Dual Rates Flashcards
A Gold Coast fun park is erected on leased land and returns the operator $3,000,000 p/a before land rent. The fixed land rental is $600,000 p/a with 10 years remaining on the lease.
What is the value of the operator’s interest assuming a remunerative rate of 18% p/a and a Capital Replacement rate of 1.5% p.a.
Note – complete your calculations assuming cashflows are annual in arrears.
Between 8,777,248.497 and 8,777,250.497
ANSWER
$3,000,000 less $600,000 = $2,400,000 NET LEASE INCOME
$2,400,000 x 1 / 0.18 + PMT = (FV 1, N10, I 1.5) end mode
$2,400,000 x 1/ 0.18 + 0.09343177
$2,400,000 x 1 / 0.273434177
$ 2,400,000 X 3.65718729
= $ 8,777,249.497
PROOF
ANNUAL NET INCOME $ 2,400,000
LESS RETURN ($ 8,777,249.497 X 0.18 ) = $ 1,579,904.909
SINKING FUND CONTRIBUTION = $ 820,095.091
FV = (PMT $820,095.091, N 10, I 1.5)
FV = $8,777,249.501
An investor purchases a fixed term head-lease on a Waterfront Hotel with 15 years remaining on the head-lease. It returns $800,000 per annum net.
The investor requires a 20% return on investment. Bank deposit rates are 2% per annum. You have been asked to assess the value of the head lease for lending purposes.
Note – complete your calculations assuming cashflows are annual in arrears.
$800,000 x 1 / 0.20 + PMT = (FV 1, N15, I 2) end mode
$800,000 x 1/ 0.20 + 0.057825472
$800,000 x 1/ 0.257825472
$800,000 x 3.878592725
= $ 3,102,874.18
PROOF
ANNUAL INCOME $800,000
LESS RETURN (20% X $3,102,874) = $ 620,574.84
SINKING FUND CONTRIBUTION = $ 179,425.16
FV = (PMT $179,425.16, N 15, I 2)
FV = $3,102,874.10
A sandstone quarry is currently leased with 8 years left to run on the lease. The lessee’s net profit at the end of each year is $200,000 per annum. If the rate of return on the operation is considered to be 30% per annum and the investor can invest the money received at the end of each at 15% per annum, what is the current market value of the lease?
Note: Calculations to 4 decimal places, answer rounded to nearest whole dollar.
$536,340
Step 1: Calculate the Sinking Fund Factor
PV = 0
N = 8
I = 15
FV = -1
COMP PMT = 0.0729
Step 2: Calculate the Dual Rate Factor
= 1 / ( 0.30 + 0.0729)
= 2.6817
Step 3: Multiply the Dual Rate Factor by Income
= 2.6817 x 200,000
Therefore PV = 536,340
What is the correct formula for valuing a cashflow than is not “in perpetuity” and where the remunerative rate is the same as the accumulation rate?
A. Capitalisation formula
B. PV of $1 per annum formula - dual rate version
C. PV of $1 per annum formula - single rate version
D. Sinking fund formula
C. PV of $1 per annum formula - single rate version
Answer “PV of $1 per annum formula - dual rate version” is for cashflows where the remunerative rate is different to the accumulation rate
Answer “Sinking fund formula” is used for calculating a payment based on the necessity to achieve a future value
Answer “Capitalisation formula” is only used for cashflows in perpetuity
What is the value of $10,000 received at the beginning of each month for a period of 15 years. Use a remunerative rate of 12% pa and a replacement rate of 7% pa compounded monthly.
Step 1: Calculate the Sinking Fund Factor
* n = 15 x 12
* i = 7 / 12
* PV = 0
* FV = -1
* PMT = ?
Answer = 0.0032
Step 2: Calculate the Dual Rate Factor
Dual rate factor (arrears)
1/(0.12/12+0.0032)
= 76.0170
Step 3: adjust the ordinary annuity (arrears) dual rate factor to advance
Dual rate factor (advance)= 76.0170 x (1 + 0.07/12) = 76.4604
Step 4: Multiple the Dual Rate Factor by the Income
Therefore PV
= 10,000 x 76.4604
= $764,604.49
What is the value of $10,000 received at the end of each month for a period of 15 years. Use a remunerative rate of 12% pa and a replacement rate of 7% pa compounded monthly.
Step 1: Calculate the Sinking Fund Factor
* n = 15 x 12
* i = 7 / 12
* PV = 0
* FV = -1
* PMT = ?
Answer = 0.0032
Step 2: Calculate the Dual Rate Factor
Dual rate factor (arrears)
1/(0.12/12+0.0032)
= 76.0170
Step 3: Multiple the Dual Rate Factor by the Income
Therefore PV
= 10,000 x 76.0170
= $760,170.16
What is the value of $10,000 received at the beginning of each year for a period of 15 years. Use a remunerative rate of 12% pa and a replacement rate of 7% pa effective.
Step 1: Calculate the Sinking Fund Factor
* n = 15
* i = 7
* PV = 0
* FV = - 1
* PMT = ?
Answer = 0.0398
Step 2: Calculate the Dual Rate Factor
Dual rate factor (arrears)= 1/(0.12+0.0398)
=1/0.1598
= 6.2580
Step 3: adjust the ordinary annuity (arrears) dual rate factor to advance
Dual rate factor (advance)
= 6.2580 x 1.07
= 6.6961
Step 4: Multiple the Dual Rate Factor by the Income
Therefore PV
= 10,000 x 6.6961
= $66,960.95
What is the value of $10,000 received at the end of each year for a period of 15 years? Use a remunerative rate of 12%
pa and a replacement rate of 7% pa effective.
Step 1: Calculate the Sinking Fund Factor
* n = 15
* i = 7
* PV = 0
* FV = - 1
* PMT = ?
Answer = 0.0398
Step 2: Calculate the Dual Rate Factor
Dual rate factor (arrears)
= 1/(0.12+0.0398)
= 1/0.1598
= 6.2580
Step 3: Multiple the Dual Rate Factor by the Income
Therefore PV
= 10,000 x 6.2580
= $62,580.33
What is a sinking fund?
In dealing with freehold interest, sinking fund is the freehold interest at any time which can be sold in perpetuity.
Need to get a return on the purchase price
AND
Replace purchase price (as cannot sell the asset in perpetuity).
What are the two major levels of market risk?
Property Risks (Internal)
Market / Regulatory Risks (External)
What are two areas of market risk?
Spatial Market Risks
Risks related to cyclical nature of the market which introduces the risk that there may be a divergence between supply and demand.
Capital Market Risks:
Capital market fundamentals and the availability of capital (debt and equity). Periods of restricted capital can soften valuations due to limited demand
