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

Define a callable bond, What is a callable bond?  What is a putable bond?  ... What is a callable bond?  What is a putable bond?  How do each of these features affect their respective market interest rates? A callable bond may be retired untimely at the dis

Management accounting, Management Accounting: Management accounting on ... Management Accounting: Management accounting on the other hand tends to focus internally. Reports generated through management accounting processes will be used by the organisa

Weighted average cost of capital, Chu Chu Train Systems is expected to pay ... Chu Chu Train Systems is expected to pay a $3.25 annual dividend (D1 = $3.25), the dividend is expected to grow at a constant rate of 5.50% a year, and the common stock currently s

Determination of spread, Determination of spread Daily interest rate = ... Determination of spread Daily interest rate = 5.11/ 365 = 0.014% per day Variance of cash flows = 1000 × 1000 = $1000000 per day Transaction cost = $18 per transaction

Describes net income approach to capital structure, Q. Describes Net Income... Q. Describes Net Income Approach to Capital Structure? Net Income Approach: - As-per to the Net Income Approach as suggested by Durand the capital structure decision is applica

Determine about the zero interest bonds, Determine about the Zero Interest ... Determine about the Zero Interest Bonds (ZIBs) Very much alike DDBs, only crucial difference is that these are issued at face values (DDBs are issued at a discount to face valu

Determine the investment to maximize the return, Assume that the treasurer ... Assume that the treasurer of a company has an extra cash reserve of $1,000,000 to invest for six months. The six-month interest rate is 8% per year in the U.S. and 6% per year in G

Explain the meaning of - purchase consideration, Explain the meaning of - P... Explain the meaning of - Purchase consideration The  type  of  offer  made  to  target  company's  shareholders  would have  a  big  impact on acceptance. Apparently the price

.FMAC 503 assignment, solution to assignement solution to assignement

Setting budget goals and objectives, Setting Budget Goals and Objectives: ... Setting Budget Goals and Objectives: Having collected and analysed all relevant information, and made general forecasts as to the key areas of concern / opportunity and special