In: Economics
(Need fully working process please) What is the annual rate of return for a bond that you paid $3500 today and matures in 6 years if it had a face value of $5000 and a coupon rate of 9%?
Solution: Coupon payment = 5000 * 0.09 = 450
Present value of the bond = 3500.
So ,
PV of the bond = 5000/(1+r)^n + 450 { 1 - 1/(1+r)^n} / r
3500 = 5000/(1+r)^n + 450{ 1 - 1/(1+r)^n} / r
Solve for n using linear approximation formula:
r = R1 + NPV1 (R2-R1) / (NPV1 +NPV2)
We have to select by trail and erroe method two rates R1 and R2 which will give us values greater than and lower than 3500. so let us find out the rate .
If r =10 % .
then RHS OF THE PRESENT VALUE OF BOND WILL BE :
5000/(1.1)^6 +450 { 1 -1/(1.1)^6} /0.1 =2822.36 + 1960.= 4782.22.
At 10 % we find that the present value is higher than 3500.
So let us choose one more value for which the present value will be lower than 3500.
5000/(1.15)^6 + 450 {1 - 1/(1.15)^6} /0.15 = 2161.63+ 1703.01 = 3864.
This value is also greater than 3500.
Let us increase the interest rate to 20.
5000/(1.2)^6 + 450{ 1 -1/1.2^6} /0.2 = 1674.48 .+ 1496.47 = 3170.95.
So now we have found two interest rate which are giving values greater than 3500 and lower than 3500.
so using the interpolation formula :
15 % + 3864 ( 20% -15 %) / (3864+3170.95) = 0.15 + 0.027 = 0.177 =17.7 %