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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