Question

Distinguish the differences among the following interest rates for bonds payable: yield rate, nominal rate, stated rate, market rate, and effective rate. Please give an example of each rate applied to actual practice.

Answer 1

Nominal Rate is the stated interest rate of the Bond. If the stated interest rate is 10% for a bond, the nominal rate is 10%. If face value of a bond is $10,000 and the stated interest rate is 10% payable semi-annually, the interest payable is $500 (10000*(0.1/2))in each semi- annual period.

Yield rate is the internal rate of return for purchasing a bond.

Suppose, the above bond is available in the market at $ 9,500.

Maturity of bond after 3 years

Semi-annual payment =$500

Number of payments=3*2=6

Payment at maturity =$10,000

Yield Rate(Using RATE function of excel with Nper=6,Pmt=500, Pv=-9500,Fv=10000)

Semiannual Yield Rate=6.02%

Annual Yield Rate=6.02*2=12.04%

Market Rate is the current rate in the market for similar bonds.

Assume , the market rate of similar bond is =8% per annum

Semi annual market rate =4%

The market value of the bond will be present value of future cash flows at current market Rate

Market value of the above bond, if the market rate is 8%,

Using PV function of excel with Rate=8%, Nper=6, Pmt=-500, Fv=-10000,

Current Market Value=$10,524.21

Effective Rate is the rate which is actually earned . If compounding period is less than one year, the effective rate will be higher than the nominal rate.

In the above case the nominal rate is 10% compounded semi annually.

Effective Rate =((1+0.05)^2)-1=0.1025=10.25%

Effective Rate=r

Nominal rate=i

n=number of compounding in a yer

r=((1+(i/n))^n)-1