KAL_II
Loan Servicing Valuation Model
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Questions about Valuation Parameters and Results
1. What is the difference between Present Value and Break-even Price? Why aren't they always the same?
The Present Value of Servicing is defined as "the
sum of the after-tax monthly cash flows discounted at the After-tax
Discount rate given the input purchase price (or NO purchase price)
stipulated (which may have been higher or lower than actual present
value)."
From a mathematical point of view, it is relatively
straightforward to calculate the present value. You need to calculate
the After Tax Cash Flow and then discount this at the stated After
Tax Discount Rate. As you increase or decrease the Purchase Price,
the Present Value will change.
The Break-even Price is the Purchase Price (net of
Conversion Costs) that will generate an Internal Rate of Return
equal to the After Tax Discount Rate. The return you REQUIRE
will be equal to the return GENERATED by that portfolio, given
stated company and portfolio characteristics.
Computing the Break-even Price is an iterative, or
repetitive calculation, much like calculating Internal Rate of
Return. IRR can also be computed manually by increasing or decreasing
the discount rate to make the present value of cash inflows equal
to the present value of cash outflows. Similarly, a portfolio's
purchase price can be changed up or down, until the IRR is equal
to the After Tax Discount Rate.
Instead of forcing you to make repeated efforts at
finding this price, the program internally changes the purchase
price until it arrives at one which will make the IRR equal to
Return on Investment required. The price it arrives at is the
Break-even Price.
Present Value and Break-even Price will only be the
same when you are purchasing at the Break-even Price and you have
no conversion costs. There are no other circumstances in which
the two will be equal.
There will be a different PV everytime you change the purchase price. This is as it should be, but there will be only one Breakeven Price. Despite the fact that you can pay more or less for a portfolio, this will not change the purchase price at which your IRR is equal to your AT Discount Rate.
Economic Duration quantifies the relative sensitivity
of a portfolio's price with respect to changes in the discount
rate. The greater the duration, the greater the price change of
the portfolio with each one percent change in the discount rate.
The economic duration numbers generated by the model
have little use by themselves. They are much more helpful in
comparing one portfolio with another and which one's value will
change more as the discount rate changes.
3. What is Modified Internal Rate of Return? How is it calculated?
What inputs are needed?
Pre-Tax Reinvestment Rate is the key variable used
to calculate the Modified Internal Rate of Return. This represents
what interest rate your company feels future cash flows will earn.
The "unmodified" internal rate of return
is defined as the discount rate which equalizes future cash flows
to the initial cash outlay. Both the timing and amount of future
cash flows are taken into account by this computation.
From the HP-12C Manual:
"The traditional Internal Rate of Return (IRR)
technique has several drawbacks which hamper its usefulness in
some investment applications. The technique implicitly assumes
that all cash flows are either reinvested or discounted at the
computed yield rate. This assumption is financially reasonable
as long as the rate is within a realistic borrowing and lending
range. When the IRR becomes significantly greater or smaller,
the assumption becomes less valid and the resulting value less
sound as an investment measure.
IRR also is limited by the number of times the sign
of the cash flow changes (positive to negative or vice versa).
For every change of sign, the IRR solution has the potential
for an additional answer.
This Modified Internal Rate of Return procedure (MIRR)
is one of several IRR alternatives which avoids the drawbacks
of the traditional IRR technique. The procedure eliminates the
sign change problem and the reinvestment (or discounting) assumption
by using user stipulated reinvestment and borrowing rates.
Positive cash flows are reinvested at a reinvestment rate which reflects the return on an investment of comparable risk. An average return rate on recent market investments might be used.
Using the Debt Repayment Analysis module, you calculate
your After-tax, After-debt Service monthly cash flows. After
you sum them you need to discount that cash flow stream. Instead
of using the After Tax Discount Rate (as you used in the Cash
Flow module), you use the After Tax Equity Discount Rate.
The PV of Cash Flows after Debt Service is NOT affected
by the Reinvestment Rate because the Discount Factor used is the
After- Tax Equity Discount Rate. For the same reason, Reinvestment
Rate does NOT affect the Net Present Value to Equity.
This is the discount rate used in the Debt Repayment
analysis which compounds equity invested to final cash balance.
Unlike the IRR and MIRR, which equalize future cash flows to
the initial cash outlay, Modified Internal Rate of Return on Equity
Invested looks at your final cash balance. The Reinvestment Rate
DOES affect MIRREI. because this is the rate used in the calculation.
The Reinvestment Rate is used in the Debt Repayment
Analysis to reward cash balances that build up after debt service.
The Reinvestment Rate will always be adjusted for After-Tax analysis.
Mechanics of Debt Repayment Analysis:
If you change ONLY the Reinvestment Rate, what will
be affected are:
Modified Return on Invested Equity (goes up with higher Reinvestment Rate and goes down with lower B/T Reinvestment Rate).
1) Debt at start of Year stays the SAME
2) Bank Interest for Year stays the SAME
3) The Cash at Start of Next Year will CHANGE, because End of Previous Year's Cash Balance will have changed
4) Cash Flows are changed due to A/T Interest Earned
5) After Tax Servicing Income stays the SAME
6) Amortization of Purchase Price stays the SAME
7) A/T Bank Interest stays the SAME
8) Cash Available to Repay Debt CHANGES
9) End of Year Cash Balance CHANGES
10) After Tax Book Income CHANGES
The Equity Discount Rate --used only in Debt Repayment
Analysis-- represents the required rate of return on the equity
put up to purchase servicing. The concept is the same as the
"cost of equity" mentioned in After-Tax Discount Rate.
This is the Discount Rate that applies to equity
profits after expenses, debt repayment, and taxes. Since flows
to equity are essentially after-tax, the discount rate should
be set accordingly.
Some other names used instead of After-Tax Equity
Discount Rate are After-Tax Required Rate as well as After-Tax
Required Rate of return on Equity. They all mean the same thing.
Equity Discount Rate does NOT affect the Modified
Return on Invested Equity (the rate which compounds equity to
reach final cash balance).
Equity Discount Rate DOES affect the PV of Cash Flows after Debt Service, because PV of Cash Flows after Debt Service is the sum of the after-tax monthly cash flows (net of debt interest and principal repayment) discounted at the Equity Discount Rate.
Equity Discount Rate DOES affect Net Present Value to Equity.
Equity Discount Rate does NOT affect the Cash Flows. If you change NLY Equity Discount Rate, the cash flows after Debt Service will not change, but the discount rate used for A/T Equity Discount will affect:
1) PV of Cash Flows after Debt Service
2) Therefore Net Present Value to Equity
3) Modified Internal Rate of Return
Net Present Value of Equity is calculated by taking
your PV of Cash Flow after Debt Service and then subtracting Invested
Equity and After Tax Conversion Costs. If NPV to Equity is negative,
the financial value of the investor's assets will be decreased.
If NPV to Equity is zero, the financial value of the investor's
assets would not change. Finally, if NPV of Equity is positive,
the financial value of the investor's assets would be increased.