Suppose a banking system has $100,000 in deposits, a required reserve ratio of 25 percent, and total bank reserves for the whole
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To find the change in the price of the bonds, first need to find the price of individual Bond.
Bond Price is directly related to the change in the YTM of the bond. If the YTM rises by 2%, the price of the bond will fall.
Bond J :
(WHEN YTM IS 8%)
Coupon Rate: 5%
Coupon Amount (PMT): $1,000 * 5% = $50/2 = $25 (Semi annual coupon amounts)
Number of years (NPER) = 13*2 = 26
YTM (rate) = 8%/2 = 4%
Face Value: $1000
Price (PV0) : ?
To find the price of the bond, can either use excel or with formula.
When input the below formula in excel,
PV =pv(rate,nper,pmt,fv,type)
P0 =pv(4%,26,-25,-1000)
When input the formula in excel, we get PV as $760.26
(WHEN YTM RISES BY 2%, NEW YTM IS 10%)
Coupon Amount (PMT): $25 (Semi annual coupon amounts)
Number of years (NPER) = 26
YTM (rate) = 10%/2 = 5%
Face Value: $1000
Price (PV1) : ?
To find the price of the bond, can either use excel or with formula.
When input the below formula in excel,
PV =pv(rate,nper,pmt,fv,type)
P1 =pv(5%,26,-25,-1000)
When input the formula in excel, we get PV as $640.62
CHANGE IN THE BOND PRICE OF BOND J DUE TO THE CHANGE IN THE YTM
%change = (P1 – P0)/P0
%change = ($640.62 - $760.26)/$760.26
%change = -18.68%
Therefore, with the increase in 2% YTM of BOND J, the price falls by 18.68%
Bond K :
(WHEN YTM IS 8%)
Coupon Rate: 11%
Coupon Amount (PMT): $1,000 * 11% = $110/2 = $55 (Semi annual coupon amounts)
Number of years (NPER) = 13*2 = 26
YTM (rate) = 8%/2 = 4%
Face Value: $1000
Price (PV0) : ?
To find the price of the bond, can either use excel or with formula.
When input the below formula in excel,
PV =pv(rate,nper,pmt,fv,type)
P0 =pv(4%,26,-55,-1000)
When input the formula in excel, we get PV as $1,239.74
(WHEN YTM RISES BY 2%, NEW YTM IS 10%)
Coupon Amount (PMT): $55 (Semi annual coupon amounts)
Number of years (NPER) = 26
YTM (rate) = 10%/2 = 5%
Face Value: $1000
Price (PV1) : ?
To find the price of the bond, can either use excel or with formula.
When input the below formula in excel,
PV =pv(rate,nper,pmt,fv,type)
P1 =pv(5%,26,-55,-1000)
When input the formula in excel, we get PV as $1,071.88
CHANGE IN THE BOND PRICE OF BOND K DUE TO THE CHANGE IN THE YTM
%change = (P1 – P0)/P0
%change = ($1071.88 - $1239.74)/$1239.74
%change = -13.54%
Therefore, with the increase in 2% YTM of BOND k, the price falls by 13.54%
SIMILALRY IF THE BOND PRICES FALLS BY 2%, the YTM WILL BE 6%/2 = 3% **(REFER THE IMAGE ATTACHED)
