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Time Value of Money
Money today and money tomorrow
Money tomorrow
• Would you rather have:
• £1,000 today or
• £1,000 in 2 years time?
• You would rather have £1,000 today because:
• You might be dead by next year
• With inflation, £1,000 next year will not buy as much as today
• You could invest the £1,000 today, and earn interest on it
Money tomorrow 2
• Would you rather have;
• £1,000 today or
• £1,200 next year or
• £3,000 in 5 years time?
• There is a way of calculating this/
Interest
• Assume you invest £10,000 at 5% interest
• After 1 year you have £10,000 plus interest of £500 = £10,500
• You start the next year with £10,500
• Add interest on £10,500 @5% = £525.
• You now have £11, 025 at the end of the second year
• At the end of year 3 you have £11,025 plus interest of £551 = £11,576
• At the end of year 4 you have £11576 plus interest £579 = £12,155
• At the end of year 5 you have £12,155 plus interest £608 = £12,763
Net Present Value
• Today you have £10,000
• After 5 years you have £12,763
• £10,000 today is worth £12,763 in 5 years time.
• So
• £12,763 in 5 years time is only worth £10,000 now.
• The NET PRESENT VALUE of £12,763 in 5 years time is £10,000
Calculating Future Amount
• We added the capital and interest year by year to find the future amount.
• We could have used the formula (1+i)n
• I = the interest rate
• N = the number of years
Period
Capital
at start
of period Rate Interest
Capital
at end
of period
1 10,000 0.05 500 10,500
2 10,500 0.05 525 11,025
3 11,025 0.05 551.25 11,576
4 11,576 0.05 578.8125 12,155
5 12,155 0.05 607.7531 12,763
Using the formula
• (1+i)n =
• (1+.05)5 =
• 1.2763
• Multiply by £10,000 =
• £12,763
• Alternatively, we can use the Amt formula in Excel, or we can look it
up in a table.
Calculating the Present Value
• We can simply use the inverse of the Future Amount formula
• 1/(1+i)n
• We have a new van. We are going to replace it in 5 years time.
• 5 year old vans sell for about £8,000
• We will receive £8,000 in 5 years time.
• 1/(1+.05)5 = 0.783
• £8,000 * 0.783 = £6268
• Say £6250
• Or, we could just look it up in Excel or in tables.
Interest rate.
• The interest rate, also known as:
• Risk rate or
• Yield
• The more risky an investment, the higher the rate.

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Time value of money

  • 1. Time Value of Money Money today and money tomorrow
  • 2. Money tomorrow • Would you rather have: • £1,000 today or • £1,000 in 2 years time? • You would rather have £1,000 today because: • You might be dead by next year • With inflation, £1,000 next year will not buy as much as today • You could invest the £1,000 today, and earn interest on it
  • 3. Money tomorrow 2 • Would you rather have; • £1,000 today or • £1,200 next year or • £3,000 in 5 years time? • There is a way of calculating this/
  • 4. Interest • Assume you invest £10,000 at 5% interest • After 1 year you have £10,000 plus interest of £500 = £10,500 • You start the next year with £10,500 • Add interest on £10,500 @5% = £525. • You now have £11, 025 at the end of the second year • At the end of year 3 you have £11,025 plus interest of £551 = £11,576 • At the end of year 4 you have £11576 plus interest £579 = £12,155 • At the end of year 5 you have £12,155 plus interest £608 = £12,763
  • 5. Net Present Value • Today you have £10,000 • After 5 years you have £12,763 • £10,000 today is worth £12,763 in 5 years time. • So • £12,763 in 5 years time is only worth £10,000 now. • The NET PRESENT VALUE of £12,763 in 5 years time is £10,000
  • 6. Calculating Future Amount • We added the capital and interest year by year to find the future amount. • We could have used the formula (1+i)n • I = the interest rate • N = the number of years Period Capital at start of period Rate Interest Capital at end of period 1 10,000 0.05 500 10,500 2 10,500 0.05 525 11,025 3 11,025 0.05 551.25 11,576 4 11,576 0.05 578.8125 12,155 5 12,155 0.05 607.7531 12,763
  • 7. Using the formula • (1+i)n = • (1+.05)5 = • 1.2763 • Multiply by £10,000 = • £12,763 • Alternatively, we can use the Amt formula in Excel, or we can look it up in a table.
  • 8. Calculating the Present Value • We can simply use the inverse of the Future Amount formula • 1/(1+i)n • We have a new van. We are going to replace it in 5 years time. • 5 year old vans sell for about £8,000 • We will receive £8,000 in 5 years time. • 1/(1+.05)5 = 0.783 • £8,000 * 0.783 = £6268 • Say £6250 • Or, we could just look it up in Excel or in tables.
  • 9. Interest rate. • The interest rate, also known as: • Risk rate or • Yield • The more risky an investment, the higher the rate.