Real Estate Finance & Investments, Midterm Diagnostic Exam
Your name:____Answers________________________________ ID#_____________________
Answer all of the questions in the space provided below each one. Think about your answer
before you start writing, and organize your thoughts. Please write clearly and legibly. (Make
notes or outline on the back if that helps you organize, but those won’t count in the
marking.)
1. (15 pts) Explain in your own words what is “the NPV Investment Decision Rule”, and why
it makes sense, what it is based on.
The NPV Decision Rule says: “Maximize the NPV across all mutually exclusive
available and feasible investment alternatives, and never make an investment
with NPV < 0.”
The NPV is the present value of the investment benefit (or gross asset value)
minus the present value of the cost or price of making the investment: NPV = B
– C, or = V – P, where the benefits (V) and the costs (P) are measured in
equivalent risk-adjusted (certainty-equivalent) present value money.
This investment decision rule makes sense because it is based on the “Wealth
Maximization” criterion. If the investor wants to maximize his/her wealth,
he/she must apply the NPV Decision Rule. Any other rule not consistent with
the NPV rule would “leave money on the table”, that is, reduce the investor’s
net wealth value compared to using the NPV rule.
2. (20 pts) Define and contrast: “Market Value” (MV), and “Investment Value” (IV). Use a
market supply and demand diagram to illustrate the difference between these two values.
(Clearly label and define all axes, lines, and points in the chart.) Explain how the DCF
computation of MV and IV differ in their use or treatment of investors’ income taxes.
“Market Value” (MV) is the value you can expect to sell the asset for in the
asset market (aka “exchange value”). MV is common to all (“Law of One
Price”), for a given asset at a given point in time.
, “Investment Value” (IV) is what the asset is worth to you (a specified owner)
ignoring its MV (as if you would never sell it). IV is unique to each given
investor.
In DCF computation of value, for MV you use before-tax cash flows discounted
at before-tax OCC, but;
You use your (the subject investor’s) after-tax cash flows discounted at the
market’s (i.e., the marginal investor’s) after-tax OCC (reflecting the tax rate of
the marginal investors in the relevant market).
In a supply/demand diagram of an asset market, the demand and supply
schedules reflect the IVs of potential buyers and sellers (respectively), and the
point of intersection gives the equilibrium price (MV) at which price trading
tends to occur, allowing intra-marginal traders to make positive NPV from an
IV perspective, as seen below.
Price IVbuyers Supply
IVbuyer
P = MV IV of marginal traders
IVseller
Demand
IVsellers
Volume of Trading
Intra-Marginal Equilibrium
Trading Quantity of
Trading
,3. (10 pts) What is the difference between a property’s Net Operating Income (NOI) and its
Property Before-Tax Cash Flow (PBTCF)?
The difference is capital improvement expenditures: PBTCF = NOI – CI.
4. (20 pts) Suppose a property can be bought for $1,000,000 and it will provide
$100,000/year net cash flow forever, and you can borrow a perpetual interest-only
mortgage secured by that property at an 8% interest rate, up to an amount of $750,000. (a)
Does this present “positive” or “negative leverage”, and (b) why? (c) Will the expected
return to the levered equity be less than 8%, exactly 8%, between 8% and 10%, exactly
10%, or greater than 10%? (d) Do you think that the use of leverage in this case will
increase the NPV of the investment for the equity investor in the property? (e) Why or why
not?
(a) Positive Leverage;
(b) Because the expected return on the property (10%) exceeds that on the loan
(8%).
(c) Greater than 10%, due to the effect of the above-noted “positive leverage”.
(d) No,
(e) because there is no reason to think that the 8% loan is subsidized, and no mention
of investor’s tax rate, so we must be considering MV (not IV), and therefore
borrowing should be NPV=0.
5. (10 pts) Do you think in general (or typically on average) the going-in cap rate is larger or
smaller than the going-out or terminal cap rate? Why?
In general (typically on average) the going-in cap rate should be at least a little lower
than the going-out cap rate, due to the aging of the property, and hence its typically
becoming a little more risky, or moving from a more “institutional quality” property
toward a more “non-institutional quality” property.
, 6. (25 pts) Below is a 10-year projection of a before-tax cash flow stream. Suppose that the
market before-tax OCC for cash flows of this type of risk is 10% per annum, and the
marginal investor in the market for the type of asset that produces these cash flows faces a
35% income tax rate, but you face a 25% income tax rate. The reversion amount of $10,000
in Year 10 is not subject to any income tax. What is: (a) the market value (MV) of this cash
flow stream? (b) the investment value (IV) to you of this cash flow stream? (Show your
computations.)
Year 1 2 3 4 5 6 7 8 9 10
$1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $11,000
MV = PV(10%, 10, $1000, $10000) = $10,000.
IV = PV((1-.35)*10%, 10, (1-.25)*$1000, $10000) = PV(6.5%, 10, $750, $10000) =
$10,719.
Formulas that may (or may not) be useful in this exam . . .
a + da + d2a + . . . + dn-1a = a(1-dn)/(1-d). = a/(1-d) if n = ∞ and < 1.
PMT/(1+r) + PMT/(1+r)2 + . . .+ PMT/(1+r)n = (PMT/r)[1 – 1/(1+r)n].
CF + CF/(1+r) + CF/(1+r)2 + . . .+ CF/(1+r)n-1 = (1+r)(CF/r)[1 – 1/(1+r)n].
CF/(1+r) + (1+g)CF/(1+r)2 + (1+g)2CF/(1+r)3 + . . . (forever) = CF/(r-g).
EAY = (1+CEY/2)2-1; MEY=((1+EAY)(1/12)-1)*12.
