Finance 2000_Finished Chapters_5,8,9,10,11,12,13,14.2-14.5...

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Fundamentals of Corporate Finance (Brealey) Weiting Xu Professor: Andreanne Tremblay Chapter Reading Notes FINE 2000 CHAPTER 5 – TIME VALUE OF MONEY (“TVM”)* 1. FUTURE VALUES AND COMPOUND INTEREST Future Value (FV): amount to which an investment will grow after earning interest Compound Interest: interest earned on interest Simple Interest: interest earned only on original investment; no interest is earned on interest FMV of $I investment = I (1 + r) t Future Value Interest Factor or Future Value Factor: future value of current cash flow of $1 FV = I x Future Value Factor = I x FVIF(r,t) = I x (1+r) t Compound growth means that value increases each period by factor (1 + growth rate). The value after t periods will equal the initial value times (1+ growth rate) t - When money is invested at compound interest, the growth rate is the interest rate 2. PRESENT VALUES Present Value (PV): value today of a future cash flow PV = - PV are always calculated using compound interest - Thus, PV decline, other things being equal, when future cash payments are delayed PV = I x discount factor = I x PVIF(r,t) = I x Finding the Interest Rate - Solve for the r in the equation Finding the Investment Period - Finding the t in the equation 3. MULTIPLE CASH FLOWS Page 1 of 42
Fundamentals of Corporate Finance (Brealey) Weiting Xu Professor: Andreanne Tremblay Chapter Reading Notes FINE 2000 Future Value of Multiple Cash Flows - Stream of cash flows: when there are many payments To find value at some future date of a stream of cash flows, calculate what each CF will be worth at that future date, then add up these FV PV of Multiple Cash Flows - If there is more than one future CF, we simply need to work out what each flow would be worth today and then add these PVs 4. LEVEL CASH FLOWS: PERPETUITIES AND ANNUITIES Annuity: equally spaced and level stream of cash flows Perpetuity: stream of level cash payments that never ends How to Value Perpetuities e.g. British gov’t borrowed by issuing perpetuities. Instead of repaying these loans, British gov’t pays investors holding these securities a fixed annual payment in perpetuity PV of Perpetuity = Warnings about the formula: 1. A payment of $1 at end of one year has a PV 1/(1+r) the perpetuity has a value of 1/r 2. Tells us the value of a regular stream of payments starting one period from now How to Value Annuities Two ways: 1. Slow – value each cash flow separately and add up PVs 2. Simplification process PV of t-year annuity = C x [] Or, PV of t-year annuity = payment x annuity factor = C x PVA(r,t) Annuities Due Level stream of cash flows starting immediately - In general, PV of an annuity due of t payments of $1 per period is the same as $1 plus the PV of an ordinary annuity providing the remaining t – 1 payments PV Annuity Due = 1 + PV Ordinary Annuity of t – 1 payments = 1 + [] Future Value of an Annuity FVA(r,t) = PV of Annuity of $1 per year x (1 + r) t of $1 per year, FVA (r,t) FVA(r,t) = If the first cash flow comes immediately, FV of CF stream is greater, since each flow

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