FIN 323 Chapter 7 Homework
Treasury bills are currently paying 7 percent and the inflation rate is 2.7 percent. What is the approximate real rate of interest? What is the exact real rate?
Apx.RealRateOfInterest = bill rate - inflation rate 7% - 2.70% = 4.3 RealRateof Return = (1+bill rate)/(1+inflation rate)-1 (1+7%)/(1+2.70%)-1 = 0.04187 of 4.187%, rounded to 4.19%
DMA Corporation has bonds on the market with 19.5 years to maturity, a YTM of 6.6 percent, and a current price of $1,043. The bonds make semiannual payments and have a par value of $1,000. What must the coupon rate be on these bonds?
Coupon Amount = pmt(rate,nper,pv,fv) Coupon Amount = pmt(6.6%/2,19.5*2,-1043,1000) Coupon Amount = $ 34.98 Coupon rate = Coupon Amount*2/Face Value Coupon rate = 34.98*2/1000 Coupon rate = 7.00% Calculator: N=
Heginbotham Corp. issued 15-year bonds two years ago at a coupon rate of 8.5 percent. The bonds make semiannual payments. If these bonds currently sell for 106 percent of par value, what is the YTM?
The yield to maturity is given by rate function in excel as =rate(nper,pmt,pv,fv) where nper = 15 * 2 = 30 semiannual periods pmt = 0.085 *1000 = 85/2 = 42.5 pv = 1060 FV =1000 Hence semiannual yield = rate(30,42.5,-1060,1000) = 3.9069% Hence annual yield = 3.9069*2 = 7.8139% = 7.81%
Bourdon Software has 10.4 percent coupon bonds on the market with 16 years to maturity. The bonds make semiannual payments and currently sell for 108 percent of par. What is the current yield on the bonds? Current yield % What is the YTM? YTM % What is the effective annual yield? Effective annual yield %
coupon rate: 10.4 maturity (years): 16 price % of par: 108% price: 108%*1000=1080 coupon: 104%*1000=104 current yield: 10% (coupon/price) N= years *2 = 32 I/Y=? PV=-1080* PMT=104/2=52 FV=1000 4.71*2=9.42 --> YTM EAR = (1 + 0.0471)^2-1 = 9.64 *important to enter as a negative number
Suppose the real rate is 4% and the inflation rate is 5.6 percent. What rate would you expect to see on a treasury bill?
from fisher equation (1+R) = (1+r) * (1+h) R = (1+0.04) * (1+0.056) - 1 R = 1.098 - 1 R = 0.09824 R = 9.8%
Sqeekers Co. issued 11-year bonds a year ago at a coupon rate of 8.9 percent. The bonds make semiannual payments and have a par value of $1,000. If the YTM on these bonds is 7.2 percent, what is the current bond price?
$1,119.72 rate: 7.2%/2 nper: (11-1)*2 pmt: -1000*8.9%/2 fv: -1000 cmpt pv
Say you own an asset that had a total return last year of 11.7 percent. If the inflation rate last year was 6.9 percent, what was your real return?
