InvestorQ : How does the frequency of cash flow compounding impact the present value and the future value of the bonds?
Bhavik Nehru made post

How does the frequency of cash flow compounding impact the present value and the future value of the bonds?

Answer
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Niraj Mehta answered.
1 year ago


Bonds have different ways of compounding the cash flows. You could either have annual compounding, half yearly compounding, quarterly compounding or even monthly compounding. As the frequency of compounding increases, the future value and the present value get impacted. Let us start off here with the base once again where an annual contribution of Rs.5000 is compounded annually at 8% for 10 years. Check the table below.

Present Value Calculator (For a Series of cash flows)

Enter the type of cash flow that you are discounting =

GA

[S=Simple;

A=Annuity;

GA=Growing Annuity;

P=Perpetuity;

GP=Growing Perpetuity]

Enter the dollar amount of the cash flow =

? 5,000.00

For S: Enter the single cash flow

For A and P: Enter the cash flow each period

For GA and GP: Enter the current year's cash flow]

Enter the number of years for the cash flow =

10

For S: Specify the year of the cash flow

For A and GA: Enter the number of years for annuity

For P and GP: Leave blank

Enter the annualized discount rate to use on cash flows =

8.00%

Enter the annualized discount rate

Enter the expected growth rate in the cash flow =

0%

Leave blank for S, A and P

Enter the annualized growth rate for GA and GP

Specify the number of compounding periods per year =

1

If semi-annual enter 2, if monthly enter 12 ….

Output for Present Value and Future Value

Discount Rate per period =

8.00%

Number of periods =

10

Present Value of Cash Flow(s) =

? 33,550.41

Future Value of Cash Flow(s) =

? 72,432.81

In the above instance, annual contributions of Rs.5000 over 10 years entail a nominal contribution of Rs.50,000 overall. This has a present value of Rs.33,550 and a future value of Rs.72,434. What happens if we split the contribution into 2500 every 6 months instead of Rs.5,000 for the full year. Here the total contribution remains the same but now it gets compounded more frequently. As can be seen from the above illustration, the present value and the future value increase through half yearly compounding instead of annual compounding. Will it increase further if you opt for quarterly compounding? Let us assume here that the investor contributes Rs.1250 every quarter and the compounding is also every quarter. Check the sheet below as to how the contribution impacts the PV and the FV.

Present Value Calculator (For a Series of cash flows)

Enter the type of cash flow that you are discounting =

GA

[S=Simple;

A=Annuity;

GA=Growing Annuity;

P=Perpetuity;

GP=Growing Perpetuity]

Enter the dollar amount of the cash flow =

? 1,250.00

For S: Enter the single cash flow

For A and P: Enter the cash flow each period

For GA and GP: Enter the current year's cash flow]

Enter the number of years for the cash flow =

10

For S: Specify the year of the cash flow

For A and GA: Enter the number of years for annuity

For P and GP: Leave blank

Enter the annualized discount rate to use on cash flows =

8.00%

Enter the annualized discount rate

Enter the expected growth rate in the cash flow =

0%

Leave blank for S, A and P

Enter the annualized growth rate for GA and GP

Specify the number of compounding periods per year =

4

If semi-annual enter 2, if monthly enter 12 ….

Output for Present Value and Future Value

Discount Rate per period =

1.94%

Number of periods =

40

Present Value of Cash Flow(s) =

? 34,540.78

Future Value of Cash Flow(s) =

? 74,570.96

Quite clearly, the present value and the future value of cash flows have increased in this case when the compounding is made quarterly instead of half yearly. This series can continue.