Your best friend Sue has always wanted to be an FBI agent for the U.S. government. However, because of the recent restructured c
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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)
Answer:
NPV with a 14.9% discount rate: 6,329.06
The toy should be produced as the NPV is positive.
IRR = 26.65%
Explanation:
First we calculate for the NPV using the given discount rate of 14.9%
We will calculate the present value of each year cash inflow:
Year 1 cash inflow: 47,500.00
time 1.00
rate 0.149
PV 41,340.30
Year 2 cash inflow: 18,600.00
time 2.00
rate 0.149
PV 14,088.76
Then, we add them and subtract the investment to get NPV
NPV = 14,088.76 + 41,340.3 - 49,100 = 6,329.06
The toy should be produced as the NPV is positive.
Now for the IRR
That is the rate at which NPV equals zero we can solve for this using the quadratic equation as there are only two cash flow:
Year 1 will discount at (1+IRR)
Year 2 will be discount at (1+IRR )^2
So we can express and recreate the quadratic formula:
18,600 X^2 + 47,500 X - 49,500 = 0
A = 18,600
B = 47,500
C = -49,100
We can solve and get:
x1 = 0.78957
x2 = -3.3433
We take the positive value.
and now solve for IRR
IRR = 0,2665121 = 26.65%
This will be the IRR for the project.