

KEY INPUTS

Cash Flows

Timing

Discount Rate

BOND YIELDSBOND YIELDS

Nominal Yield Current Yield Yield to Maturity Yield to Call Realised Yield to Maturity

BOND YIELDS• CURRENT YIELD

ANNUAL INTEREST PRICE

• YIELD TO MATURITY C C C M

P = + + …. + (1+r) (1+r)2 (1+r)n (1+r)n

8 90 1,000 800 = +

t=1 (1+r)t (1+r)8

AT r = 13% … Price = 808 AT r = 14% … Price = 768.1

808 - 800YTM = 13% + (14% - 13%) = 13.2%

808 - 768.1 C + (M - P) / n

YTM ≃ 0.4M + 0.6 P

• YIELD TO CALL n* C M*

P = + t=1 (1+r)t (1+r)n

REALISED YIELD TO MATURITYFUTURE VALUE OF BENEFITS

0 1 2 3 4 5

• INVESTMENT 850

• ANNUAL INTEREST 150 150 150 150 150

• RE-INVESTMENT PERIOD (IN YEARS) 4 3 2 1 0

• COMPOUND FACTOR (AT 16 PERCENT) 1.81 1.56 1.35 1.16 1.00

• FUTURE VALUE OF INTERMEDIATE CASH FLOWS 271.5 234.0 202.5 174.0 150.0

• MATURITY VALUE 1000

• TOTAL FUTURE VALUE = 271.5 + 234.0 + 202.5 + 174.0 + 150.0 + 1000 = 2032

(1+r*)5 = 2032 / 850 = 2.391 r* = 0.19 OR 19 PERCENT

BOND PRICE AND YIELDBOND PRICE AND YIELD

Market interest rate increases Required rate of return by investors increases Discounted value of bond payment decreases

when higher discount rate is applied. Present value of bond declines Bond price declines

PRICE - YIELD RELATIONSHIPPRICE

YEILD

PRICE CHANGES WITH TIMEVALUE OF BOND PREMIUM BOND: rd = 11%

A

PAR VALUE BOND: rd = 13%

BDISCOUNT BOND: rd = 15%

8 7 6 5 4 3 2 1 0

YEARS TO MATURITY

YTM- AN APPROXIMATIONYTM- AN APPROXIMATION

YTM = C+(M-P)/n -------------- 0.4M+0.6P

C- Annual Interest PaymentM-Maturity value P- Present price of the bondn-Years to maturity