Time value of money

Bond Valuation and Analysis in R

Clifford Ang

Senior Vice President, Compass Lexecon

Time value of money (TVM)

  • $\$1$ today is worth more than $\$1$ tomorrow
  • Suppose you won $10,000 in a game, what would you choose?
    • Receive the $10,000 today?
    • Receive the $10,000 one year from now?
Bond Valuation and Analysis in R

Future value

  • The future value is the value of $1 at some point in the future
  • Prefer $1 today, so would have to be compensated to agree to receive the cash flow in the future
  • Future value (fv) one and two years from now can be calculated as:
fv1 <- pv * (1 + r)
fv2 <- pv * (1 + r) * (1 + r)

r - interest rate

pv - present value

Bond Valuation and Analysis in R

Present value

  • Reverse logic of future values
  • The value of $1 in the future is worth less today
  • So you will be willing to take less than $\$1$ today instead of waiting to receive $1 one or two years from now
  • This can be calculated as follows:
pv <- fv1 / (1 + r)
pv <- fv2 / ((1 + r) * (1 + r))

r - interest rate

fv1 - future value 1 year from now, fv2 - future value 2 years from now

Bond Valuation and Analysis in R

TVM applied to bonds

  • We can apply this time value of money concept to bonds
  • Example:
    • $100 par value, 5% coupon rate (= $5), 5 years to maturity
    • Price = $100 today
Bond Valuation and Analysis in R

Bond investor's trade-off

Cash outflow and inflow over time

Bond Valuation and Analysis in R

Comparing cash flows

Cash outflow and inflow over time

Bond Valuation and Analysis in R

Let's practice!

Bond Valuation and Analysis in R

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