BONDSâ€™ VALUATION:Long Bond - Risk Theory, Bond Portfolio Theory, Interest Rate Tradeoff

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Financial Management MGT201

Lesson 14

BONDS' VALUATION

Learning Objectives:

After going through this lecture, you would be able to have an understanding of the following topic.

· Bonds Valuation and Theory

In the Previous lecture, we have studied about bonds and their different characteristics.

In this lecture, we would study about the Bonds valuation & bond pricing.

We use similar tools for the bond valuation which we have studied in capital budgeting.

Basic principal behind Valuation of direct claim securities:

Value of a Direct Claim Security such as a Bond derives from direct cash flows the form of Coupon

Receipts and Par Recovery at maturity. The value of the bond is directly tied to the Value of the

Underlying Real Assets of the Business (whose operations generate cash receipts from sales of goods

and services). It means that income from the bond starts from the real assets. The coupon payments

made by the company are generated from the cash flows from the real assets of the company.

Now, we would calculate the value of the bond by using Net Present Value or Present Value

formula that we have studied in the capital budgeting. That is called fair or intrinsic value of the bond.

We compare the fair value with the market value of that bond. Whether there is a difference between the

fair value and market value of the bond.

Let's review the present value formula for the bond in detail.

The relationship between present value and net present value

NPV = -Io + PV

When we talk about the present value it is equal to net present value + initial investment.

We calculate the present value of the direct claim securities because it gives us intrinsic value of that

direct claim security should be. It is the starting point of comparing them

Present Value formula for the bond:

PV= ∑ CFt / (1+rD)t =CF1/(1+rD)+CFn/(1+rD)2 +..+CFn/ (1+rD) n +PAR/ (1+rD) n

t =1

In this formula

PV = Intrinsic Value of Bond or Fair Price (in rupees) paid to invest in the bond. It is the Expected or

Theoretical Price and NOT the actual Market Price.

rD = it is very important term which you should understand it care fully. It is Bondholder's (or

Investor's) Required Rate of Return for investing in Bond (Debt).As conservative you can choose

minimum interest rate. It is derived from Macroeconomic or Market Interest Rate. Different from the

Coupon Rate!

Recall Macroeconomic or Market Interest Theory: i = iRF + g + DR + MR + LP + SR

CF = cash flow = Coupon Receipt Value (in Rupees) = Coupon Interest Rate x Par Value. Represents

cash receipts (or in-flow) for Bondholder (Investor). Often times an ANNUITY pattern. Coupon Rate

derived from Macroeconomic or Market Interest Rate. The Future Cash Flows from a bond are simply

the regular Coupon Receipt cash in-flows over the life of the Bond. But, at Maturity Date there are 2

Cash In-flows: (1) the Coupon Receipt and (2) the Recovered Par or Face Value (or Principal)

n = Maturity or Life of Bond (in years)

In the next lectures, you would study that how the required rate of return is related to market rate of

return.

The fair value of the bond is the value that we expect the bond to be. We have to compare this value

with the actual price of the bond in the market. The actual price of the bond (market value) varies on the

supply and demand of the bond in the market and it will vary depending upon the interest rate in the

bond.

On the basis of above comparison we decide whether to invest in a particular bond or not.

The market rate of interest prevailing in the market effects price of the bond. Because, market rate

of return will have an impact on rD which is the required rate of return expect by the investor of the

bond.

When Market Interest Rate (ie. Investors' Required Rate of Return) Increases, the Value (or

Price) of Bond Decreases. Check using formula. This is known as Interest Rate Risk. This is a

Financial Management MGT201

simple relationship because rD which will rise and fall with the general interest rate is in the

denominator of the equation. So, when interest rate in denominator goes up the present value (price)

will decrease.

When Market Interest Rate have went behind the coupon interest rate. As the coupon interest

rate has been fixed by the bond issuer .The issuer have to pay that rate but the market rate fluctuates

on daily and hourly basis.

