# Yield to maturity

The yield to maturity for bond with different maturity term has been calculated, ranging from six months to around ten years. However, it can be assessed that no coupon rate implemented on bond term ranging from six months to a year, as these types of bonds were considered as short term investments. Furthermore, the face value of the bond was estimated at \$100 and different coupon rates were implemented on two years onwards bond terms, as represented in the exhibit below in which, the bond terms, issue date and maturity dates are represented, as well as the Coupon rates and quoted prices.

 Term Maturity Issue Date Coupon Rate Price 0.5 8-Jun-17 8-Jun-16 - 99.692 1 7-Dec-17 7-Dec-16 - 99.170 2 30-Nov-18 30-Nov-16 1.000% 99.795 3 15-Nov-19 15-Nov-16 1.000% 98.924 5 30-Nov-21 30-Nov-16 1.750% 99.661 7 30-Nov-23 30-Nov-16 2.125% 99.637 10 15-Nov-26 15-Nov-16 2.000% 96.563

Furthermore, 0.5 represented six months term period with respect to the bond. However, in order to calculate the yield to maturity, the quote price present value is calculated in which, the quote price is treated as an expense. Moreover, the numbers of period are calculated, in which, it was determined that two period were present in a year. Therefore, to calculate, the numbers of periods were multiplied by the term period with respect to each bond. Additionally, the PMT was calculated by multiplying the coupon rate with the face value of the bond and dividing the figures by 2, which is the number of periods in a year. In addition to this, the Semi-annual yield to maturity could be calculated using the rate function in Excel in which the number of periods, PMT, Present value of quoted price and the future value of the bond were used under the rate function to determine the YTM. Furthermore, Semi-annual YTM could be multiplied by 2 to get the Annual YTM of the bonds under consideration.

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# Bond Pricing and YTM

 Semi Annual Coupon bond YTM calculation Term Maturity Issue Date Coupon Rate Price Present Value No. of Period PMT YTM Semi-Annual Payment YTM Annual Payment Accrued interest 0.5 8-Jun-17 8-Jun-16 - 99.692 (99.692) 1 - 0.309% 0.618% - 1 7-Dec-17 7-Dec-16 - 99.170 (99.170) 2 - 0.418% 0.835% - 2 30-Nov-18 30-Nov-16 1.00% 99.795 (99.795) 4 0.500 0.552% 1.104% 2.192% 3 15-Nov-19 15-Nov-16 1.00% 98.924 (98.924) 6 0.500 0.684% 1.367% 6.301% 5 30-Nov-21 30-Nov-16 1.75% 99.661 (99.661) 10 0.875 0.911% 1.821% 3.836% 7 30-Nov-23 30-Nov-16 2.12% 99.637 (99.637) 14 1.063 1.091% 2.181% 4.658% 10 15-Nov-26 15-Nov-16 2.00% 96.563 (96.563) 20 1.000 1.194% 2.388% 12.603%

The figures in the exhibit above were calculated on a Semi-annual compounding basis in which two periods consisting of 6 months were present in a year, where the discount factor was estimated using the formula depicted below.

(1+discount rate) ^-n, where n= no. of years

& t= 0.5, 1, 1.5, to 9.5, 10

Therefore, the 6 monthly discount factor was calculated represented in the exhibit below.

 Assuming @ 10% D/F t Discount factor 0.50 0.95 1.00 0.91 1.50 0.87 2.00 0.83 2.50 0.79 3.00 0.75 3.50 0.72 4.00 0.68 4.50 0.65 5.00 0.62 5.50 0.59 6.00 0.56 6.50 0.54 7.00 0.51 7.50 0.49 8.00 0.47 8.50 0.44 9.00 0.42 9.50 0.40 10.00 0.39

Furthermore, the price of a 3 year Semi-annual coupon bond has been calculated with annual coupon rate 3% and face value amounting to \$100 in which it was determined that the bond value after maturity would amount to 109.27 as represented in the exhibit below. However, the future value of the bond was calculated by multiplying the face value of the bond by the return factor of the coupon rate using the formula represented as (1+ coupon rate) ^No. of years.

 Calculation Years Bond term 3 Annual coupon rate 3% face value \$100 Future Value at maturity 109.2727

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