Time Value of Money

• Problems in corporate finance involve comparison of alternatives that are associated with future cash flows that differ in timing and amounts. Selecting among these alternatives require an understanding of the concept of time value of money and the related calculations techniques.

Time Value Concepts

• The time value of money has applications in many areas of corporate finance including Capital Budgeting, Bond Valuation, and Stock Valuation.

• The time value of money concepts will be grouped into:

• 1. Future Value

• 2. Present Value

FUTURE VALUE

• Future Value represents what an investment today will grow to in the future if it is earn a specific interest rate.

• The process of calculating the future value is called COMPOUNDING. Under the compounding technique, the interest is calculated on the original cash flow or investment including accumulated interest.

Future Value of a Single Cash Flow

• Example:

• How much will P10,000 deposited today at 6% compounded annually be worth after 5 years?

• Formula: FV = PV x FV factor (i,n)

• =10,000 x FV factor (6,5)

• =10,000 x 1.388

• =13,380

Future Value with Frequent Compounding

• What will be the value of a P10,000 deposit at 6% compounded semi-annually at the end of 5 years?

• Procedure: • 1. Adjust the n based on the actual discounting periods

(5 x 2=10).• 2. Adjust the i by dividing it by the number of discounting

periods (6%/2=3%)• 3. Apply formula: FV=PV x FV factor (3,10)• 4. FV= 10,000 x 1.344• 5, =13,440•

Future Value of a Series of Cash Flows (Same Amounts/Annuity)

• Example:• If you deposit in your special saving account,

P2,000 every year, how much would be your account at the end of 5 years if the bank pays 6% compounded annually?

• Solution:• FV = 2,000 x FVA factor (6,5)• = 2,000 x 5.637• = 11,274

PRESENT VALUE

• It is the current value equivalent of future cash flow or series of cash flows.

• The process of calculating the present value is called DISCOUNTING.

Present Value of a Single Cash Flow or Lump Sum Payment

• Example:• How much should be deposited today in a

savings account that yields an interest of 5% compounded annually if you expect to accumulate P10,000 at the end of 4 years?

• Formula: PV =FV x PV factor (5,4)• =10,000 x 0.823• =8,230

Present Value of an Annuity• Example:• Consider a 3-year P10 M term loan at 20% interest to be

paid quarterly. How much will be your quarterly loan amortization?

• Solution:• Adjust the i = 20%/4 = 5%• Adjust the n= 3 x 4 = 12• Formula: PVA=10,000/PVA factor(5,12)• = 10,000 / 8.863• = 1,128,286*• *To compute for the principal and interest, prepare a

loan amortization schedule for 12 periods.

Present Value of a Perpetuity

• Perpetuity is a series of Perpetual Series of Future cash flows or payments (equal amounts).

• Example:• If a company is paying a fixed P1,000 annual

dividends and the current interest rate is 14%, what is the present value of these dividends to an investor?

• Formula: PVp=Periodic Payments / Int. Rate• =1,000 / 0.14• =7,142.86

CAPITAL BUDGETING

• Is the process of identifying, evaluating, planning, and financing capital investments projects of a business organization.

• Characteristics of Capital Investments

• 1. Require huge amounts of resources.

• 2. Long-term impact on the operations.

• 3. Difficult to reverse or terminate.

Capital Budgeting Process

• 1. Identify potential projects.

• 2. Estimate costs and benefits.

• 3 Evaluate various projects.

• 4. Approve and implement best project(s).

• 5. Reevaluate projects.

Types of Capital Investments

• 1. Replacement of existing capital investment items.

• 2. Improvement of product or process.

• 3. Expansion of facilities.

CAPITAL BUDGETING

• The goal of capital budgeting is to find long-term investments that will increase the wealth of the stockholders.

• There are two basic techniques of capital budgeting:

• 1. Non-Discounting Techniques• -Payback• -Accounting Rate of Return• 2. Discounting Techniques -Net Present Value Method (NPV) -Internal Rate of Return (IRR)

PAYBACK METHOD

• The Payback Method simply seeks to measure the length of time that it will take to recover the initial cost of investments.

• Formula: (if annual cash inflows (CF) are • identical)

Payback Period = Investments/cash flows• (if cash annual cash inflows (CF) are • not identical)• Payback Period = CF1+CF2+…CFt • Where CFt is the net cash inflow to payback

period.

Pros & Cons of Payback Method

• PROS:• 1. Simple to calculate.• 2. It immediately measures the degree of risk of

a project. The shorter the payback, the lower the risk of a project.