So, When Market Interest Rate < Coupon Interest Rate, Market Value (or Price) of Bond > Par

Value. Because when market is offering lower rate of return then the bond then the bond becomes

valuable. This is known as a Premium Bond. If Required Rate = Coupon Rate then Market Value =

Par Value. Check using formula. As Maturity Date approaches, Market Value of Bond will

approach its Par Value. Note: Market Rate varies but Coupon Rate is fixed.

Bonds have the limited life and as the life of a bond expires the bond approaches its maturity

date the market value of the bond approaches to par value of the bond.

Long Bond - Risk Theory:

Interest Rate Risk for Long Term Bonds (i.e. 10 year bonds) is more than the Interest Rate Risk

for Short Term Bonds (i.e. 1 year bonds) provided the coupon rate for the bonds is similar. When

investor buy a long term bond he is locked in investment for long term period there are more chances of

fluctuation in interest rate and the inflation rate.

So, the impact of interest rate changes on Long Term bonds is greater. Long Term Bond Prices

fluctuate more because their Coupon Rates are fixed (or locked) for a long time even though Market

Interest Rates are fluctuating daily; therefore the price of Long Bonds has to constantly keep adjusting.

Price of the long term bond fluctuates more as compared to the short term bond. Because, you

have a long term bond with fix coupon rate but the market interest rate is fluctuating in between the

years

Bond Portfolio Theory:

Changes in Market / Macro Interest Rates have 2 Major Impacts on the Portfolio (collection of bond

investments) of the Bondholder:

(1) Interest Rate Risk: In this, the value of Bond Portfolio Drops if interest rates Rise) and

(2) Reinvestment Risk: In this, the overall Rate of Return (or Yield) on the Bond Portfolio

Rises when interest rates rise the opportunity cost for the bond holder has changed. For

example, somebody may have bought a short term bond with coupon rate of 15 % for one

year. At maturity there is a risk that bondholder may not find another investment that can

yield as much as 15%.

When old bonds mature, bondholders are forced to invest in

bonds at lower coupon rates). It is higher for short term bonds.

Interest Rate Tradeoff:

The 2 Effects Cancel Each Other Out. When market Interest Rates Rise, Bond Prices Drop

(Interest Rate Risk Goes Up) BUT Overall Returns on future reinvestment in bonds go up (ie.

Reinvestment Risk Goes Down).

Bond Maturity (Life) Tradeoff:

SHORT-life bonds (ie. 1 year) have less Interest Rate Risk than long Bonds (ie. 10 years) but

the Short-life bonds have MORE Reinvestment Rate Risk.

Bond Valuation - Café Case Study

Example:

You do not have enough money to start your business so you approach a bank. The bank offers

to lend you Rs 100,000 and you sign a bond paper. The bank asks you to issue a bond in their favour on

the following terms required by the bank:

Par Value = Rs 100,000 (ie. Loan Principal Amount)

Maturity = 2 years

Coupon Rate = 15% mark-up paid at end of each year

Security = Property Deed for the canteen space

Note: This is a simplified case where we are treating a short-term bank loan like a Bond.

For the Bank, what is the Value of Investing in a Bond with you?

CF = Cash Flow = Coupon Value

= Coupon Rate x Par Value

Financial Management MGT201

= 15% x Rs 100,000 = Rs15,000 pa.

The bank will receive Rs 15,000 in interest every year for two years from you because you have

agreed to pay 15% mark-up.

Assume the Bank's Required Return (rD) = 10% pa. The bank's opportunity cost is 10% because it

can earn this much by investing risk free in T-bills

Now compute the PV or Fair Price of Bond:

PV = 15,000 / 1.1 + 15,000 / (1.1)2 + 100,000 / (1.1)2 = 13,636 + 12,397 + 82,645 =

+Rs. 108,678 (= PV and NOT NPV!)

So, what is the Value of this Financing Deal to the Bank? Lending (ie. negative Rs 100,000) to you

today at 15% mark-up for 2 years is worth positive Rs 108,678 to the bank today, i.e. A net gain in

value for the bank. BUT, if some other bank offers to pay Rs 110,000 to this bank to buy this deal

from them, then this bank should sell!

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