Ch. Ch. 5 Discounted Cash Flows & Valuation In Chapter 5,

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1 Ch. 5 Discounted Cash Flows & Valuation In Chapter 5, we found the PV & FV of single cash flows--either payments or receipts. In this chapter, we will do the same for multiple cash flows. 2 Multiple Cash Flows Different CFs Identical CFs = annuities 3 1

2 Different Cash Flows Using Timelines The use of a timeline is very helpful with different CFs. Make sure each CF is placed at the correct point in time. 4 Different Cash Flows Future Value Calculate the FV of each CF. Watch the number of compounding periods very carefully! Add all of the FVs together to determine a single FV for all CFs collectively. 5 Different Cash Flows Present Value Do the same as with FVs: Use a timeline. Calculate the individual PV for each CF. Sum all of the PVs. 6 2

3 Remember If you have calculated the FV of a series of CFs,, then that single value (the FV) can be used to calculate the PV of the same series of CFs without re- entering the individual CFs!!!!! Likewise: PV FV!!!!! 7 Level Cash Flows: Annuities 8 Annuity A stream of equal payments or receipts Home mortgage Automobile loan Retirement investments 9 3

4 Annuity With an annuity, use the TVM Pmt key. Whether the annuity is actually a payment or a receipt 10 2 Types of Annuities Ordinary annuity: : Payment or receipt is at the end of the period. Most annuities are ordinary. Annuity due: : Payment or receipt is at the beginning of the period. 11 Ordinary Annuities Payment at the end of the period 12 4

5 If we know any 4 of the 5 variables, the 5 th can de calculated. l 13 FV of an Annuity The FV of either an ordinary annuity or an annuity due can easily be made w/ your financial calculator s TVM registry. Pmt FV % $0 $1000? 14 PV of an Annuity The PV of either an ordinary annuity or an annuity due can also be made easily w/ your financial calculator s TVM registry Pmt FV %? $1000 $0 15 5

6 n or i of an Annuity n & i can also be calculated:? 5.50% $0 Pmt FV. $1000 $20,000 $0 $1000 $20,000 Pmt FV. 30? $0 $1000 $20, n, i & Pmt Pmt FV % $0 ($1200) $94,870 Pmt FV % $0 ($600) $97,832 Pmt FV % $0 ($100) $100, Caveat The most common TVM error: Failing to correctly enter the signs of cash flows: PV, Pmt & FV. At least one must be negative. PV is usually negative. 18 6

7 Loan Repayment & Amortization 19 Loan Repayment (1) Bullet loan: All principal & % (P + i) paid at end Balloon loan: Large final payment Interest-only payments Interest plus partial principal 20 Loan Repayment (2) Increasing payments Payment holiday Negative amortization Initial low P+I, but growing Full amortization 21 7

8 Amortization The repayment of a loan w/ equal payments over the life of the loan. Periodic payments (e.g., monthly) Equal payments -- covering both principal and interest The FV of an amortized loan = $0. 22 Amortization For the debtor, the annuity is a payment. For the investor, the annuity is a receipt. Whether payment or receipt, the CF is entered as Pmt in TVM. 23 Amortized Loan All payments are equal. Early payments of a long loan may include mainly interest and only a small amount of principal. Later payments will be mostly principal. 24 8

9 Loan-Amortization Schedule A spreadsheet which shows: The loan balance at the beginning & end of each payment period Payment made (or due) each period How much of the payment was interest How much of the payment was principal 25 Amortization Table for a 5-Yr, $10,000 Loan Annuity Due An annuity where the payment / receipt is at the beginning of the period. Ex: Retirement income at the beginning of each month Ex: Rent or lease payments Calculator must be set for beg. 27 9

10 Annuity Due The PV & FV of annuity dues are always greater than for an ordinary annuity. Why???? 28 Perpetuity An annuity where the payments / receipts continue forever Examples: Preferred stock Consols 29 Interest Rates 30 10

11 Interest Rates % rates are quoted in a number of different ways. Nominal interest rate Annual percentage rate (APR) Effective annual rate (EAR) 31 Nominal Interest Rate = the stated rate = the coupon rate 32 Annual Percentage Rate (APR) The nominal annual rate (e.g., 6.00% per year) Simple % -- not compound % 33 11

12 Consumer Protection Acts The Truth-in-Lending Act and Truth-in-Savings Act require that APR be used for both loans and savings plans (e.g., CDs). 34 Effective Annual Rate (EAR) The actual effective rate when payments are made more than once per year Compounds monthly or quarterly Although APR is mandated by law, EAR is more accurate. 35 APR vs. EAR Ex: If the APR is 6.00% w/ monthly payments, the monthly interest would nominally be 0.50% (i.e., 6.00% / 12). The APR would be 0.50% * 12 = 6.00% The EAR would be ( ) 12 = 6.17% 36 12