44 - Fixed Income Valuation Flashcards
Interest rates have fallen over the seven years since a $1,000 par, 10-year bond was issued with a coupon of 7%. What is the present value of this bond if the required rate of return is currently four and one-half percent? (For simplicity, assume annual payments.) . What is it asking?
PV at year 7. The present value can also be determined with a financial calculator. N = 3, I = 4.5%, PMT = $1,000 × 7%, FV = $1,000. Solve for PV = $1,068.724.
Consider a bond selling for $1,150. This bond has 28 years to maturity, pays a 12% annual coupon, and is callable in 8 years for $1,100. The yield to maturity is closest to:
The callable option is irrelevant for this question. N = 28; PMT = 120; PV = –1,150; FV = 1,000; CPT I/Y = 10.3432.
Current yield
Coupon/PV value of bond
Assume the following government spot yield curve.
One-year rate: 5%
Two-year rate: 6%
Three-year rate: 7%
If a 3-year annual-pay government bond has a coupon of 6%, its yield to maturity is closest to:
First determine the current price of the bond:
= 6 / 1.05 + 6 / (1.06)2 + 106 / (1.07)3 = 5.71 + 5.34 + 86.53 = 97.58
Then compute the yield of the bond:
N = 3; PMT = 6; FV = 100; PV = -97.58; CPT → I/Y = 6.92%
A bond has a yield to maturity of 7% with a periodicity of 4. The bond has a face value of $100,000 and matures in 13 years. Each coupon payment will be $1,800. The current price of the bond is closest to:
Remember what periodicity means. N = 13 × 4 = 52; FV = 100,000; PMT = 1,800; I/Y = 7 / 4 = 1.75; CPT → PV = 101,698.
Whitetail Company issues 73-day commercial paper that will pay $1,004 at maturity per $1,000 face value. The bond-equivalent yield is closest to:
The add-on yield for the 73-day holding period is $1,004 / $1,000 – 1 = 0.4%. The bond-equivalent yield, which is an add-on yield based on a 365-day year, is (365 / 73) × 0.4% = 2.0%.
(Module 44.3, LOS 44.h)
A 10-year spot rate is least likely the:
YTM is not a spot rate.
A 10-year spot rate is the yield-to-maturity on a 10-year zero-coupon security, and is the appropriate discount rate for the year 10 cash flow for a 20-year (or any maturity greater than or equal to 10 years) bond. Spot rates are used to value bonds and to ensure that bond prices eliminate any possibility for arbitrage resulting from buying a coupon security, stripping it of its coupons and principal payment, and reselling the strips as separate zero-coupon securities. The yield to maturity on a 10-year bond is the (complex) average of the spot rates for all its cash flows.
