Bond Valuation Slides

8/13/2019 Bond Valuation Slides

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Debt instruments promise to pay a stipulated stream ofcash flows. A bond is a debt instrument

It pays periodic interest payments based on the stated(coupon) rate and return the principal at the maturity.

Cash flows on a bond are fairly certain and the price ofbond equals the present value of future interestpayments plus the present value of the face value

(which is returned at maturity).

BOND VALUATION


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BOND VALUATION

Bond valuation is the process of determining the fairprice of a bond. As with any security, the fair value of

a bond is the present value of the stream of cash flowsit is expected to generate.

The value of a bond is determined by discounting the

bonds expected cash flows to the present using theappropriate discount rate.


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BOND VALUATION

Therefore, the price of a bond is given by the following formula:

Example1

Navaratna Ltd. Issued debentures with a face value ofRs. 1000 and the maturity period is 5 years. The rateof interest payable by the company on the debentureis 10% per annum. The appropriate capitalization rate

is 8%. Calculate the present value of the debentures.

Th f th i f b d i i b th f ll i f l


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BOND VALUATION


Example2

Th f th i f b d i i b th f ll i f l


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BOND VALUATION


Example3

A five year bond with a coupon payment of Rs. 11 andthe maturity value of Rs. 80 is currently selling at Rs.110. The required rate of return is 10%. Advise theinvestor whether to buy or not this security.


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BOND VALUATION

Example4

A Rs.100 par value bond bearing a coupon rate of 12percent will mature after 5 years. What is the value ofbond, if the discount rate is 15%

Therefore the price of a bond is given by the following formula:


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Yield to Maturity (YTM)


If the current price/value of a bond is given,together with details of coupons and redemption

date, then this information can be used tocompute the required rate of return or yield tomaturity of the bond (YTM)

Yield-to-maturitythe yield an investor wouldreceive by purchasing a bond at today's marketprice and holding it until its maturity date,receiving all interest coupon payments and the

bond's maturity value on schedule. Therefore the price of a bond is given by the following formula:


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Example 1

A bond with a face value of Rs. 100 is currently

available at Rs. 800. The coupon rate of interestis 9%. The bond will mature after 8 years.Calculate the yield to maturity (YTM) of the bond.

If the current purchase price is higher than theface value, r must be lower than coupon rate



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R = A + C * (B-A)-----

DA - is the rate at the lower trial;B - is the rate at the higher trial;

C - is the excess of value at the lower trial than themarket value/ purchase price

D - is the difference between value of the lower

trial and the value of higher trail Therefore the price of a bond is given by the following formula:


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Example 2

A bond paying a coupon of 7% is redeemable in

five years at par (Rs.1000 and is currently tradingat Rs. 106.62. Estimate its yield (required rate ofreturn)



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Example 3

Suppose you buy a Rs. 1000 face value coupon

bond with a coupon rate of 10% and a maturityof 4 years

1) If purchase price is Rs. 800, what is the yield tomaturity?

2) If purchase price is 1200, what is the yield tomaturity?



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Example 4

A 5 year bond, paying 6 percent interest on the face valueof Rs. 1000 and currently selling for Rs. 883.40. Calculatethe yield to maturity.



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Example 5

A bond of Rs. 10000 bearing coupon rate 12% andredeemable in 8 years at par is being traded at Rs. 10,600. Find out the yield to maturity of the bond.



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Example 6

An investor buys a 10% bond (FV=1000) for Rs. 1029today. The remaining maturity period is 4 years. Find outthe YTM



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Example 7

A five year Rs. 100 debenture of a firm can be sold for anet price of Rs. 95.90. The coupon rate of interest is 14%per annum, and the debenture will be redeemed at 5percent premium on maturity. Compute the yield to

maturity.



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Example 8

The current value of a 8% debenture, of Rs. 1000redeemable after 5 years at par is Rs.924.28. Find out theyield to maturity or internal rate of return



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Example 9

Cannon Corporation is selling a new issue of bonds to raise

money to finance its new line of yogurt products. Thebonds will pay a coupon rate of 5% and will mature in 15years. The face value of the bonds is Rs.1,000 each;interest is paid semi-annually.

A) The market rate of interest is currently 6% for similarbonds. What is the fair price for an investor to pay for oneof these bonds?

B) The current market price is $920 for each bond. If youpaid this price, what would be your yield-to-maturity?



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Yield to Maturity (YTM):

(Approximate Method)

YTM = I + (RVBo)/N--------------------

(RV + Bo)/2

I = Annual Coupon Interest PaymentRV = Redemption Value

Bo = Market Value/ Purchase price

N = Number of years


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Yield to Call (YTC):

Some bonds have a feature, referred to as a , call feature,that allows the bond issuer to buy back the bonds from theinvestor at a specified price the call price- during aspecified period prior the bonds maturity date. A bondwith this feature is referred to as callable bonds.

Calculation of Yield to call is similar to yield to maturity



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Example 1:

Surya Ltd has a 14% debenture with a face value of Rs. 100that matures at par in 15 Years. The debenture is callablein 5 years at Rs. 114. It currently sells for Rs. 105.Calculate Yield to call and yield to maturity


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Example 3:

A 7-year, $1,000 par bond has an 8% annualcoupon and is currently yielding 7.5%. The bondcan be called in 2 years at a call price of $1,010.What is the bond yielding, assuming it will be called(known as the yield to call)?



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Example 4:

A Rs. 1000 par value bond has 7.5% coupon rate.The bond has a maturity period of 15 years. YTM is6%.

If bond is callable after 7 years for Rs. 1075, whatwould be the yield to call?




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Bond Duration

(Macaulay Duration)

Duration is defined as the weighted average of the lengths oftime until the remaining cash flows are received.

Duration is the weighted average measure of a bonds life.The various time periods in which the bond generates cashflows are weighted according to the relative size of thepresent value of those cash flows.



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As the bondholder receives a coupon payment, the amountof the cash flow is no longer on the time line, which

means it is no longer counted as a future cash flow thatgoes towards repaying the bondholder.

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