Illustration

Consider a Rs.1,000 par value bond whose current market price is Rs.850. The bond carries a coupon rate of 8% and has a maturity period of 9 years. What would be the rate of return that an investor earns if he purchases the bond and holds till maturity?

Solution

The rate of return earned, also referred to as yield to maturity, is the value of k_d in the following equation:

         P₀               =     

         Rs.850          =     

                            =     Rs.80 (PVIFA_{kd%, 9 yrs}) + Rs.1,000 (PVIF_{kd%, 9 yrs.}).

Where,

         I        =   Interest

         F       =   Face value

         k_d      =   Cost of debt

         P₀      =   Current market price.

To find out the value of k_d in the above equation, several values of k_d will have to be tried out in order to reach the input value. Therefore, to start with, consider a discount rate of 12% for k_d for which the expression becomes equal to:

         = Rs.80 (PVIFA _{12%, 9 yrs}) + Rs.1,000(PVIF_{12%, 9 yrs.})

         = Rs.80 x 5.328 + Rs.1,000(0.361)

         = Rs.426.24 + Rs.361 = Rs.787.24.

Since the above, value is less than the market price, we have to try with a less discounting rate (k_d). So, let k_d = 10%, then the equation becomes:

         = Rs.80(PVIFA_{10%, 9 yrs.}) + Rs.1,000 (PVIF_{10%, 9 yrs.})

         = Rs.80 x 5.759 + Rs.1,000 x 0.424

         = Rs.460.24 + Rs.424 = Rs.884.72

From the above, it is clear that k_d lies between 10% and 12%. Now, we have to use linear interpolation in the range of 10% and 12%. k_d is determined as follows:

 

                        = 10% + (12 - 10%)      

 

                   = 10% + 2% 

 

                   = 10% + 2% x 0.356

                   = 10% + 0.71

                   = 10.71%

The yield to maturity is 10.71%.

An Approximation: As trial and error methods of calculation are tedious, the following approximation formula can be employed to find out the approximate YTM on a bond.

 

         YTM =        

 

Where,

           YTM          =     Yield to maturity.

                   I       =     Annual interest payment.

                   F       =     Par value or redemption value of the bond.

                   P       =     Current market price of the bond.

                   N       =     Years to maturity.

Therefore,

 

         YTM =         

                            

Posted Date: 9/10/2012 1:43:38 AM | Location : United States

Ask an Expert

Related Discussions:- How to calculate rate of return?, Assignment Help, Ask Question on How to calculate rate of return?, Get Answer, Expert's Help, How to calculate rate of return? Discussions

Write discussion on How to calculate rate of return?
Your posts are moderated

Write your message here..

Related Questions

Personal budget project, 15 points) You need to develop a personal budget. ... 15 points) You need to develop a personal budget. Try to be as realistic as possible. If you are going to school and not working then do some research to find out what salary you w

Valuing mortgage-backed and asset-backed securities, A cash-flow yield is t... A cash-flow yield is the discount rate that makes the price of a mortgage-backed or asset-backed security equal to the present value of its cash flows. It is built

Money market mutual funds (mmmfs), Since the operations in the money ... Since the operations in the money market are dominated by institutional players, the retail investor's participation in the market seems to be limited. To overcom

Determine the advantages of explicit cost, Determine the advantages of expl... Determine the advantages of explicit cost Explicit cost of an interest bearing debt will be the discount rate which equates present value of the contractual future payments of

Define the risk of cost of capital, Risk of cost of capital A straight... Risk of cost of capital A straightforward assumption of traditional cost of capital analysis is that firm's business and financial risk are unaffected by acceptance and financ

Public financial statements of a company, Public Financial Statements of a ... Public Financial Statements of a Company The final exercise is the valuation of a publicly held company's equity. You must base your valuation on the company's public financia

Social assistance program for the elderly, Social Assistance Program for th... Social Assistance Program for the Elderly For the elderly destitutes, the Central and many State Governments have designed several social assistance programs. Under the nationa

Margin trading, Margin Trading: Suppose an investor wants to buy 100 Re... Margin Trading: Suppose an investor wants to buy 100 Reliance Energy shares, whose market price is Rs.500. This transaction requires Rs.50,000 but the investor has only Rs.30,0

What is an annuity, What is an annuity? An annuity is a series of equiva... What is an annuity? An annuity is a series of equivalent cash flows, spaced consistently over time.

Specialized stock indexes, Specialized Stock Indexes The most regularly... Specialized Stock Indexes The most regularly quoted market indices are those that include the stocks of the largest listed companies on a nation's largest stock exchange. Examp