Question

Assuming today is 3/20/20, your firm wants to purchase a $10,000 par value U.S. Treasury bond with 30 years to maturity, annual coupon rate of 2.00% with semiannual coupon payments. The market annual yield to maturity on 30-year "T" bonds, found in the US Treasury Yield curve, is 1.55%. http:/www.treasur es ab curte interest rates/Page Test Virw. danield Dab 1 mo 2 momomo 1 yr yr y syy 320/2020 0.04 0.05 0.05 0.05 0.15 0.37 0.41 0.52 0.82 0.92 1.35 1.56 What is the asked price (market price) for the bond? rate Hint: YTM from US Treasury Yield Curve = 1.55% or semiannual Also, 11-(1+rd)-N VB = INT + M (1+rd) VB = B. If the 30 US Treasury Bond annual rate jumps immediately to 2.20%, what is the new price for the 30-year "T" bond in part A, above? How much, in percent, would you lose or gain if you had purchased the bond in part A. VB= Gain Loss%={price@r=2.20%) - (price@r=1.55%) (price@r=1.55%)

Answer 1

The question gives all the hints and formula required to calculate the value:

VB=INT1- (1+ rd)-Nrd+M(1+rd)-N

where;
VB=value of bond
INT = interest received on bond = coupon rate * face value = 2%/2 * 10,000 = $ 100
rd=effective yield rate = 0.775%
N = no of payments received = 30 * 2 = 60
M = maturity amount = $ 10,000

A) Plugging the values given in the question:

VB=INT1- 1+ rd-Nrd+M1+rd-N

VB=100*1- 1+ 0.775%-600.775%+10,000*1+0.775%-60=

VB=100*47.84+10,000*0.6293

VB=$ 11,077

B) Similarly calculating bond value when yield rate is 2.2% and hence effective yield rate = 1.1%

VB'=$ 9,562

Therefore Gain/Loss % = ((price @ r = 2.2%) – ( price @ r = 1.55%) )/ (price @ r = 1.55%)

                                                                = (9562 – 11077)/11077 = - 0.14

                                                                = 14% loss