please answer question 5 and 6 and 7 FIN A46000-Assignment #1 September, 2018 An
ID: 2809552 • Letter: P
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please answer question 5 and 6 and 7
FIN A46000-Assignment #1 September, 2018 Answer questions on a separate piece of paper. Show your work. 1. A recent listing for a Treasury bill in the Wall Street Journal gave an Asked Discount Yield of 2.25%. Its maturity was 120 days. a. What is the T-bill's coupon (bond) equivalent yield? b. What price would a bank pay for this T-bill? c. What is the effective annual yield for the T-bill? d. If the Bid Discount Yield was 2.40%, what was the dealer's "spread" on the bill (in Sy 2. An investor just purchased a 182 day maturity Treasury bill for 98.625. a. What is the coupon equivalent yield? b. What is the bank discount yield? 3, A Treasury note with a maturity of eight years and a coupon interest rte of 4.50% was quoted at a 4. An IBM zero coupon bond with a maturity in September, 2026, has a price of 53.5 (percent). What is 5, An Exxon bond (par value-100) has a maturity of 15 years and a coupon interest rate of 6.3%. If price of 98. What is this T-note's yield to maturity? the bond's yield to maturity? you require a yield to maturity of 7% on similar risk bonds, what is the value (price) of this bond? 6, A Citigroup zero coupon bond has a maturity of six years and a yield of 7% . Interest rates are expected to increase by 1.25%. Based on duration what price change do you expect for this bond? 7. An ATT bond (100 par value) which matures in exactly three years (September, 2021) has a coupon of 6.8%. The price of the bond is 96.8547. Your required rate of return is 8%. a. What is this bond's modified duration? b. Ifyou expect yields to decrease by 1% (100 basis points), what is the approx inate price c. Compute the actual price change. change expected on this ATT bond?Explanation / Answer
5. Face Value of bond (FV) = $100 (i.e at Expiration of the bond, the investor gets $100 along with the last coupon payment)
Coupon rate = 6.3%
-> Coupon payments each year = 6.3% of FV = (6.3/100)*$100 = $6.30
Maturity of bond = 15 years and YTM = 7%
Price of the bond today = Present of all the coupon payments+Present Value of the Face Value
Since coupon payments occur at the end of every year for 15 years, the PV of all coupons is nothing but the PV of an annuity of $6.3 every year for 15 years
Therefore Price of bond = [C(1-(1/(1+YTM)n)))/YTM ]+ [FV/(1+YTM)n]
= 6.3(1-1/(1.0715))/0.07 + 100/(1.07)15
= $93.62
Bond Price = $93.62
6. %Change in price = -duration*change in interest rate*100
Duration is a value that takes in to account 1% change in interest rate and calculates the change in the price of the bond for this 1% change in interest rate.
For zero coupon bonds, Duration is equal to the maturity of the bond.
-> Duration = 6 years
therefore %change in price = -duration*change in interest rate*100
=-6*(1.25/100)*100
= -7.5%
Since the interest rate increased, the bond price falls.
Thus the change in bond price is expected to be -7.5%
7. Coupon payments = coupon rate*FV = 6.8%*100 = $6.8; fv=$100, T=3 Years, Price of bond = $96.8547
Since YTM is not given, lets calculate the YTM using the excel formula of RATE(nper,pmt,pv,fv) where nper = 3 years, pmt=$6.8,pv=-96.8547,fv=100
Thus YTM = 8.02%
a) Modified duration = Macaulay Duration /(1+YTM/n) where n= no. of coupon payments in a year = 1
Macaulay Duration = Sum of (PV of cash flow*Time period of cash flow)/Market price of the bond
At Year 1, CF = $6.8 -> PV = 6.8/(1+YTM)=6.8/(1.0802)= $6.295
At Year 2, CF = $6.8 -> PV = 6.8/(1+YTM)2=6.8/(1.08022) = $5.827
At Year 3, Cash flow = $6.8+$100 = $106.8 -> PV = 106.8/(1+YTM)3=106.8/(1.08023) = $84.732
Macaulay duration = ((1*6.295)+(2*5.827)+(3*84.732))/96.8547
= 2.8098
Modified Duration = 2.8098/(1+(0.0802/1)) = 2.6
Therefore bond's modified duration = 2.6 Years
b) change in yield = -1%
-> %Change in bond price = -modified duration*change in yield*100
=-2.6*-1%*100
=2.6%
% Change in bond price = 2.6%
c) Actual Bond Price when yield reduced by 1% = Bond price when YTM = 8.02%-1% = 7.02%
Bond Price = 6.8/(1.0702)+6.8/(1.07022)+106.8/(1.07023) = $99.42
Actual change in bond price = (99.42-96.8547)*100/96.8547 = 2.65%
Actual change in bond price = 2.65%
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