Bond valuation (CH6) Flashcards
6-1: bond valuation with annual coupons 1
Find the price of a $1,000 par value bond that matures in 10 years if it pays interest annually, if it is based on a 6% coupon rate, and if the market rate of interest is 7%.
- 60 PMT
10 N - 1,000 FV
7 I/y
CPT PV = 929.76
- be careful with the signs
-2: Bond Valuation with Annual Coupons 2
Find the price o fa $1,000 par value bond that matures in 10 years. It pays interest annually, is based on a 6% coupon rate, and the market rate of interest is 5%.
- 60 PMT
10 N - 1,000 FV
5 I/y
CPT PV = 1,077.22
-3: bond valuation with Semi-Annual Coupons
Determine the price of a 15 year bond that pays interest semi-annually and has a par value of $1,000 and a coupon rate of 5%, when the appropriate market rate is 6%.
- 25 PMT (50 / 2)
30 N - 1,000 FV
3 I/y
CPT PV = 902.00
6-4: Estimating prices for bonds with different terms to maturity
Consider the bond form example 6-3 with a $1,000 par value and a coupon rate of 5%, paying interest semi-annually, with market rates at 6%. Recalculate the price on this bond, assuming that the term to maturity is not 15 years, but is either
a. 5 years or
b. 30 years
a)
PMT -25 N 10 FV -1,000 I/Y 3 CPT PV = 957.35
B) PMT - 25
N 60
FV -1,000
I/Y 3
CPT PV = 861.62
6-5: Estimating prices for bonds with different coupon rates
Consider the semi-annual, $1,000 par value, 5% bond examined in example 6-3 (call it bond1) along with another 15 year bond that pays semi-annual coupons based on a 6% coupon rate (bond 2) calculate the price o each bond when market rates
a. 5 percent
b. 6 percent
PMT -30 N 30 FV -1,000 I/Y 2.5% CPT PV = 1,104.65
b) PMT -25 N 30 FV -1,000 I/Y 3 CPT PV = 902.00
6-6 the cash Price of a bond
Consider the bond in example 6-3 which pays interest semi-annually, has a $1,000 maturity value and a 5% coupon rate, and is sold on July 14 at a quoted price of $902. Assume this bond matures on June 30, which implies the semi-annual interest payments on this bond are made on June 30 and on Dec 31.
Calculate the cash price of this bond.
Cash price =
Quoted price + Accrued Interest
902 + (1,000 x 0.05 x (14/365))
= 902 + 1.92
=903.92
6-7: Estimating the YTM on an Annual-Pay bond
Estimate the YTM on a 10 year, 5% bond that pays annual coupons and is selling for $980.
50 PMT -980 PV 1,000 FV 10 N CPT PV = 5.26% which is an annual rate so YTM (annual) = 5.26%
6-8: estimating the YTM on a Semi-annual bond
Estimate the YTM on a 20 year, 6% bond that pays semi-annual coupons and is selling for $1,030.
30 PMT
-1,030 PV
1,000 FV
40 N
CPT I/Y = 2.87% which is a semi-annual rate (Kb)
so we multiply by 2 to find the annual YTM
YTM = 2.87% x2 = 5.74%
6-9: Estimating the Yield to Call (YTC)
Estimate the YTC on a 20 year, 6% bond that is callable in 5 years at a call price of $1,050, if the bond pays semi-annual coupons and is selling for $1,030
30 PMT
-1,030 PV
1,050 FV
10 N
CPT i/y = 3.081% which is a semi-annual rate (Kb)
so we multiply by 2 to find the annual YTM
YTM = 3.081% x2 = 6.16%
6-8: estimating the YTM on a Semi-annual bond
Estimate the Current Yield on a 20 year, 6% bond that pays semi-annual coupons and is trading for $1,030.
B = 1,030
Annual interest = 30 x 2 = 60 Or 1000 x 0.06)
CY = Annual interest / B
60 / 1030 = .0583 or 5.83%
6-11: Estimating the Real Rate of Return
If T-bill rates are currently 4.5% and the expected level of inflation is 2%, estimate the approximate real rate of return.
Real rate = 4.5 -2 =2.5%
6-12: Determining the Price of T-Bills
Find the price of a 91 day T-bill with a face value of $10,000 that has a quoted yield of 4.2%
p = F/ (1+kbey N/365)
F = 10,000 Kbey = 0.042 n = 91
10,000 / 1.010471233 = 9,896.37
6-13: Estimating the yield on a T-Bill
Estimate the yield on a 182 day T-bill that is currently selling at a price of $98.20.
Kbey = F-P / P x 365/N
F = 100 P = 98.20 N = 182
(100 -98.20) / 98.2 x 365 / 182 = 0.018329939 x 2.005494505 = 0.03676 = 3.676%
6-14: Estimating the YTM on a semi-Annual bond
Determine the price of a 15 year zero coupon bond with the face value of $1,000 and a market yield of 5%.
B = F x (1/ (1+kb) exponent n
F = 1000 N = 15 x2 = 30 Kb = 0.05 / 2 = 0.025
Calculator
PMT 0 N 30 FV 1,000 I/Y 2.5 CPT PV = -476.74
6-15: estimating the YTM on a zero coupon bond
Determine the YTM on a 10 year zero coupon bond with a face value of $1,000 that is selling for $560
PMT 0 N 20 FV 1,000 PV -560 CPT I/Y = 2.94%
double this gives us a YTM of 5.88%
