The Reinvestment Rate Assumption and Modified Internal Rate of Return

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The Reinvestment Rate Assumption and Modified
Internal Rate of Return

• Business 4099

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The Nature of Compound Interest

• When we assume compound interest, we are
  implicitly assuming that any credited interest is
  reinvested in the next period, hence, the growth
  of the fund is a function of interest on the
  principal, and a growing interest upon interest
  stream.
• This principal is demonstrated when we invest
  10,000 at 8 per annum over a period of say 4
  yearsthe terminal value of this investment can
  be decomposed as follows...

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FV4 of 10,000 _at_ 8
Of course we can find the answer using the
formula FV4 10,000(1.08)4 10,000(1.36048896
) 13,604.89
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Annuity Assumptions

• When using the unadjusted formula or table values
  for annuities (whether future value or present
  value) we always assume
• the focal point is time 0
• the first cashflow occurs at time 1
• intermediate cashflows are reinvested at the rate
  of interest for the remaining time period
• the interest rate is unchanging over the period
  of the analysis.

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FV of an Annuity Demonstrated
When determining the Future Value of an
Annuitywe assume we are standing at time zero,
the first cashflow will occur at the end of the
year and we are trying to determine the
accumulated future value of a series of five
equal and periodic payments as demonstrated in
the following time line...
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FV of an Annuity Demonstrated
We could be trying find out how much we would
accumulate in a savings fundif we saved 2,000
per year for five yearsbut we wont make the
first deposit in the fund for one year...
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FV of an Annuity Demonstrated
The time value of money formula assume that each
payment will be invested at the going rate of
interest for the remaining time to maturity.
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FV of an Annuity Demonstrated
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FV of an Annuity Demonstrated
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FV of an Annuity Demonstrated

• In summary the assumptions are
• focal point is time zero
• we assume the cashflows occur at the end of every
  year
• we assume the interest rate does not change
  during the forecast period
• the interest received is reinvested at that same
  rate of interest for the remaining time until
  maturity.

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PV of an Annuity Demonstrated
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Yield to Maturity
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Yield to Maturity ...
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Yield to Maturity ...
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Yield to Maturity ...
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Yield to Maturity ...
Now instead of earning 9.2 she will only earn
8.478 because of the poor reinvestment rate
opportunities.
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The Reinvestment Rate Assumption

• It is crucial to understand the reinvestment rate
  assumption that is built-in to the time value of
  money.
• Obviously, when we forecast, we must make
  assumptionshowever, if that assumption not
  realisticit is important that we take it into
  account.
• This reinvestment rate assumption in particular,
  is important in the yield-to-maturity
  calculations in bondsand in the Internal Rate of
  Return (IRR) calculation in capital budgeting.

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Bond Applications

• Bonds are typically purchased by life insurance
  companies.
• These firms plan to buy and hold the bonds until
  they mature.
• These firms require a given return in order to
  accumulate a terminal value 20, 25 or 30 years
  out into the future.however, they are acutely
  aware that the reinvestment of the coupon
  interest can dramatically affect their realized
  return (making it different than the
  yield-to-maturity.)\
• They have some alternativeschoose zero coupon
  bonds, or immunize themselves from interest rate
  fluctuations (using duration matching strategies)