Question

A $5000 face value industrial bond can be purchased for $4920. Its dividend rate is 9% and it pays dividends semianually and will mature in eight years. What are the rate of return, and the effective rate of return that the purchaser can expect to receive if the bond is purchased?

Answer 1

Solution

Here

t= 8 years

Dividend rate= 9% paid semiannually therefore each divident =4.5%

n= number of periods= 8*2=16

Face value=$5000

Market price=4920

Dividend amount=.045*5000=225

The present value of dividend+maturity value = 225(P/A,r,16)+5000(P/F,r,16)

Here The present value of dividend+maturity value =Market price=4920

The present value of dividend+maturity value should be equal to Market price=4920 at the rate of return

4920=225(P/A,r,16)+5000(P/F,r,16)

Using hit and trial

If r= 7%

present value of dividend+maturity value=5604.70 which is greater than 4920

If r= 9%

present value of dividend+maturity value=5000 which is greater than 4920

Solving further we get r= 9.29%

Rate of return= 9.29%

Now to find effective rate of return

Effective rate of return= (1+r/2)^2= (1+9.29/2)^2

=9.5%

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