UTS Business School Finance 25721: Investment Management Assignment

This assignment solution delves into the intricacies of zero coupon bonds, explaining their characteristics, valuation methods, and yield calculations. It begins by defining zero coupon bonds as debt securities that do not pay periodic interest, instead offering returns through the difference between the purchase price and the face value at maturity. The solution provides a numerical example to illustrate the calculation of a bond's present value, considering factors like maturity, yield, and face value. The assignment further explores the relationship between bond prices and yields, highlighting the inverse relationship. A table presents the present value calculations for various Treasury bonds with different coupon rates and maturities. The document also references relevant academic literature to support the analysis. This assignment is designed to help students understand the concepts of zero coupon bonds in investment management.

INVESTMENT MANAGEMENT
Zero coupon bond is referred as a debt security, in which no yield is payable by the company.
Although it is issued at a deep discount, therefore at the maturity investor will generate the profit
by redemption at par value. This type of bond is also known as accrual bond (Hung, and Liu,
2016). In other words, it can be said that zero coupon bond is sold at less than the face value of
the bond, and there is no payment of interest to the holder of the bond. In the Zero Coupon Bond,
only at the time of maturity of the bond, the investor will get the coupon payment. Therefore, the
computation of the present value by the present value of the annuity formula is not essential.
Rather than, at the maturity present value of the par value should be calculated (Ang,& et al.
2017). The holder of the bond generates the profit by gradual enhancement in the value of the
security, which is redeemed at face value on the date of maturity. This can be better understood
by the numerical example.
Let us assume, a zero coupon bond has the maturity of five years, which gives the yield at the
rate of 6%. The face value of this bond is $1000.
Determination of the number of periods
Generally, the yield of the zero coupon bond is based on semiannual coupon payment. Therefore,
in this 6% yield is adjusted for semiannual payment, so the number of the period will be twice to
10 periods, which is computed by 5*2.
Determination of the yield
For this, the rate of yield should be divided by two because the number of the period is twice.
Thus, the yield for this bond is .06/2 = 3%.

Determination of the bond price
Formula
= M/(1+i)n
= 1000/ (1+0.03)10
= $744.09
It has been noted that Zero coupon bonds are always priced at a discount. If the zero coupon
bond sold at par, then it suggest that investor will not generate any profit from them, and no
return would be generated by the investor.
Along with this, generally, the investment in the zero coupon bond is for the long term period,
which has a maturity period of 10 years or more. However, it does not give the current income;
therefore, some investors do not want to make the investment in such type of security. Buying of
the zero rates coupon bonds is most beneficial at the time when the rate of interest is high
(Metzler, and Reesor, 2015).
Apart from the above aspect, generally yield means the return on the investment, determined by
as a percentage on the original investment. Bond yield means, annual return generated by the
holder of the bond if the investment (Kaufman, and Hopewell, 2017). It is based on the purchase
price of the bond and the coupon payment. Generally, the coupon rate of the bond is fixed, its
price changes regularly because of the fluctuation in the rate of interest, maturity time, the credit
quality of the specific bond, the demand of the instrument. There is an inverse relationship
between the price of the bond and its yield (Gzyl, and Mayoral, 2016).

Table 1: Calculation of present value of Treasury Bonds
Code
Coup
on
Maturity
(years)
Face
value
Maturity
(years)
Zero-Coupon
Yields
Present
Value
GSBS19
2.75
% 0.5 100 0.50 1.340% ₹ 98.65
GSBG20
4.50
% 1 100 1.00 1.270% ₹ 95.69
GSBU20
1.75
% 1.5 100 1.50 1.260% ₹ 97.43
GSBI21
5.75
% 2 100 2.00 1.280% ₹ 89.42
GSBW21
2.00
% 2.5 100 2.50 1.320% ₹ 95.17
GSBM22
5.75
% 3 100 3.00 1.370% ₹ 84.56
GSBU22
2.25
% 3.5 100 3.50 1.410% ₹ 92.51
GSBG23
5.50
% 4 100 4.00 1.450% ₹ 80.72
GSBG24
2.75
% 4.5 100 4.50 1.490% ₹ 88.51
GSBG25
3.25
% 5 100 5.00 1.520% ₹ 85.22
GSBG26
4.25
% 5.5 100 5.50 1.540% ₹ 79.54
GSBG27
4.75
% 6 100 6.00 1.560% ₹ 75.70
GSBU27
2.75
% 6.5 100 6.50 1.590% ₹ 83.83
GSBI28
2.25
% 7 100 7.00 1.610% ₹ 85.58
GSBG29
3.25
% 7.5 100 7.50 1.630% ₹ 78.67
GSBU29
2.75
% 8 100 8.00 1.660% ₹ 80.49
GSBG33
4.50
% 8.5 100 8.50 1.680% ₹ 68.79
GSBK35
2.75
% 9 100 9.00 1.700% ₹ 78.34
GSBK39
3.25
% 9.5 100 9.50 1.730% ₹ 73.80
GSBK40
2.50
% 10 100 10.00 1.750% ₹ 78.12

On the basis of the above calculations, a person will buy the bond only if it is available at a price
less than its present value.

REFERENCES
Hung, K. and Liu, S., 2016. Are pre-funded bonds good substitutes for zeros in corporate
financing?. International Journal of Bonds and Derivatives, 2(4), pp.365-378.
Ang, A., Green, R.C., Longstaff, F.A. and Xing, Y., 2017. Advance refunding of municipal
bonds. The Journal of Finance, 72(4), pp.1645-1682.
Metzler, A. and Reesor, R.M., 2015. Valuation and analysis of zero-coupon contingent capital
bonds. Mathematics and Financial Economics, 9(2), pp.85-109.
Kaufman, G.G. and Hopewell, M.H., 2017. Bond price volatility and term to maturity: A
generalized respecification. In Bond Duration and Immunization (pp. 64-68). Routledge.
Gzyl, H. and Mayoral, S., 2016. Determination of zero-coupon and spot rates from treasury data
by maximum entropy methods. Physica A: Statistical Mechanics and its Applications, 456,
pp.38-50.