Question

34. Components of Bond Returns Bond P is a premium bond with a coupon rate of 8.2 percent. Bond D is a discount bond with a coupon rate of 5.9 percent. Both bonds make annual payments and have a YTM of 7 percent, a par value of $1,000, and five years to maturity. What is the current yield for Bond P? For Bond D? If interest rates remain unchanged, what is the expected capital gains yield over the next year for Bond P? For Bond D? Explain your answers and the interrelationships among the various types of yields.

Answer 1

Current Yield = Annual Cash Flows
Market Price of Bond

Market Price of Bond =

summation C/(1+r)* + FaceValue/(1+r)

Bond P & D market Value

Bond P valuation
Year	1	2	3	4	5	5	Market Value
Cashflow	82	82	82	82	82	1000	-
PVF	1.0700	1.1449	1.2250	1.3108	1.4026	1.4026	-
PV of Cashflow	76.64	71.62	66.94	62.56	58.46	712.99	1049.20
Bond D valuation
Year	1	2	3	4	5	5	Market Value
Cashflow	59	59	59	59	59	1000	-
P.V.F	1.0700	1.1449	1.2250	1.3108	1.4026	1.4026	-
PV of Cashflow	55.14	51.53	48.16	45.01	42.07	712.99	954.90

Bond P Current Yield = 82/1049.20 = 7.82%
Bond D Current Yield = 59/1049.20 = 6.18%

If interest rates remain unchanged, what is the expected capital gains yield over the next year for Bond P? For Bond D?

For 4 years remaining to maturity Market value for Bond P & D will be 1040.65 & 962.74 respectively (Solved in the same way as above, just take cashflow of 4 years instead of 5)

Expected Capital gain on Bond P = -8.55
Expected Capital gain on Bond D = 7.84

If Interest rates remain unchanged the Premium Bond will lose value each year & Discount bond will gain value each year.

Current Yield signifies the return an investor would earn if he purchases the bond and holds it for a Year's span.
Yield to maturity signifies the return an investor would earn if he holds the bond till maturity.