Which security has a higher effective annual interest rate? a.
Effective annual rate on 3-month T-bill: 100,000 ( 97,645 )4 – 1 = 1.024124 – 1 = .10 or 10%
b.
Effective annual interest rate on coupon bond paying 5% semiannually: (1.05)2 – 1 = .1025 or 10.25%
Two bonds have identical times to maturity and coupon rates. One is callable at 105 and the other at 110. Which should have the higher yield? The bond callable at 105 10 5 should sell at a lower price because b ecause the call provision is more valuable to the firm. Therefore, its YTM should be higher. higher.
Consider a bond paying a coupon rate of 10% per year semiannually when the market interest rate is only 4% per half a year. The bond has 3 years until maturity. The bond pays $50 every 6 months
Current price $50 Annuity factor(4%, 6) + $1000 PV factor(4%, 6) = $1052.42 ×
×
Assuming the market interest rate remains 4% per half year:
Price 6 months from now = $50 Annuity factor(4%, 5) + $1000 PV factor(4%, 5) = $1044.52 ×
×
b. Rate of return
=
=
$50 + ($1044.52 – $1052.42) $1052.42 $50 – $7.90 $42.10 = $1052.42 $1052.42 = .04 or 4% per six months
A bond with a coupon rate of 7% makes semiannual coupon payments on January 15 and July 15 of each year. The quoted price for the bond on January 30 is 100.02. What is the invoice price of the bond? The coupon period has 182 days. The reported bond price is 100.02 percent of par, which equals $1,000.20. However, 15 days have passed since the last semiannual coupon was paid, so accrued interest equals $35 (15/182) = $2.885. The invoice price is the reported price plus accrued interest, or $1003.085. ×
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A bond has a current yield of 9% and a yield to maturity of 10%. Is the bond selling above or below par? If the yield to maturity is greater than the current yield, the bond must offer the prospect of price appreciation as it approaches its maturity date. Therefore, the bond must be selling below par value.
Calculate the real and nominal rates of return on the RRB bond in the second and third years Inflation in year Time just ended Par value Coupon payment Principal repayment 0 $1,000.00 1 2% $1,020.00 $40.80 0 2 3% $1,050.60 $42.02 0 3 1% $1,061.11 $42.44 $1,104.55 The nominal rate of return on the bond in each year is: Nominal rate of return =
Real rate of return =
interest + price appreciation . initial price
1 + nominal return − 1 1 + inflation
Second year Nominal return =
Real return =
42.02 + 30.60 = .071196 1020
1.071196 – 1 = .04, or 4% 1.03
Third year 42.44 + 10.51 = .05040 1050.60
1.05040 1.01 – 1 = .04, or 4%
The real rate of return in each year is precisely the 4% real yield on the bond.
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A 30-year maturity, 8% coupon bond paying coupons semiannually is callable in 5 years at a call price of $1100. The bond currently sells at a yield to maturity of 7% (3.5% semiannual) Yield to call: The bond sells for $1,124.72 based on the 3.5% yield to maturity. [n = 60; i = 3.5%; FV = 1,000; PMT = 40] Therefore, yield to call is 3.368% semiannually. [n = 10 semiannual periods; PV = (–)1,124.72 ; FV = 1,100; PMT = 40] If the call price were $1,050, we would set FV = 1,050 and redo part (a) to find that yield to call is 2.976%. With a lower call price, the yield to call is lower. What is the yield to call if the call price is $1,100 but the bond can be called in two years instead of 5 years? Yield to call is 3.031% semiannually. [n = 4; (–)PV = 1,124.72 ; FV = 1,100; PMT = 40]
Suppose that today’s date is April 15. A bond with a 10$ coupon paid semiannually every January 15 and July 15 is listed as selling at an ask price of 101.125. If you buy the bond a dealer today, what price will you pay for it? April 15 is midway through the semiannual coupon period. Therefore, the invoice price will be higher than the stated ask price by an amount equal to one-half of the semiannual coupon. The ask price is 101.125 percent of par, so the invoice price is: $1011.25 +
½
×
$50 = $1036.25
A newly issued bond pays its coupons once annually. Its coupon rate is 5%, its maturity is 20 years, and its yield to maturity is 8%. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 7% by the end of the year. Initial price, P0 = 705.46 [n = 20; PMT = 50; FV = 1000; i = 8] Next year's price, P1 = 793.29 [n = 19; PMT = 50; FV = 1000; i = 7] HPR =
50 + (793.29 – 705.46) = .1954 = 19.54% 705.46
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A 20-year maturity bond with a par value of $1,000 makes semiannual coupon payments at a coupon rate of 8%. Find the bond equivalent and effective annual yield to maturity of the bond price if Selling at $950: Use the following inputs: n = 40, FV = 1000, PV = (–)950, PMT = 40. You will find that the yield to maturity on a semi-annual basis is 4.26%. This implies a bond equivalent yield to maturity of 4.26% 2 = 8.52%. ×
2
Effective annual yield to maturity = (1.0426) – 1 = .0870 = 8.70% Since the bond is selling at par ($1000), the yield to maturity on a semi-annual basis is the same as the semi-annual coupon, 4%. The bond equivalent yield to maturity is 8%. 2
Effective annual yield to maturity = (1.04) – 1 = .0816 = 8.16% Keeping other inputs unchanged but setting PV = (–)1050, we find a bond equivalent yield to maturity of 7.52%, or 3.76% on a semi-annual basis. 2
Effective annual yield to maturity = (1.0376) – 1 = .0766 = 7.66%
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