This document discusses the differences between capital and revenue items and how to value them. Capital refers to one-time payments in or out, while revenue consists of regular recurring payments. To value revenue streams, we can use the present value of £1 per year or the amount of £1 per year to calculate their worth today or in the future. For example, if we receive £1,000 annually for 5 years at a 5% interest rate, the future value would be £12,577.80. The document also discusses using annual sinking funds to calculate how much to set aside each year to meet a known future expense.

1. Capital and Revenue
Capital Sums and Revenue Streams

2. Capital
• A single one –off payment is Capital
• That can be a payment out – we buy a new company
car; or a payment in, we sell off the old company car.
• One off payments are known as Capital Expenditure
(often called Cap Ex for short)
• Even if we pay several times, this could still be a Capital
Expenditure. We have a rolling programme to replace
all our office equipment after 3 years.
• Even if they are regular payments, it is still, probably,
Capital Expenditure

3. Revenue
• Regular payments in or out are Revenue
items.
• Examples:
– Paying out rent
– Regular payments to contractors, e.g. cleaning
contracts
– Variable repeating payments, e.g. energy bills

4. Valuing Revenue Streams
• In a previous Lecture, we considered Present
and Future Values of one-off amounts, i.e.
Capital sums.
• This is known as discounting
• We can also discount revenue streams using
similar methods.

5. Amount of £1 per annum
• Pay a lump sum into an account and let it earn
interest
• Use Amount of £1 or Future Value (1+i)n
• What if we pay, say, £1,000 every year into an
account and earn interest @, say 8%?
• Use the Amount of £1 per annum or Future
Value of 1 per period or Annuity Factor
• Formula (1+i)n-1
i

6. Examples of Using the Amount of £1
pa or FV 1 per period or Annuity Factor
• If I save £1,000 every year into an account
giving me 5% interest; how much will I have
after 10 years?
• (1+i)n-1 or (Amt of £1 -1)/i
i
= (1+.05)10-1 = 1.62889 -1 = .62889 = 12.5778
.05 .05 .05
£1,000 * 12.5778 = £12,577.80

7. Present Value of £1 per annum
• The reciprocal, of course, is the Present Value
of £1 pa, or Year’s Purchase or Present Worth
• Formula
• 1 – (1/(1+i)n-1)
i

8. The Formulae
• If you are not mathematically minded, don’t
worry about the formulae.
• The figures have all been calculated for you on
a spreadsheet available on the website.
• Enter the appropriate rate per cent (the
discounting rate) then look up the figure from
the table

9. Financial Tables
COMPOUND INTEREST TABLES
7PER CENT
Yrs Amt of £1
(Amount to which a
capital sum will
accrue)
PV of £1
(Present Value of a
Capital Sum)
Amt of £1 pa
(Amount to which an
income stream will
accrue at a given rate)
PV of £1 pa
(Present Value of a
income or
expenditure stream)
Annual Sinking Fund
1 1.070000 0.934579 1.000000 0.934579 1.000000
2 1.144900 0.873439 2.070000 1.808018 0.483092
3 1.225043 0.816298 3.214900 2.624316 0.311052
4 1.310796 0.762895 4.439943 3.387211 0.225228
5 1.402552 0.712986 5.750739 4.100197 0.173891
6 1.500730 0.666342 7.153291 4.766540 0.139796

10. When to use the Amount of £1
pa/Year’s Purchase/Future Worth
• We can rent out that spare office floor for 5
years, until we need it again. That will give us
an income of £20,000 pa.
• What’s that worth as a capital sum, assume a
rate of 7%?
• £20,000 * PV £1pa for 5 years @ 7%
• From the tables = £20,000 * 4.100197
• = £82,000 Capital Value

11. Annual Sinking Fund
• Can calculate how much to put aside for a
given number of years to meet a known future
expenditure.
• This is known as an Annual Sinking Fund
• We are sinking money away every year for
some known eventuality

12. ASF Example
• This lift (elevator) is nearing the end of its life. It will
have to be replaced in the next 10 years at a cost of
£12,000. How much should we put aside every year to
meet that cost when it arises? Let’s assume a return of
4%
• From tables
• ASF 10 years @ 4% = 0.083291
• £12,000 * 0.083291 = £999.49,
• Say £1,000 per year.
• NB For simplicity for these exercises, ignore the impact
of tax on any interest

13. RECAP
• For Capital Items
• Present Value: What is the value today of a future sum of
money?
• Amount of £1: How much will a sum of money amount to
after a given number of years?
• For Revenue Items
• Present Value of £1 pa: What is the value today of a future
revenue stream?
• Amount of £1 pa: If I put away so much per year for a
given number of years, how much will that be worth?
• Annual Sinking Fund: How much do I need to put away
each year to amount to a given sum?

14. Thank you for your attention