Present Value

Study guides: Exam FM-2, Exam MAS-I

The present value (PV) is the value today of a future payment, discounted at an interest rate. Because a dollar received in the future is worth less than a dollar today — it could have been invested to earn interest — future cash flows are multiplied by the discount factor v = (1+i)^{-1} raised to the number of periods. A payment of FV due in n periods at effective rate i has present value:

PV = FV \cdot (1+i)^{-n}

= FV \cdot v^n

• For multiple cash flows C_t at various times t, the total present value is \displaystyle PV = \sum_t C_t\, v^t.
• Present value is the fundamental building block of annuity, NPV, and deferred annuity calculations.

Present Value of a Lump Sum An investor will receive 5000 in 6 years. If the effective annual interest rate is i = 7\%, what is the present value of this payment?

Answer PV = \frac{5{,}000}{(1.07)^{6}} = 5{,}000 \times v^6 = \frac{5{,}000}{1.500730} \approx \$3{,}331.71