The outstanding bonds of Winter Time Products provide a real rate of return of 3.00 percent. The current rate of inflation is 2.
1 answer:
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Answer:
Year 1 = $1,100
Year 2 = $1,330
Year 3 = $1,550
Year 4 = $2,290
(a) If the discount rate is 6 percent, then the future value of these cash flows in Year 4:
To solve this problem, we must find the FV of each cash flow and add them. To find the FV of a lump sum, we use:
= $6737.51
(b) If the discount rate is 14 percent, then the future value of these cash flows in Year 4:
= $7415.17
(c) If the discount rate is 21 percent, then the future value of these cash flows in Year 4:
= $8061.47
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)