Your name:____Answers________________________________ ID#_____________________
Answer all of the questions in the space provided below each one. Think about your answer
before you start writing, and organize your thoughts. Please write clearly and legibly. (Make
notes or outline on the back if that helps you organize, but those won’t count in the
marking.)
1. (15 pts) Explain in your own words what is “the NPV Investment Decision Rule”, and why
it makes sense, what it is based on.
The NPV Decision Rule says: “Maximize the NPV across all mutually exclusive
available and feasible investment alternatives, and never make an investment
with NPV < 0.”
The NPV is the present value of the investment benefit (or gross asset value)
minus the present value of the cost or price of making the investment: NPV = B
– C, or = V – P, where the benefits (V) and the costs (P) are measured in
equivalent risk-adjusted (certainty-equivalent) present value money.
This investment decision rule makes sense because it is based on the “Wealth
Maximization” criterion. If the investor wants to maximize his/her wealth,
he/she must apply the NPV Decision Rule. Any other rule not consistent with
the NPV rule would “leave money on the table”, that is, reduce the investor’s
net wealth value compared to using the NPV rule.
2. (20 pts) Define and contrast: “Market Value” (MV), and “Investment Value” (IV). Use a
market supply and demand diagram to illustrate the difference between these two values.
(Clearly label and define all axes, lines, and points in the chart.) Explain how the DCF
computation of MV and IV differ in their use or treatment of investors’ income taxes.
“Market Value” (MV) is the value you can expect to sell the asset for in the
asset market (aka “exchange value”). MV is common to all (“Law of One
Price”), for a given asset at a given point in time.
, “Investment Value” (IV) is what the asset is worth to you (a specified owner)
ignoring its MV (as if you would never sell it). IV is unique to each given
investor.
In DCF computation of value, for MV you use before-tax cash flows discounted
at before-tax OCC, but;
You use your (the subject investor’s) after-tax cash flows discounted at the
market’s (i.e., the marginal investor’s) after-tax OCC (reflecting the tax rate of
the marginal investors in the relevant market).
In a supply/demand diagram of an asset market, the demand and supply
schedules reflect the IVs of potential buyers and sellers (respectively), and the
point of intersection gives the equilibrium price (MV) at which price trading
tends to occur, allowing intra-marginal traders to make positive NPV from an
IV perspective, as seen below.
Price IVbuyers Supply
IVbuyer
P = MV IV of marginal traders
IVseller
Demand
IVsellers
Volume of Trading
Intra-Marginal Equilibrium
Trading Quantity of
Trading
,3. (10 pts) What is the difference between a property’s Net Operating Income (NOI) and its
Property Before-Tax Cash Flow (PBTCF)?
The difference is capital improvement expenditures: PBTCF = NOI – CI.
4. (20 pts) Suppose a property can be bought for $1,000,000 and it will provide
$100,000/year net cash flow forever, and you can borrow a perpetual interest-only
mortgage secured by that property at an 8% interest rate, up to an amount of $750,000. (a)
Does this present “positive” or “negative leverage”, and (b) why? (c) Will the expected
return to the levered equity be less than 8%, exactly 8%, between 8% and 10%, exactly
10%, or greater than 10%? (d) Do you think that the use of leverage in this case will
increase the NPV of the investment for the equity investor in the property? (e) Why or why
not?
(a) Positive Leverage;
(b) Because the expected return on the property (10%) exceeds that on the loan
(8%).
(c) Greater than 10%, due to the effect of the above-noted “positive leverage”.
(d) No,
(e) because there is no reason to think that the 8% loan is subsidized, and no mention
of investor’s tax rate, so we must be considering MV (not IV), and therefore
borrowing should be NPV=0.
5. (10 pts) Do you think in general (or typically on average) the going-in cap rate is larger or
smaller than the going-out or terminal cap rate? Why?
In general (typically on average) the going-in cap rate should be at least a little lower
than the going-out cap rate, due to the aging of the property, and hence its typically
becoming a little more risky, or moving from a more “institutional quality” property
toward a more “non-institutional quality” property.
, 6. (25 pts) Below is a 10-year projection of a before-tax cash flow stream. Suppose that the
market before-tax OCC for cash flows of this type of risk is 10% per annum, and the
marginal investor in the market for the type of asset that produces these cash flows faces a
35% income tax rate, but you face a 25% income tax rate. The reversion amount of $10,000
in Year 10 is not subject to any income tax. What is: (a) the market value (MV) of this cash
flow stream? (b) the investment value (IV) to you of this cash flow stream? (Show your
computations.)
Year 1 2 3 4 5 6 7 8 9 10
$1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $11,000
MV = PV(10%, 10, $1000, $10000) = $10,000.
IV = PV((1-.35)*10%, 10, (1-.25)*$1000, $10000) = PV(6.5%, 10, $750, $10000) =
$10,719.
Formulas that may (or may not) be useful in this exam . . .
a + da + d2a + . . . + dn-1a = a(1-dn)/(1-d). = a/(1-d) if n = ∞ and < 1.
PMT/(1+r) + PMT/(1+r)2 + . . .+ PMT/(1+r)n = (PMT/r)[1 – 1/(1+r)n].
CF + CF/(1+r) + CF/(1+r)2 + . . .+ CF/(1+r)n-1 = (1+r)(CF/r)[1 – 1/(1+r)n].
CF/(1+r) + (1+g)CF/(1+r)2 + (1+g)2CF/(1+r)3 + . . . (forever) = CF/(r-g).
EAY = (1+CEY/2)2-1; MEY=((1+EAY)(1/12)-1)*12.
