Transcript Finance Theory and Real Estate Returns

Conventional Yield Measures
 Special Case: Investment with Only 1
Cash Flow
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Derivation:
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Ex. Suppose that a financial instrument currently
selling for $62,321.30 promises to pay $100,000
six years form now. What is the yield?
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
Conventional Yield Measures
 Current Yield
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Current Yield =
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Ex. 15 year, 7% coupon bond with a $1,000 PAR
value, currently selling for $769.40. What is the current
yield?
 Strengths:
 Weaknesses:
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
Conventional Yield Measures
 Current Yield for Mortgages
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Current Yield =
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Ex. 15 year, monthly payment mortgage, with a 7%
interest rate, and an original loan amount of $200,000.
What is the current yield?
 Strengths:
 Weaknesses:
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
Conventional Yield Measures
 Yield-To-Maturity (YTM)
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Yield-To-Maturity =
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Ex. Consider a 15 yr., 7% semi-annual coupon
bond with a $1,000 PAR value, currently selling for
$769.40. What is the yield-to-maturity?
 Strengths:
 Weaknesses:
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
Conventional Yield Measures
 Yield-To-Maturity (YTM) for Mortgages
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Yield-To-Maturity =

Ex. Consider a 15 year, $200,000 monthly
payment mortgage, with a 7% contract rate.
Monthly payments on the loan are $1,797.66.
What is the yield-to-maturity if you purchased this
loan on the secondary market five years after
origination at a price of $141,910.32?
 Strengths:
 Weaknesses:
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
Conventional Yield Measures
 Yield-To-Call (YTC)
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Yield-To-Call =
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Ex. Consider a 15 yr., 7% semi-annual coupon
bond with a $1,000 PAR value, currently selling for
$769.40. In addition, the bond is callable after five
years at a call price of $1,050. What is the yieldto-call?
 Strengths:
 Weaknesses:
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
The Cost of Mortgage Credit
 Effective Borrowing Cost (EBC)
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EBC =
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Ex. Consider a 15 year, $200,000 monthly payment
mortgage, with a 7% contract rate. Monthly payments
on the loan are $1,797.66. If the loan also requires
borrowers to pay 2 discount points up-front, what is the
effective borrowing cost on this loan?
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
The Cost of Mortgage Credit
 Early Repayment and the EBC
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EBC =

Ex. Consider a 15 year, $200,000 monthly payment
mortgage, with a 7% contract rate. Monthly payments
on the loan are $1,797.66. If the loan also requires
borrowers to pay 2 discount points up-front, what is the
effective borrowing cost on this loan if the mortgage is
repaid after 7 years?
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
The Cost of Mortgage Credit
 Prepayment Penalties and the EBC

EBC =

Ex. Consider a 15 year, $200,000 monthly payment
mortgage, with a 7% contract rate. Monthly payments
on the loan are $1,797.66. If prepaid, the loan also
requires borrowers to pay a 2% prepayment penalty.
What is the effective borrowing cost on this loan if the
mortgage is repaid after 7 years? What if the loan also
requires two discount points be paid up-front?
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
Yield Decompositions
 Potential Sources of a Bond’s Dollar Return
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Ex. Decompose the yield on a 15 year, 7%
S.A. coupon bond, with a YTM of 10% and a
PAR value of $1000.
 Conclusions:
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
Yield Decompositions
 Potential Sources of a Mortgage’s Dollar Return
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Ex. Decompose the yield on a 15 year, monthly
payment mortgage, with a 7% nominal rate of
interest and an original loan balance of $200,000.
 Conclusions:
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
Total Return
 Methodology:
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David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
Total Return Examples
 Ex. Consider an investor with a 3 year investment horizon,
evaluating a 20-year, $1,000 PAR, 8% S.A. coupon rate bond
which is currently selling for $828.40. The stated YTM on the
bond is currently 10%, but coupon payments may only be
reinvested at 6%. In 3 years, the outstanding bond is expected to
be selling to offer a YTM of 7%. What is the total [expected] return
offered by this security?
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
Total Return Examples
 Total Return with non-constant reinvestment rates
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Ex. Suppose an investor has a 6-year investment horizon and is
considering a 13-year, 9% S.A. coupon bond, currently selling at
its PAR value ($1,000). The investor expects to be able to
reinvest the first 4 semi-annual coupons at 8% (over their entire
reinvestment interval), but expects to be able to reinvest the last 8
coupons at 10%. The required YTM on 7-year bonds of similar
risk at the end of the investment horizon is expected to be 10.6%.
What is the total [expected] return offered by this security?
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Limitations of Total Return:
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University