lecture 3 valuation of fixed income securities (b) · valuation of fixed income securities (b) ......

Faizan Ahmed

Financial Management SZABIST

Faizan Ahmed

SZABIST

Lecture 3 Valuation of Fixed Income Securities (b)

Since we all now have a basic idea of how time value of money works, it is time we put the techniques we learned to some use…

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Faizan Ahmed


Bond Valuation Conceptual Review…

• A bond is a long-term debt instrument and a contract under which a borrower agrees to make payments of interest and principal on specific dates to the holders of the bond.

• Based upon the definition, it is clear that the holder will receive two genres of cash flows. One is the coupon interest payment and the other is the principal repayment at maturity.

• Also recall that the fair value of any financial asset is the present value of all the expected cash flows. So in case of bonds, its fair value will be the present value of coupon payments and principal repayment. That is,

Bond Fair Value = PVCoupon Payments + PVPrincipal Repayment

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Faizan Ahmed


Financial Assets Bond Valuation…

• Here,

– Bond’s Value = Present value of all the expected future cash flows;

– Kd% = Applicable discount rate used to calculate the present value of the bond’s cash flows;

– Interest = Interest payment made by the issuer of the bond as per the coupon rate;

– N = Number of years/periods before the bond matures.

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0 1 2 3 N

Bond’s Value

Interest

Kd% Kd% Kd% Kd%

Interest Interest Interest + Face value

Faizan Ahmed


Government Debt Securities Pakistan Investment Bonds (PIBs) & Treasury Bills…

• Adverse imbalances between the expenditures and receipts of the government over an extended period of time has resulted in persisting fiscal deficits. With expenditures almost always exceeding the quantum of inflows, the Government of Pakistan consequently relies on domestic debt as a source of bridging the gap;

• As per the latest debt profile of the government, our government has borrowed approximately PKR 5,349 billion from domestic sources;

• Out of the total domestic debt outstanding, approximately 52% has been raised by issuing treasury bills (T-Bills) while 10% of it has been funded by issuing Pakistan Investment Bonds (PIBs).

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Faizan Ahmed


Pakistan Investment Bonds (PIBs) Government Debt Securities…

• With the aim of fulfilling the longer term appetite of the government, Pakistan Investment Bonds (PIBs) were launched in December 2000. This newer instrument succeeded Federal Investment Bonds (FIBs) which were the initial source of government’s long-term funding and were suspended in June 1998;

• Categorically speaking, PIBs are coupon paying bonds and are issued in seven different tenors of 3, 5, 7, 10, 15, 20 and 30 years;

• Each bond has a face value of PKR 100, pays interest semiannually and bears the following rates of interest:

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Maturity Coupon Maturity Coupon Maturity Coupon

3 Year 11.25% 5 Year 11.50% 7 Year 11.75%

10 Year 12.00% 15 Year 12.50% 20 Year 13.50%

30 Year 13.75%

Faizan Ahmed


Pakistan Investment Bonds (PIBs) Government Debt Securities…

• Financial valuation of PIBs is synonymous to that of any coupon paying bond. Therefore, we can demarcate the associated cash flows into two categories:

– Interest payments;

– Principal repayment upon maturity.

PIB Fair Value = PVCoupon Payments + PVPrincipal Repayment

• Since coupon payments here are fixed, we can combine the interest payments to constitute an annuity. Thus,

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Faizan Ahmed


Pakistan Investment Bonds (PIBs) Putting Valuation in Practice…

• Consider its January 01, 2011, you’re required to calculate the fair values of the following Pakistan Investment Bonds (PIBs):

• As per the latest published data, following are the discount rates which are to be used while valuing government securities:

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Maturity PKRV Rate Maturity PKRV Rate Maturity PKRV Rate

2 Year 14.01% 7 Year 14.33% 15 Year 14.60%

3 Year 14.23% 9 Year 14.17% 20 Year 14.79%

5 Year 14.25% 10 Year 14.26% 30 Year 14.96%

Maturity Years

Remaining Coupon Rate Maturity

Years Remaining

Coupon Rate

5 Year 5 Year 11.50% 15 Year 2 Year 12.50%

10 Year 8 Year 12.00% 30 Year 19 Year 13.75%

Faizan Ahmed


Treasury Bills (T-Bills) Government Debt Securities…

• Unlike PIBs, treasury bills or T-Bills for short are government securities designed to bridge the short term funding gap of the government;

