PRESENT VALUE OF AN ANNUITY - QUESTIONS
Present value of a level annuity of fixed duration
Question 1
You have won first prize in the Readers’ Digest draw!! You can choose one of two prizes:
a)
£100,000 in five years’ time
b)
£10,000 at the end of each of the next ten years
Which would you choose, assuming an investment return rate of 5% per annum?
Question 2
How much would you pay for the right to receive £50,000 per annum over the next 15 years
assuming average investment returns of 8% per annum?
Question 3
What about if the £50,000 per annum in Question 2 was receivable over the next:
a)
60 years
b)
1,000 years?
c)
What do you notice?
d)
What about fact that rental growth occurs?
e)
How do we analyse comparable evidence?
Question 4
Your client has a rental income of £1,000 pa for the next 3 years, the first income being
received in one year’s time (i.e. in arrears). Assuming a discount rate of 8% p.a. what is the
capital value of these incomes?
Question 5
What is the present value of the right to receive £100,000 of rent annually in arrears for three
years assuming a discount rate of 10%?
Question 6
Calculate the value of the right to receive £100 every year for five years payable annually in
arrears assuming a discount rate of 8%
⃝ £399.27
⃝ £462.28
⃝ £68.06
⃝ £146.93
Question 7
Calculate the present value of the right to receive £100 every year for ten years payable
annually in arrears assuming a discount rate of 5%
⃝ £772.17
⃝ £61.39
⃝ £1000
⃝ £693.21
Question 8
The same shop was let two years ago on a 15 year FRI lease with upward only rent reviews
every five years at £75,000 per annum. What is the value of the right to receive the £75,000
for three years (WHY IS IT FOR THREE YEARS?) receivable annually in arrears assuming
a capitalisation rate/yield of 7.5%?
⃝
£193,311
⃝
£225,000
⃝
£195,039
⃝
£223,452
Present value of level annuity of fixed duration – cash flow model
Question 9
A commercial property has just been let on a 5-year lease at a net rent of £40,000 per
annum. The rent is payable annually in arrears. Using a discount rate of 5%, calculate the
total present value of the rents to be received during the term of the lease. You may use
the table below for your calculations.
Rent
Received
£40,000
£40,000
£40,000
£40,000
£40,000
Total Discounted Value
PV of £1 @ 5%
Present (discounted) value
Present value of a stepped annuity of fixed duration – cash flow model
Question 10
A retail property has a current rent of £30,000 per annum. The rent is payable annually in
arrears. Set out a table similar to that shown in Question 8 above but incorporate a rent
review after 3 years. The new rent, which will then be fixed for the following 3 years, will be
based upon an anticipated growth of 3% per annum over the next 3 years. Assume a discount
rate of 5%.
Question 11
Your client proposes to purchase an older industrial property currently let for £40,000 per
annum receivable annually in arrears. There are no opportunities to review the rent until the
lease expires in five years time. It is anticipated that £25,000 will need to be spent after three
years to renew the roof, which is the landlords’ responsibility. Assuming a discount rate of
7.5% per annum and using the table below, calculate the total present value of the net cash
flow.
Rent/Expense
Received/Paid
PV of £1 @ 7.5% pa
Present Value
Question 12
A commercial property has just been let on a five-year lease at a net rent of £40,000 per
annum. The rent is payable annually in arrears. Using a discount rate of 5%, calculate the total
present value of the rents to be received during the term of the lease. You anticipate paying
£10,000 for unexpected repair work at the end of year 2.
Question 13
You are deciding on the discount rate to apply to a retail property in your valuation.
Indicate whether you would increase or decrease your proposed rate in view of each of
the following circumstances:
Circumstances
You have secured a first-class tenant
You have heard that planning permission for a new retail
mall nearby has been granted
+ or -
The property has been recently modernised
The tenant wants to take a short lease
There is a public right of way running across part of the rear
service yard
Question 14
A property is expected to produce a rent of £1,000 per annum for three years followed by
£1,500 per annum for the following three years followed by £2,000 per annum for the final
three years of a nine year lease. The rents are paid annually in arrears. Using a yield of 8% to
discount the rents, value this property.
