when we calculate the present value of bond i.e. coming at 947.35 rupees because in the market rate of interest for the same type of bond has increased at 12% p.a. compunded quartely for two years ( effective rate-12.55%)
when we calculate the total cash flow it is becoming 22.5*7+1022.5=1180
so if we pay 947.35 for the bond now we should get 1200 at the end of two years to get the effective interest but we are getting only 1180 from the cash flows. SO I DID NOT UNDERSTAND IT
and in my view the present value should be
1180/(1.03^8)=931.50
please tell me where I am going wrong and whether my concept is right or wrong.
Hi, I understand your doubt. Let me answer your question without getting into whether your sum is done correctly or not
Question : If I compound 947.35 for two years, I should be getting 1200 at the end of the two years, but the total of the cash flows from the bond is 1180. Why this difference?
But there is one factor you seem to have missed.
You are getting some of these cash flows before the end of two years. I am talking about the coupon payments.
This is exactly what Time Value of Money is all about. Money received now is worth more than money to be received in the future.
Think of it this way
What would you prefer? Receiving “x” amount right now, or 10 years from now?
You would probably say “right now” because I will be able to earn some interest on that amount, and 10 years from now, this can easily grow to be worth more than “x”.
Similarly, the earlier coupon payments are slightly more valuable (than the last coupon payment) because once you receive the money, you can simply earn interest on that money (12% in this example)
So while discounting, the present value of the earlier coupons are slightly more than the present value of the later coupons
Mathematically, this is happening because of the discounting factor.
You are multiplying 22.5 by 1/1.03 for the first coupon whereas by 1/(1.03^8) for the last coupon.
Implying 22.5 x 0.97 vs 22.5 x 0.789
Present value of first coupon is 21.825
Present value of last coupon is 17.75
Therefore, the present value of the bond (947.35) is the present value of the future payments (adjusted for the time of their payments)
This is entirely different from calculating the present value of 1180 (sum of cash flows in your example) being received after two years.
I hope this answer helps.