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Corporate Finance ­FIN 622
VU
Lesson 03
TIME VALUE OF MONEY
Time Value of Money offers an overview of the information required to calculate the future and present
values of individual cash flows, ordinary annuities, due perpetuities and investments with uneven cash flows.
TVM is based on the concept that a dollar that you have today is worth more than the promise or
expectation that you will receive a dollar in the future. Money that you hold today is worth more because
you can invest it and earn interest. After all, you should receive some compensation for foregoing spending.
This hand out has been divided into following topics, which will be explained in detail:
1. PRESENT VALUE
2. FUTURE VALUE
3. ANNUITIES
4. PERPETUITY
PRESENT VALUE
The present value of a future cash flow is the nominal amount of money to change hands at some future
date, discounted to account for the time value of money. A given amount of money is always more valuable
sooner than later because this enables one to take advantage of investment opportunities.
The present value of delayed payoff may be found by multiplying the payoff by a discount factor which is
less than 1. If C1 denotes the expected payoff at period 1, then
Present Value (PV) = discount factor. C1
This discount factor is the value today of $1 received in the future. It is usually expressed as the reciprocal
of 1 plus a rate of return.
Discount Factor = 1 / 1+r
The rate of return r is the reward that investors demand for accepting delayed payment.
The present value formula may be written as follow:
PV = 1 / 1+r. C1
To calculate present value, we discount expected payoffs by the rate of return offered by equivalent
investment alternatives in the capital market. This rate of return is often referred to a the discount rate,
hurdle rate or opportunity cost of capital. If the opportunity cost is 5 percent expected payoff is $200,000,
the present value is calculated as follows:
PV = 200,000 / 1.05 = $190,476
FUTURE VALUE
Future value measures what money is worth at a specified time in the future assuming a certain interest rate.
This is used in time value of money calculations.
To determine future value (FV) without compounding:
Where PV is the present value or principal, t is the time in years, and r stands for the per annum interest
rate.
To determine future value when interest is compounded:
Where PV is the present value, n is the number of compounding periods, and i stands for the interest rate
per period.
The relationship between i and r is:
Where X is the number of periods in one year. If interest is compounded annually, X = 1. If interest is
compounded semiannually, X = 2. If interest is compounded quarterly, X = 4. If interest is compounded
monthly, X = 12 and so on. This works for everything except compounded continuously, which must be
handled using exponential.
Similarly, the relationship between n and t is:
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Corporate Finance ­FIN 622
VU
For example, what is the future value of 1 money unit in one year, given 10% interest? The number of time
periods is 1, the discount rate is 0.10, the present value is 1 unit, and the answer is 1.10 units. Note that this
does not mean that the holder of 1.00 unit will automatically have 1.10 units in one year, it means that
having 1.00 unit now is the equivalent of having 1.10 units in one year.
ANNUITY
An annuity is an equal, annual series of cash flows. Annuities may be equal annual deposits, equal annual
withdrawals, equal annual payments, or equal annual receipts. The key is equal, annual cash flows. Annuities
work in the following way.
Illustration:
Assume annual deposits of $100 deposited at end of year earning 5% interest for three years.
Year 1: $100 deposited at end of year
= $100.00
Year 2: $100 × .05 = $5.00 + $100 + $100 = $205.00
Year 3: $205 × .05 = $10.25 + $205 + $100 = $315.25
There are tables for working with annuities. Future Value of Annuity Factors is the table to be used in
calculating annuities due. Just look up the appropriate number of periods, locate the appropriate interest,
take the factor found and multiply it by the amount of the annuity.
For instance, on the three-year 5% interest annuity of $100 per year. Going down three years, out to 5%,
the factor of 3.152 is found. Multiply that by the annuity of $100 yields a future value of $315.20.
The present value of annuity can be finding out by the following formula:
Present value of annuity = C [1/r-1/r(1+r)t]
The expression in brackets is the annuity factor, which is the present value at discount rate r of an annuity
of $1 paid at the end of each of t periods.
PEPETUITY
Perpetuity is a cash flow without a fixed time horizon.
For example if someone were promised that they would receive a cash flow of $400 per year until they died,
that would be perpetuity. To find the present value of a perpetuity, simply take the annual return in dollars
and divide it by the appropriate discount rate.
The present value of perpetuity can be finding out by the following formula:
Present value of perpetuity=C/r
Where C is the annual return in dollars and r is the discount rate.
Illustration:
If someone were promised a cash flow of $400 per year until they died and they could earn 6% on other
investments of similar quality, in present value terms the perpetuity would be worth $6,666.67.
