How to calculate rate of return?, Financial Management

Assignment Help:

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 kd in the following equation:

         P0               =     1034_rate of return.png

         Rs.850          =     821_rate of return1.png

                            =     Rs.80 (PVIFAkd%, 9 yrs) + Rs.1,000 (PVIFkd%, 9 yrs.).

Where,

         I        =   Interest

         F       =   Face value

         kd      =   Cost of debt

         P0      =   Current market price.

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

         = Rs.80 (PVIFA 12%, 9 yrs) + Rs.1,000(PVIF12%, 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 (kd). So, let kd = 10%, then the equation becomes:

         = Rs.80(PVIFA10%, 9 yrs.) + Rs.1,000 (PVIF10%, 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 kd lies between 10% and 12%. Now, we have to use linear interpolation in the range of 10% and 12%. kd is determined as follows:

 

2292_rate of return2.png

                        = 10% + (12 - 10%)   2245_rate of return3.png   

 

                   = 10% + 2% 1276_rate of return4.png

 

                   = 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 = 699_rate of return5.png       

 

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 =         1053_rate of return6.png

                            615_rate of return7.png


Related Discussions:- How to calculate rate of return?

What are the benefits of holding inventories, Q. What are the Benefits of H...

Q. What are the Benefits of Holding Inventories? (1) Timing of Demand and Supply: - Requirement to hold inventory of raw materials arises because it isn't possible for a firm

Non-traditional mortgages, Non-traditional mortgages also referred to...

Non-traditional mortgages also referred to as Alternative Mortgage Instruments (AMIs), do not have level monthly payments, but employ some other structure of payment.

Cash discount, Which one is true 1.the higher the discount rate the lower ...

Which one is true 1.the higher the discount rate the lower the cost of trade credit 2.the higher the discount rate the higher the cost of trade credit 3.cost of trade credit duri

Micro/Macro Question, You have been hired as an economic advisor to the Sou...

You have been hired as an economic advisor to the Southeastern Conference. As your first assignment they have asked you to identify three microeconomic and three macroeconomic issu

What is logistics, What is logistics? Explain the important activities in l...

What is logistics? Explain the important activities in logistics systems. Logistics - meaning . Working of logistics systems - three important activities - Order processing, I

Show the projected balance sheet method, Q. Show the Projected Balance Shee...

Q. Show the Projected Balance Sheet Method? Projected Balance Sheet Method: - Under this process an approximate is made of assets and liabilities for a future date and a projec

Computing forward rate, We can compute any forward rate using the spo...

We can compute any forward rate using the spot rate. When we tell 3 years forward rate 4 years from now, there are two elements to consider. One is the length of

What do you know about sinking funds, Q. What do you know about sinking fun...

Q. What do you know about sinking funds? sinking funds : quite often, one may be interested to accumulate a target amount over a given period inclusive of interest for the peri

Explain the difference between cash and profit, Explain the Difference betw...

Explain the Difference between cash and profit Cash flow statement shows all the cash in and cash out for the organisation for that period. It demonstrates the cash generating

Convertible bonds, Convertible bonds are the debt instruments issued which ...

Convertible bonds are the debt instruments issued which can be converted after a pre-specified date for a pre-specified number of securities (generally equity stock). I

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd