## Tuesday, January 10, 2012

### Time Value of Money, Present Value, Future Value, Bond Valuation, Net Present Value Method, Corporate Finance

TIME VALUE OF MONEY
-a dollar paid in the future is worth less than a dollar today.
-amounts to be received in the future must be discounted by some factor if one wishes to ascertain their present worth.
-the more distant the deferred service, the lower its present price.

PRESENT VALUE
P(1) = A / ( 1 + r )

6% interest rate (r)
\$1 = current value (A)
deferred 1 year (1)

FUTURE VALUE
P(t) = (1 + r)^t = A

Capital Value - current price of the rights to the stream/series of receipts.
Annuity - the sequence of future amounts due.

BOND VALUATION

PV = (5)SUM(t=1): A(t) / [(1+r))^t]
If interest paid more than once a year:
PV = A(t) / [(1+r/m)^(m*t)]

m = # of times a year interest is paid or compounded.
A = future payment
r = discount rate
t = future year

THE NET PRESENT VALUE METHOD

1.  Estimate the returns that can be expected to be realized from the investment over time.
2.  Discount those projected returns to the present value.
3.  Investment is acceptable if present value of estimated returns = or > cash outlay required to finance it.

I.e., new machine costs \$18,000.
useful life of machine = 5 years.  (value = 0 at end of 5 years).
machine adds \$5,600 after taxes to firm’s annual income for 5 year period.
assume 10% discount rate.

1.  discount cash flows of \$5,600 per year at appropriate discount rate of 10%.
2.  Compare to outlay to determine if investment has a positive net present value.

PV = \$21,224 (3.79 x \$5,600)
Net Present Value = Discounted sum of expected inflows minus cost.
(\$21,224 - \$18,000) = \$3,224 (NPV)
NPV is positive, so investment is acceptable, outlay should be made. 