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Capital and Revenue
Capital Sums and Revenue Streams
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
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
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.
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
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
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
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
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
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
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
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
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?
Thank you for your attention

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Capital and revenue

  • 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