(1 + inflation) ( 1 + real return) = (1 + total return) (1 + 6.9%)( 1 + real return) = (1 + 11.7%) (1 + real return) = (1 + 11.7%) / (1 + 6.9%) = 1.0449 Real Return = 1.0449 - 1 = 0.0449 = 4.49%
Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 7 percent, has a YTM of 5 percent, and has 11 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 5 percent, has a YTM of 7 percent, and also has 11 years to maturity. The bonds have a $1,000 par value. What is the price of each bond today? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.) Price of Bond X $ Price of Bond Y $ If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In two years? In six years? In 10 years? In 11 years? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.) Price of bond Bond X Bond Y One year $ $ Two years $ $ Six years $ $ 10 years $ $ 11 years $ $
Price of Bond X: N=11*2, I/Y=5%/2, PMT=70/2, FV=1000 ---> N=22, I/Y=2.5, PMT=35, FV=1000 CPT PV = 1167.65 Price of Bond Y: N=11*2, I/Y=7%/2, PMT=50/2, FV=1000 ---> N=22, I/Y=3.5, PMT=25, FV=1000 CPT PV = 848.33 Price of Bond X after 1 year: after 1 year = 11-1 or N=10*2 N=20, I/Y=2.5, PMT=35, FV=1000 CPT PV = 1155.89 Price of Bond Y after 1 year: after 1 year = 11-1 or N=10*2 N=20, I/Y=3.5, PMT=25, FV=1000 CPT PV = 857.88 Price of Bond X after 2 years: after 2 years = 11-2 or N=9*2 N=18, I/Y=2.5, PMT=35, FV=1000 CPT PV = 1143.53 Price of Bond Y after 2 years: after 2 years = 11-2 or N=9*2 N=18, I/Y=3.5, PMT=25, FV=1000 CPT PV = 868.10 Price of Bond X after 6 years: after 6 years = 11-6 or N=5*2 N=10, I/Y=2.5, PMT=35, FV=1000 CPT PV = 1087.52 Price of Bond Y after 6 years: after 6 years = 11-6 or N=5*2 N=10, I/Y=3.5, PMT=25, FV=1000 CPT PV = 916.83 Price of Bond X after 10 years: after 10 years = 11-10 or N=1*2 N=2, I/Y=2.5, PMT=35, FV=1000 CPT PV = 1019.27 Price of Bond Y after 10 years: after 10 years = 11-10 or N=1*2 N=2, I/Y=3.5, PMT=25, FV=1000 CPT PV = 981.00 Price of Bond X after 11 years: after 11 years = 11-11 or N=0*2 N=0, I/Y=2.5, PMT=35, FV=1000 CPT PV = 1000.00 Price of Bond Y after 11 years: after 11 years = 11-11 or N=0*2 N=0, I/Y=3.5, PMT=25, FV=1000 CPT PV = 1000.00
Both Bond Sam and Bond Dave have 9 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has four years to maturity, whereas Bond Dave has 15 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave? Percentage change in price of Bond Sam % Percentage change in price of Bond Dave % If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of Bond Sam and Bond Dave? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Percentage change in price of Bond Sam % Percentage change in price of Bond Dave %
SAM: YTM=9 N= 4*2=8 I/Y=9/2=4.5 PMT = 9%*1000, 90/2=45 FV=1000 CPT PV = 1000 YTM=11 N= 4*2=8 I/Y=11/2=5.5 PMT = 9%*1000, 90/2=45 FV=1000 CPT PV = 936.65 change in price = (63.35)* --> 1000-936.65 change in percentage -6.3* --> 63.35/1000 * make sure to put (-) if it is negative YTM=7 N= 4*2=8 I/Y=7/2=3.5 PMT = 9%*1000, 90/2=45 FV=1000 CPT PV = 1068.74 change in price = 68.74 --> 1068.74-1000 change in percentage 6.9 --> 68.74/1000 DAVE: YTM=9 N= 15*2=30 I/Y=9/2=4.5 PMT = 9%*1000, 90/2=45 FV=1000 CPT PV = 1000 YTM=11 N= 15*2=30 I/Y=11/2=5.5 PMT = 9%*1000, 90/2=45 FV=1000 CPT PV = 854.66 change in price = (145.34)* --> 1000-854.66 change in percentage -14.5* --> 145.34/1000 * make sure to put (-) if it is negative YTM=7 N= 15*2=30 I/Y=7/2=3.5 PMT = 9%*1000, 90/2=45 FV=1000 CPT PV = 1183.92 change in price = 183.92 --> 1183.92-1000 change in percentage 18.4 --> 183.92/1000
Locate the Treasury issue in Figure 7.4 maturing in February 2029. Assume a par value of $10,000. What is its coupon rate? What is its bid price in dollars? What was the previous day's asked price in dollars?
the coupon rate is 5.250% bid price = [par value x bid quote] =[10,000*1.233594 (/or 123.3594%)] = $12,335.94 asked price = [par value*(asked price-change)] =[10000*(123.3594%-(-0.7031%))] =$12,406