Use Matlab to get an intuitive understanding of bonds valuation.
1. Basic knowledge:
1.1 The price equation and its six contributing factors
As we know, there are six factors that determine the expected price of bonds: the par value(F), the maturity(n) the yield to maturity(y), the coupon interest(CF), the interest payment frequency(m), and the interest rates for each period(ri).
We assume that the coupon interest is fixed, then the price of bonds(P)is the discounted cash flows of each period:
P=i=1nm(CF(1+ym)i)+F(1+ym)mn=i=1nm(CF(1+rim)i)+F(1+rnm)mn
Indeed, to intuitively understand this equation is not easy. Firstly, we can see that the yield to maturity(y) is a kind of “average” of the interest rates(ri) for each
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In order to make the chart more easy to see, we change maturity to 20(That is n=20, r =[0.051:0.001:0.07]), the code is
r=[0.051:0.001:0.07]; n=1:20;plot(n,r) hold all ytm1=ytmm(r,10,100); plot(n,ytm1)
r=[0.051:0.001:0.07]; n=1:20;plot(n,r) hold all ytm1=ytmm(r,10,100); plot(n,ytm1)
The chart is
Chart 1
Interest rates(r)
YTM
Interest rates(r)
YTM
We can see from the chart that:
① The trend of Interest rates and YTM are the same.
②
The yield to maturity on a 15-year bond is a true estimate of the cost of 30-year bond
Answer: The Coupon Rate is a generally fixed and is known as the stated rate of a bond that determines the periodic interest payments. As stated in the textbook, the annual coupon dividen by the face value is called the coupon rate of the bond. The YTM rate of return anticipated on the bond if it is held until the maturity Date. YTM is considered a long-term bond yield expressed as an annual rate.
GE has a face value of $98.40 and the coupon is 0.042%, which is equivalent to $0.00042, which is no money, rounded to the nearest hundredths. The maturity of the bond is 5 years (5/17/2021), so Billy would get $500.00 back from the GE bond issuers. Billy would make a dividend of $8 by buying the bond at a lower price than the returned money. PEP has a face value of $99.60 and the coupon percentage is 0.467%, which is 0.00467 and 0.01 rounded to the nearest hundredths. The maturity is 2 years (04/30/2018), so Billy would get $200.02 back and make a dividend of
The Yield to Maturity (YTM) of a bond is: Interest rate that makes the present value of the bond’s
Bonds are a debt investment, meaning the purchaser of the bond is loaning money to the company or government for a set period. They have a fixed interest rate, meaning the investor knows how much interest will be earned on the loan since the rate will not change.
risk free bonds. According to the Law of One Price, what must be the price of Bond C
The bonds have 20 years to maturity, pay interest at 9.3%, have a par value of $1,000 and are currently selling for $890.
The value of a bond is found as the present value of interest payments plus
1(a) Regular Treasury bonds are purchased at face value in the beginning or an adjusted price prior maturity. And in every period, normally annul or semiannual, investor will receive a coupon as an interest and at the maturity a principal plus coupon.
2. The discount rate for this bond would be 0.70%. I started with an appropriate discount rate to derive my bond purchase price, since I would not purchase a bond without finding out ahead of time what a good price should be.
Through this method, we obtained theoretical yields of the 4.25% coupon bond and 10.625% coupon bond to be 2.899% and 2.639% respectively. The corresponding theoretical prices of the bonds are $108.27 for the 4.25% coupon bond and $149.31 for the 10.625% coupon bond (see Table 1 above).
Since the interest payments are tax deductible, the aftertax cash flow from the interest payments will be:
Bond Discount represents an additional cost of borrowing and should be recorded as bond interest expense over the life of the bond. To follow the matching principle, bond discount is allocated to expense in each period in which the bonds are outstanding. This is referred to as amortizing the discount. Amortization of the discount increases the amount of interest expense reported each period. As the discount is amortized, its balance will decline and as a consequence, the carrying value of the bonds will increase, until at maturity the carrying value of the bonds equals their face amount. The journal entries are as follow:
Full Price = 90% clean price + 5% coupon rate (120 days since last coupon payment/ 360 days in the year for annual bond)
Coupon bond is one that is below its nominal value. 99.05 It is less than 100 percent of the cash value of the price, which will be traded. Above the face value of the bond premium bond. 101,15 more than 100 percent of the cash value of your price quote. Market interest rates rise above the coupon rate of the bond discount bond when the bond is. Market interest rates, the bond 's coupon rate is below the bonds when the bond underwriters.