Cash Hash » Cash Hash » Cash Flow/ Cash Flows » Help with finance homework on bonds yields, YTM, and Effective annual yield!!!!!!!?

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  #1 (permalink)
: DDS Software has 8.9 percent coupon bonds on the market with 24 years to maturity. The bonds make semiannual payments and currently sell for 111.50 percent of par.



Current yield? %

Yield to maturity? %

Effective annual yield? %
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  #2 (permalink)
: What is your question? What don't you understand? Where is your solution? Do you just want someone to do your work for you? You would learn nothing that way and it would be a disservice to you. And if you turned in the answer prepared by another person as your own work you would be committing plagiarism which is unethical.

A bond consists of two promises. It promises to pay $1,000 on the maturity date, and it promises to pay periodic interest. The interest payments are determined by the coupon rate. If the coupon rate of interest is more than the market rate, the bond will sell at a premium because it is more attractive than the rate available in the market. So it's price will be bid up. The bidding will stop when its yield to maturity equals the market interest rate. If the coupon rate is less than the market rate, the bond will sell at a discount.

By discounting the two future cash flows to the present using the market interest rate, you can find the present value of the bond, the price at which it will sell. In a diagram you have

PV - - - PMT - - - PMT - - - - - - PMT - - - PMT + $1,000

PMT is the interest payment calculated from the coupon rate. The number of payments is determined by the life of the bond. So you have variables whose values are known and you can solve for any unknown variable when you know the others. The simplest way is using a financial calculator. The variables are

Maturity value - $1,000 face value per bond
Coupon rate - determines size of PMT
PMT = periodic interest = Face value * coupon rate * time
Number of periods is usually semiannual, sometimes annual
Market rate: Used to discount future cash flows
PV = present value of the future cash flows

A bond's coupon rate is fixed and does not change during the life of the bond. But market interest change in reaction to a variety of economic conditions. So if a bond has a 5% coupon rate, and investors can now earn only 4% in the market, the 5% bond will be very attractive. Investors will all want it so they will bid for it and its price will go up. That is, when market interest rates fall below the bonds coupon rate the price of the bond will increase.

The opposite is true if market interest rates go up. The price of the bond will go down. If investors can earn 6% interest why should they buy a bond that pays only 5%. They will buy it only if the price is low enough to yield 6%. So bond prices move in opposite directions from interest rate.

In this problem you have the market value and you have to find the rate that will discount the future payments to the market value. The answer is 3.915 which translates to 7.83% YTM
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  #3 (permalink)
: Check out www.investlikeme.blogspot.com. There is an article on getting started in the market and how to read a stock profile. The author also shares his own personal portfolio which you can follow along with on twitter.
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  #4 (permalink)
: Reading notes from here http://finance.thinkanddone.com/

Finding yield (current yield) is easier than finding promised yield (YTM)

There is a formula to find current yield whereas no such thing for YTM

YTM is the market interest rate that sets equal the market price of the bond to its present value of bond's income stream

The present value of bond's income stream discounts the periodic interest payment and the terminal par value, the sum of such discounts is the market price

Solving for discount rate is not possible using formula as the variable for YTM is trapped in a polynomial leaving us to either use trial and error (your teacher most likely taught you linear interpolation) however more complex methods are available to solve such rates (called numerical methods or iterative techniques of finding roots)

Here is a complete YTM solution found using this YTM calculation http://finance.thinkanddone.com/online-ytm-calculation.html

And this tool returns only the YTM calculator http://finance.thinkanddone.com/online-ytm-calculator.html

The semi-annual YTM = 3.92%
Annual YTM = 7.84%
Effective YTM = 8%


f(i) = 100 + -111.5 * (1+i)^48 + 4.45 [(1+i)^48 - 1]/i

f'(i) = 48 * -111.5 * (1+i)^47 + 4.45 * (48 i (1 + i)^47 - (1 + i)^48 + 1) / (i^2)

i = 0.1
f(i) = -6444.6547
f'(i) = -326370.7816
i1 = 0.1 - -6444.6547/-326370.7816 = 0.080253579589887
Error Bound = 0.080253579589887 - 0.1 = 0.019746 > 0.000001

i1 = 0.080253579589887
f(i1) = -2234.8242
f'(i1) = -128688.2063
i2 = 0.080253579589887 - -2234.8242/-128688.2063 = 0.062887386455024
Error Bound = 0.062887386455024 - 0.080253579589887 = 0.017366 > 0.000001

i2 = 0.062887386455024
f(i2) = -731.7781
f'(i2) = -54261.7453
i3 = 0.062887386455024 - -731.7781/-54261.7453 = 0.049401309383704
Error Bound = 0.049401309383704 - 0.062887386455024 = 0.013486 > 0.000001

i3 = 0.049401309383704
f(i3) = -206.8715
f'(i3) = -26546.334
i4 = 0.049401309383704 - -206.8715/-26546.334 = 0.04160846364034
Error Bound = 0.04160846364034 - 0.049401309383704 = 0.007793 > 0.000001

i4 = 0.04160846364034
f(i4) = -39.1516
f'(i4) = -17102.7436
i5 = 0.04160846364034 - -39.1516/-17102.7436 = 0.039319265585915
Error Bound = 0.039319265585915 - 0.04160846364034 = 0.002289 > 0.000001

i5 = 0.039319265585915
f(i5) = -2.5041
f'(i5) = -14956.1091
i6 = 0.039319265585915 - -2.5041/-14956.1091 = 0.039151833611848
Error Bound = 0.039151833611848 - 0.039319265585915 = 0.000167 > 0.000001

i6 = 0.039151833611848
f(i6) = -0.0124
f'(i6) = -14808.5971
i7 = 0.039151833611848 - -0.0124/-14808.5971 = 0.039150998521995
Error Bound = 0.039150998521995 - 0.039151833611848 = 1.0E-6 < 0.000001

YTM = 3.92%
Annual YTM = 7.84%
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