Calculating Present & Future Values of Multiple Cash Flows in DCF - Prof. Wei Yu, Study notes of Business Finance

Download Calculating Present & Future Values of Multiple Cash Flows in DCF - Prof. Wei Yu and more Study notes Business Finance in PDF only on Docsity! 1 Chapter 6: Discounted Cash Flow Valuation  Future and Present Values of Multiple Cash Flows  Valuing Level Cash Flows: Annuities and Perpetuities Comparing Rates: The Effect of Compounding Loan Types 2 Multiple Cash Flows –FV Example  You think you will be able to deposit $4,000 at the end of each of the next three years in a bank account paying 8 percent interest. You currently have $7,000 in the account. How much will you have in three years? In four years?  Find the value at year 3 of each cash flow and add them together  FV3 = 7000 (1+8%) ^3 + 4000(1+8%)^2+ 4000(1+8%)^1  = 8,817.98 + 46 + 4665.60 + 4320 + 4000 = $21803.58  Value at year 4 5 Multiple Uneven Cash Flows – Using the Calculator  Another way to use the financial calculator for uneven cash flows is to use the cash flow keys  Press CF and enter the cash flows beginning with year 0.  You have to press the “Enter” key for each cash flow  Use the down arrow key to move to the next cash flow  The “F” is the number of times a given cash flow occurs in consecutive periods  Use the NPV key to compute the present value by entering the interest rate for I, pressing the down arrow, and then computing the answer  Clear the cash flow worksheet by pressing CF and then 2nd CLR Work 6 Multiple Cash Flows – PV Example 2  You are offered the opportunity to put some money away for retirement. You will receive five annual payments of $25,000 each beginning in 40 years. How much would you be willing to invest today if you desire an interest rate of 12%?  Formula:  Calculator: 7 Multiple Cash Flows – PV Example 2 Timeline 0 1 2 … 39 40 41 42 43 44 0 0 0 … 0 25K 25K 25K 25K 25K Notice that the year 0 cash flow = 0 (CF0 = 0) The cash flows years 1 – 39 are 0 (C01 = 0; F01 = 39) The cash flows years 40 – 44 are 25,000 (C02 = 25,000; F02 = 5) 10 Annuities -- Calculator You can use the PMT key on the calculator for the equal payment Use period interest rate The sign convention still holds 11 Annuity –Example 1  After carefully going over your budget, you have determined you can afford to pay $632 per month towards a new sports car. You call up your local bank and find out that the going rate is 1 percent per month for 48 months. How much can you borrow?  Formula:  Calculator: 12 Annuity – Example 2  Suppose you win the Publishers Clearinghouse $10 million sweepstakes. The money is paid in equal annual end-of-year installments of $333,333.33 over 30 years. If the appropriate discount rate is 5%, how much is the sweepstakes actually worth today?  Formula:  Calculator: 15 Finding the Number of Payments  You ran a little short on your spring break vacation, so you put $1,000 on your credit card. You can only afford to make the minimum payment of $20 per month. The interest rate on the credit card is 1.5 percent per month. How long will you need to pay off the $1,000? 16 Finding the Rate  Suppose you borrow $10,000 from your parents to buy a car. You agree to pay $207.58 per month for 60 months. What is the monthly interest rate? 17 Annuity – Finding the Rate Without a Financial Calculator  Trial and Error Process  Choose an interest rate and compute the PV of the payments based on this rate  Compare the computed PV with the actual loan amount  If the computed PV > loan amount, then the interest rate is too low  If the computed PV < loan amount, then the interest rate is too high  Adjust the rate and repeat the process until the computed PV and the loan amount are equal Summary: Table 6.2 PV = Present value, what future cash flows are worth today FV, = Future value, what cash flows are worth in the future r = Interest rate, rate of return, or discount rate per period—typically, but not always, one year t = Number of periods—typically, but not always, the number of years ¢ = Cash amount Fue = C x (1 +f = 1)/4 A series of identical cash flows is called an annuity, and the term [(1 +! ~ 1]/ris called Se Present PV=ECx i -[fi/0 +q]/r The term {7 — [1/(1 + ']}/ris called the annuity present value factor. A perpetuity has the same cash flow every year forever. 20 21 Effective Annual Rate (EAR)  This is the actual rate paid (or received) after accounting for compounding that occurs during the year  If you want to compare two alternative investments with different compounding periods you need to compute the EAR and use that for comparison. 22 Annual Percentage Rate  This is the annual rate that is quoted by law  By definition APR = period rate times the number of periods per year  Consequently, to get the period rate we rearrange the APR equation:  Period rate = APR / number of periods per year  You should NEVER divide the effective rate by the number of periods per year – it will NOT give you the period rate 25 EAR - Formula 1 m APR 1 EAR m        Remember that the APR is the quoted rate m is the number of compounding periods per year 26 EAR-Example 2  You are looking at two savings accounts. One pays 5.25%, with daily compounding. The other pays 5.3% with semiannual compounding. Which account should you use?  First account:  Second account: 27 Computing APRs from EARs  If you have an effective rate, how can you compute the APR? Rearrange the EAR equation and you get:      1 - EAR) (1 m APR m 1 30 Loan Types  Pure discount loans: the borrower received money today and repays a single lump sum at some time in the future;  Interest only loans: the borrower pays interest each period and repays the entire principal at some time in the future;  Amortized loans: the borrower repays parts of the loan amount over time. Pure Discount Loans  Treasury bills are excellent examples of pure discount loans. The principal amount is repaid at some future date, without any periodic interest payments.  If a T-bill promises to repay $10,000 in 12 months and the market interest rate is 7 percent, how much will the bill sell for in the market?  PV = ? 6F-31 Interest-Only Loan - Example  Consider a 5-year, interest-only loan with a 7% interest rate. The principal amount is $10,000. Interest is paid annually.  What would the stream of cash flows be?  Years 1 – 4: Interest payments of .07(10,000) = 700  Year 5: Interest + principal = 10,700  This cash flow stream is similar to the cash flows on corporate bonds, and we will talk about them in greater detail later. 6F-32