Present value of perpetuity= ($400 / .06 = $6,666.67)
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Table of Contents:
  1. INTRODUCTION TO SUBJECT
  2. COMPARISON OF FINANCIAL STATEMENTS
  3. TIME VALUE OF MONEY
  4. Discounted Cash Flow, Effective Annual Interest Bond Valuation - introduction
  5. Features of Bond, Coupon Interest, Face value, Coupon rate, Duration or maturity date
  6. TERM STRUCTURE OF INTEREST RATES
  7. COMMON STOCK VALUATION
  8. Capital Budgeting Definition and Process
  9. METHODS OF PROJECT EVALUATIONS, Net present value, Weighted Average Cost of Capital
  10. METHODS OF PROJECT EVALUATIONS 2
  11. METHODS OF PROJECT EVALUATIONS 3
  12. ADVANCE EVALUATION METHODS: Sensitivity analysis, Profitability analysis, Break even accounting, Break even - economic
  13. Economic Break Even, Operating Leverage, Capital Rationing, Hard & Soft Rationing, Single & Multi Period Rationing
  14. Single period, Multi-period capital rationing, Linear programming
  15. Risk and Uncertainty, Measuring risk, Variability of return–Historical Return, Variance of return, Standard Deviation
  16. Portfolio and Diversification, Portfolio and Variance, Risk–Systematic & Unsystematic, Beta – Measure of systematic risk, Aggressive & defensive stocks
  17. Security Market Line, Capital Asset Pricing Model – CAPM Calculating Over, Under valued stocks
  18. Cost of Capital & Capital Structure, Components of Capital, Cost of Equity, Estimating g or growth rate, Dividend growth model, Cost of Debt, Bonds, Cost of Preferred Stocks
  19. Venture Capital, Cost of Debt & Bond, Weighted average cost of debt, Tax and cost of debt, Cost of Loans & Leases, Overall cost of capital – WACC, WACC & Capital Budgeting
  20. When to use WACC, Pure Play, Capital Structure and Financial Leverage
  21. Home made leverage, Modigliani & Miller Model, How WACC remains constant, Business & Financial Risk, M & M model with taxes
  22. Problems associated with high gearing, Bankruptcy costs, Optimal capital structure, Dividend policy
  23. Dividend and value of firm, Dividend relevance, Residual dividend policy, Financial planning process and control
  24. Budgeting process, Purpose, functions of budgets, Cash budgets–Preparation & interpretation
  25. Cash flow statement Direct method Indirect method, Working capital management, Cash and operating cycle
  26. Working capital management, Risk, Profitability and Liquidity - Working capital policies, Conservative, Aggressive, Moderate
  27. Classification of working capital, Current Assets Financing – Hedging approach, Short term Vs long term financing
  28. Overtrading – Indications & remedies, Cash management, Motives for Cash holding, Cash flow problems and remedies, Investing surplus cash
  29. Miller-Orr Model of cash management, Inventory management, Inventory costs, Economic order quantity, Reorder level, Discounts and EOQ
  30. Inventory cost – Stock out cost, Economic Order Point, Just in time (JIT), Debtors Management, Credit Control Policy
  31. Cash discounts, Cost of discount, Shortening average collection period, Credit instrument, Analyzing credit policy, Revenue effect, Cost effect, Cost of debt o Probability of default
  32. Effects of discounts–Not effecting volume, Extension of credit, Factoring, Management of creditors, Mergers & Acquisitions
  33. Synergies, Types of mergers, Why mergers fail, Merger process, Acquisition consideration
  34. Acquisition Consideration, Valuation of shares
  35. Assets Based Share Valuations, Hybrid Valuation methods, Procedure for public, private takeover
  36. Corporate Restructuring, Divestment, Purpose of divestment, Buyouts, Types of buyouts, Financial distress
  37. Sources of financial distress, Effects of financial distress, Reorganization
  38. Currency Risks, Transaction exposure, Translation exposure, Economic exposure
  39. Future payment situation – hedging, Currency futures – features, CF – future payment in FCY
  40. CF–future receipt in FCY, Forward contract vs. currency futures, Interest rate risk, Hedging against interest rate, Forward rate agreements, Decision rule
  41. Interest rate future, Prices in futures, Hedging–short term interest rate (STIR), Scenario–Borrowing in ST and risk of rising interest, Scenario–deposit and risk of lowering interest rates on deposits, Options and Swaps, Features of opti
  42. FOREIGN EXCHANGE MARKET’S OPTIONS
  43. Calculating financial benefit–Interest rate Option, Interest rate caps and floor, Swaps, Interest rate swaps, Currency swaps
  44. Exchange rate determination, Purchasing power parity theory, PPP model, International fisher effect, Exchange rate system, Fixed, Floating
  45. FOREIGN INVESTMENT: Motives, International operations, Export, Branch, Subsidiary, Joint venture, Licensing agreements, Political risk