Chapter 5

1. Future value and compound Interest.

1.1. Future value: Amount to which an investment will grow after earning interest.

1.2. Compound Interest: Interest earned on interest.

1.3. Simple Interest: Interest earned only on the original investment.

2. Present Value

2.1. Present value: value today of future cash flow.

2.2. Discounted Cash Flow (DCF): Method of calculating present value by discounting future cash flows

2.3. Discount Rate: Interest rate used to compute present values of future cash flows

2.4. Discount Factor:Present value of a $1 future payment

2.5. Applications

2.5.1. Value of free credit

2.5.2. Implied Interest Rates

2.5.3. Internal Rate of Return

2.5.4. Time necessary to accumulate funds

3. FV + PV of Multiple Cash Flows

3.1. FVs = Fv = PV (1+r)+ FV = PV(1+r)2+..

3.2. PV = c1/(1+r)1+ c2/(1+r)2+....

4. Level Cash Flows: Perpetuities and Annuities

4.1. Annuity: Level stream of cash flows at regular intervals with a finite maturity.

4.2. Perpetuity: A stream of level cash payments that never ends.

4.3. How to value perpetuities?

4.3.1. Cash payment from perpetuity = interest rate x present value C= r x PV

4.3.2. PV of perpetuity = Cash payment/ interest rate PV = C/r

4.4. How to value Annuities?

4.4.1. Annuity factor or PV Annuity Factor (PVAF): The present value of $1 a year for each of t years.

4.4.1.1. PV = payment (c) x annuity factor PV = C[1/r - 1/r(1+r)t]

4.4.1.2. PVAF=[1/r - 1/r(1+r)t]

4.4.2. FV of annuity = PV Annuity x (1+r)t or = (1+r)t-1/r

4.5. Applications:

4.5.1. Value of payments

4.5.2. Implied interest rate for an annuity.

4.5.3. Calculation of periodic payments