Lecture15

# Lecture15 - Lecture 15 Time Value of Money 1 Admin Stuff...

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1 Lecture 15 Time Value of Money

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2 Admin Stuff Midterm re-grade submissions due now. Homework #5 due Monday, June 29 th . Rest of the course: – Time Value of Money – Debt – Leases – Shareholders’ Equity – Inter-corporate Investments – Financial Statement Analysis (FSA) – Maybe some Valuation Basics (Stocks, Businesses)
3 Today Time Value of Money “Present Value (PV),” “Future Value (FV)”, discount or interest rate (i), number of periods (n) Net Present Value (NPV) Types of Long Term Debt Note : a single payment due when the loan matures Mortgage : equal payments throughout the life of the loan Bond : equal payments periodically, plus final large payment at maturity Accounting for the Debt Booking the interest expense (debit) Cash (A), Note/Mortgage Payable (L); debit and credits Distinguishing current from non-current (long-term) portion of the debt

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4 Time Value of Money You are given the choice of \$1 today or \$1 a year from now. What do you prefer? Why? Simple interest formula FV = PV(1+r) n FV is Future Value PV is Present Value R is the interest rate per period n is the number of periods over which interest is compounded Note that r and n have to be in same units
5 Present Value What is the value to you today of obtaining \$100 at the end of one year? Receive \$100 Today Depends on the interest rate at which you could invest the money Assuming 5%, then the value today is \$100 / 1.05 = \$95.24 Why? Because you could have invested \$95.24 today, earned 5% interest over the course of the year, and have ended up with \$100 at the end \$95.24 x 0.05 = \$4.76 \$100 The Present Value of an amount is always lower than the amount itself Why? Because waiting makes you forego consumption at today’s purchasing power or it makes you forego investment at your earning capacity

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6 Present Value: How to Compute Plot the cash flows out over the periods in which they will be obtained Divide the cash flows by (1 + discount rate), exponentiated by the number of compounding periods away For example, 3 periods away and 5% rate: denominator = 1.05 3 \$100 / 1.05 2 Obtain \$100 at the end of 2 periods; rate is 5% Receive \$100 Today \$90.70 Why does this work?
7 Present Value: How to Compute It works because \$90.70 would compound up to \$100 if invested over 2 periods at 5% Today \$90.70 \$95.24 x 0.05 = \$4.54 x 0.05 = \$4.76 \$100

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8 Net Present Value: How to Compute If we have multiple or repeated cash flows, we need to come up with a Net or summation of all the discounted cash amounts Plot all cash flows out over the periods in which they will be obtained Divide each cash flow by (1 + discount rate), exponentiated by the number of compounding periods away Sum the discounted amounts Obtain \$100 at the end of each period over 2 years (total of \$200); rate is 5% \$100 / 1.05 2 Today \$90.70 \$100 / 1.05 \$95.24 \$185.94 Net Present Value of this series of cash flows
9 0.1486 0.1784 0.2145 0.2584 0.3118 0.3769 0.4564 0.5537 0.6730 0.8195 20 0.1635 0.1945 0.2317 0.2765 0.3305 0.3957 0.4746 0.5703 0.6864 0.8277 19 0.1799 0.2120 0.2502 0.2959 0.3503 0.4155 0.4936 0.5874 0.7002 0.8360 18 0.1978 0.2311 0.2703 0.3166 0.3714 0.4363 0.5134 0.6050 0.7142 0.8444 17 0.2176 0.2519 0.2919 0.3387 0.3936 0.4581 0.5339 0.6232 0.7284 0.8528 16 0.2394 0.2745 0.3152 0.3624 0.4173 0.4810 0.5553 0.6419 0.7430 0.8613 15 0.2633 0.2992 0.3405 0.3878 0.4423 0.5051 0.5775 0.6611 0.7579 0.8700 14 0.2897 0.3262 0.3677 0.4150 0.4688 0.5303 0.6006 0.6810 0.7730 0.8787 13 0.3186 0.3555 0.3971 0.4440 0.4970 0.5568 0.6246 0.7014 0.7885 0.8874 12 0.3505 0.3875 0.4289 0.4751 0.5268 0.5847 0.6496 0.7224 0.8043 0.8963 11 0.3855 0.4224 0.4632 0.5083 0.5584 0.6139 0.6756 0.7441 0.8203 0.9053 10 0.4241 0.4604 0.5002 0.5439 0.5919 0.6446 0.7026 0.7664 0.8368 0.9143

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