1.
a. Because their maturities are different, if the maturity is long, the coupon rate is high.
b.
Years to Maturity | value annual |
5 | $791.51 |
15 | $866.89 |
25 | $1,238.27 |
c.
Years to Maturity | value semiannual |
5 | $787.65 |
15 | $865.49 |
25 | $1,239.61 |
The bonds of maturity of 5 years and that of 15 years are selling at a discount, because their present value is lower than $1000. And that of 25 years is higher than $1000, so the bond of maturity of 25 years is selling at a premium.
d.
The effective annual rate is 10.25%.
e.
Whether a semiannual payment bond sells at a higher or lower price than an otherwise equivalent annual payment bond depends on the bond’s coupon rate and nominal rate of return.
If the coupon rate is lower than nominal rate of return, a semiannual payment bond sells at lower price than an otherwise equivalent annual payment bond.
Now we look at the 5-years bond, its semiannual present value $787.65 is lower than its annual present value $791.51. And its coupon 4.5% is lower than nominal rate of return 10%. So 5-years bond prices are consistent with my expectations.
2.
a. The Yield to maturity (YTM) or redemption yield of a bond or other fixed-interest security, such as gilts, is the internal rate of return (IRR, overall interest rate) earned by an investor who buys the bond today at the market price, assuming that the bond will be held until maturity, and that all coupon and principal payments will be made on schedule. Yield to maturity is actually an estimation of future return, as the rate at which coupon payments can be reinvested when received is unknown
b&c.
Years to Maturity | YTM | effective annual YTM |
5 | 9.63% | 9.87% |
15 | 10.00% | 10.25% |
25 | 10.18% | 10.44% |
d.
We should use effective annual YTM, because it actually shows your real return until maturity.
3.
a. Its nominal yield is 10.18%, and its effective annual YTM is 10.44%.
b.
Coupon Rate | Years to...