• Categorically speaking, T-Bills are zero-coupon bonds i.e. they are sold at a discount to their face values and are issued in three different tenors of 3, 6 and 12 months respectively;

• Each T-Bill has a face value of PKR 100, the fair value of which is computed by using the following formula:

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Faizan Ahmed


Treasury Bills (T-Bills) Putting Valuation in Practice…

• Consider its January 01, 2011, you’re required to calculate the fair values of the following treasury bills (T-Bills):

• As per the latest published data, following are the discount rates which are to be used while valuing government securities:

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Maturity PKRV Rate Maturity PKRV Rate Maturity PKRV Rate

0 – 7 Days 12.93% 31 – 60 Days 13.08% 121 – 180 Days 13.48%

8 – 15 Days 12.91% 61 – 90 Days 13.37% 181 – 270 Days 13.59%

16 – 30 Days 12.95% 91 – 120 Days 13.43% 271 – 365 Days 13.74%

T-Bill Days to Maturity T-Bill Days to Maturity

A 42 C 193

B 87 D 283

Faizan Ahmed


Corporate Debt Securities Corporate Bonds & Term Finance Certificates (TFCs)…

• Similar to the funding needs of governments, corporations in an attempt to fuel their expansions and/or cater to their funding needs issue corporate bonds of varying nature;

• Unlike PIBs and T-Bills, corporate bonds neither have any specific coupon paying structure nor do they follow a uniformed principal repayment plan. The composition of coupon payment and the manner in which principal is repaid varies from bond to bond and is specified in the offering document;

• Depending upon the frequency and structure of the coupon, we can bifurcate corporate bonds into two general categories:

– Floaters (Inverse floaters): These are the bonds over which the coupon interest is determined by a pre-specified formula and varies over the term of the bond;

– Fixed coupon paying bonds: As the name suggest they pay a fixed rate of interest over the life of the bond;

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Faizan Ahmed


Corporate Debt Securities Corporate Bonds & Term Finance Certificates (TFCs)…

• Financial valuation of corporate bonds (Be it floaters or fixed-coupon paying bonds) is based upon the same principal that:

TFC Fair Value = PVCoupon Payments + PVPrincipal Repayment

• Generically, the following formula will be used to calculate the fair values of corporate bonds:

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Faizan Ahmed


Corporate Debt Securities Putting Valuation in Practice…

• Consider its October 14, 2010, on your way to SZABIST you saw a big billboard displaying one of the latest offerings in the debt market;

• As per the information portrayed, you got to know that Engro Corporation Limited is issuing TFCs bearing profit rates of 14.5% with payments made on semiannual basis. It also said that it’s a 3 year investment avenue, the minimum investment is PKR 25,000 and the principal will be repaid upon maturity;

• The offered profit rate was alluring but before making the investment decision you decided to investigate upon the opportunity cost of capital. A little research revealed that PKRV rate for the same tenor is 13.89%. In order to compensate yourself for taking the extra credit risk, you decided that you’ll require a premium of 1.5% over the PKRV rate;

• Given the information, what is the fair value of the minimum investment?

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Faizan Ahmed


Corporate Debt Securities Putting Valuation in Practice…

• Consider its June, 2009, while skimming through the newspaper you saw a clipping covering one of the latest offerings in the debt market. As per the information portrayed, you got to know that in order to meet its funding needs FM Consultants is about to issue TFCs in the market;

• It was mentioned that its an 8 year investment with a face value of PKR 5,000. Moreover, it was also specified that these TFCs bear a coupon rate of 15.50% for the first 5 years and 16% for the last 3 years;

• While coupon payments were to be made on annual basis, it was specified that the TFC will repay 10% of the face value in each of the first four payments while the rest 60% will be repaid in equal tranches in the next four years;

• If your opportunity cost of capital is 14%, what should be the fair value of the TFC?

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lecture 3 valuation of fixed income securities (b) · valuation of fixed income securities (b) ......

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