Question 15
A retail property has just been let for its maximum (rack) rent of £50,000 per annum. It is let
on a nine-year lease with three-year rent reviews. Assuming that the rental value of the
premises increases by 4% each year, calculate the rent that can be expected at the first review
(after three years) and the second review (after six years). You may use the table below for
your answer.
Period
Rent
1–3
4–6
7-9
£50,000 pa
Question 16
Carry out a valuation of the property in Question 2 by discounting the rents individually at a
yield of 6%. For the purposes of this exercise, assume the rents are paid annually in arrears.
You may use the table below for your answer.
Rent
Year
£50,000
1
£50,000
2
£50,000
3
£
4
£
5
£
6
£
7
£
8
£
9
Total Discounted Value
PV of £1
Discounted Rent
£
Question 17
Rework the ‘valuation’ in Question 3 using a blocked income approach. A line diagram is
shown below to help you.
£
£
pa
pa
£50,000 pa
Present day
3
6
9
You may use the table below for your answer.
Period
Rent
Expected
YP @ 6%
Future
Value
PV @ 6%
Discounted
Rents
Question 18
You have discovered that the tenant company, to whom the property is about to be let, has
been having severe financial difficulties lately. Rework your valuation to reflect this situation.
You may use the table below for your answer.
Period
1-3
4-6
Rent
Expected
£50,000
YP @ ?
Future
Value
PV @ ?
Discounted
Rents
7-9
Total Discounted Value of Rental Flow
£
Present value of a constant growth annuity
Question 19
What is the present value of an eight-year lease which has an annual rent of £200 per square
metre in arrears, increasing by 1% each year? The required return is 8%.
Question 20
A landlord has offered a tenant a six-year lease with an annual rent of £250 per square metre
in arrears. The tenant has asked the landlord for a lower initial rent in return for annual
increases of 2% per annum. What should the initial rent be? The discount rate is 10%.
Present value of a perpetual level annuity
Question 21
What is the value of the right to receive £100,000 per annum annually in arrears in perpetuity
assuming a discount rate of 10%?
Question 22
A freehold shop investment is for sale and currently produces an annual rent of £80,000 pa. If
investors generally require a 5% return on investments of this sort what is the capital value of
this investment?
Question 23
What is the value of the right to receive £100,000 annually in arrears in perpetuity assuming a
discount rate of 5%?
⃝
£2,000,000
⃝
£5,000
⃝
£5,000,000
⃝
£500,000
⃝
None of the above
Question 24
a)
b)
c)
What is the present value of the right to receive £100,000 of rent annually in arrears in
perpetuity assuming a discount rate of 10%?
What is the present value of the right to receive £100,000 in perpetuity annually in
arrears starting in three years time (so that the first payment is actually in four years
time) assuming a discount rate of 10%?
What is the present value of the right to receive £100,000 annually in arrears for the next
three years plus £150,000 annually in arrears in perpetuity starting in three years time
assuming a discount rate of 10%?
Question 25
A shop has just been let on a 15-year FRI lease with upward only rent reviews every five
years at £100,000 per annum annually in arrears. What is its value assuming a capitalisation
rate or yield of 10%?
⃝ £826,466
⃝ £1,100,000
⃝ £1,000,000
⃝ £760,608
⃝ None of the above
Question 26
a)
What is the present value of the right to receive £100 every year in perpetuity (forever)
receivable annually in arrears assuming a discount rate of 5%?
⃝ £500
⃝ £1250
⃝ £2100
⃝ None of the above
b)
What is the present value of the right to receive £100 every year in perpetuity (forever)
receivable annually in arrears starting in three years’ time (i.e. first payment is received
in four years) assuming a discount rate of 5%?
⃝ £1727.67
⃝ £1645.40
⃝ £1681.23
⃝ £1645.40
⃝ £2000
c)
What is the present value of the right to receive £50 every year for three years receivable
annually in arrears plus £100 every year in perpetuity (forever) receivable annually in
arrears starting in three years’ time assuming a discount rate of 5%?
⃝ £1782
⃝ £1864
⃝ £1121
⃝ None of the above
Question 27
What is the value of the right to receive £100,000 in perpetuity receivable annually in arrears
but starting in three years’ time assuming a capitalisation rate or yield of 7.5%?
⃝
£1,073,281
⃝
£1,100,000
⃝
£1,000,000
⃝
£1,123,452