• CONS:• 1. It ignores the concept of Time Value of

Money.• 2. It ignores salvage value and cash inflows

beyond the payback period.

PAYBACK METHOD

• Example:

• Suppose Project A will entail a P10M investments and the expected annual

• cash inflow is P 1M.

• The Payback Period = P10M / P1M

• = 10 years

Payback with Uneven Cash Inflows

• Supposing the forecasted annual cash inflows from the investments of P10 M are as follow:

• Balance Payback• Years Est. ACFs Investments Period (Yr)• 0 P10 M• 1 P 2.5 M 7.5 M 1 • 2 3.0 M 4.5 M 1• 3 4.0 M .5 M 1• 4 2.0 M - 0.25 (.5 / 2.0)• 5 1.0 M - ____• Payback Period 1.25 yrs.

Accounting Rate of Return (ARR)

• ARR focuses on Profitability. Under this method, the net income (based on the accrual basis of accounting) is divided by the project’s investments.

• Example:• Assume that the company is planning to acquire

a new machine that will cost P60,000 and expected to generate an annual net income of P12,000. What is the ARR for this project>

• ARR = 12,000 / 60,000• = 20%

NET PRESENT VALUE (NPV)

• Under this method, all cash inflows and outflows related to the investments are discounted at (in most cases) the firm’s cost of capital.

• Procedure:• Present value of cash inflows xxx• Less: Present value of cash outflows xxx• Net Present Value xxx• The Project is ACCEPTABLE if the NPV is

POSITIVE

Net Present Value (NPV)

• Example:• Assume that PSJ Oil Mills, Inc. is planning

to purchase a new machine costing P350,000 that is expected to generate cash inflows of P120,000 per year during its economic life of 5 years. Salvage value of P50,000 is expected to be recovered at the end of the 5th year. Cost of capital is 20%. Compute for the company’s NPV.

Net Present Value

• Year Cash Inflows PVF Present Value• 1 P120,000 0.833 P 99,960 • 2 120,000 0.694 83,280• 3 120,000 0.579 69,480• 4 120,000 0.482 57,840• 5 120,000 0.402 48,240• 50,000 0.402 20,100 • Total PV of Cash Inflows P378,900 Less: Cost of Investments 350,000 Net Present Value P 28,900 Note: For the annuity of P120,000, you can use the PVA factor of 2.990

Net Present Value

• Profitability Index• It is the ratio of PV of Cash Inflows to the PV of

Cash Outflows or Cost of Investments: • Total PV of Cash Inflows• Total PV of Cash Outflows• or• Cost of Investments• Note: If the Profitability Index is 1.0 or more, the

project is acceptable.

Net Present Value

• Net Present Value Index

• Is a variation of Profitability Index. It is the ratio of the NPV to Total PV of Cash Outflows or Cost of Investments.

• Note: A positive NPV Index indicates that the project is acceptable.

Present Value Payback Method

• The conventional payback method does not consider the time value of money. To correct this weakness, the Present Value Payback Method converts the cash flows to their present value before computing the payback period.

Internal Rate of Return (IRR)

• Sometimes called Discounted Cash Flow Rate of Return (DCFRR).

• IRR is the discount rate that equates the present value of cash inflows with the investments. When the IRR is used as a discount rate, the PV of the Cash Inflows is equal to the PV of Cash Outflows, resulting to ZERO NPV.

IRR

• Let us take the example problem of NPV

• (PSJ Oils Mills, Inc.): i @ 20%, n=5

• Total PV of Cash Inflows P378,900

• Less: Cost of Investments 350,000

• Net Present Value P 28,500

• Obviously, since the NPV is not Zero, 20% in not the IRR. Compute for the IRR.

IRR

• Computation of the IRR:• 1. determine the PVfactor for the IRR.• PVf (IRR) = Cost of Investment• Annual Cash Inflow• = 350,000/120,000• = 2.917• 2. Under the PVA table, 2.917 at n=5,is

between 20% (2.991) and 22% (2.864), therefore, the IRR is between 20% and 22%.

• If you want to get the precise IRR, you can interpolate.

IRR Interpolations

• 1. If the annual cash inflows are equal, the interpolation formula is:

• IRR = LR + (HR-LR)x PVAf(lr)-PVAf(irr)• PVAf(lr)-PVA(hr)• Where: LR = lower rate• HR = Higher rate• Note: PVAfactors are taken from the PVA table.•

IRR Interpolations

• When annual cash inflows are uneven, the interpolation formula is:

• IRR = LR + (HR-LR) x NPV(lr) – 0• NPV(lr)-NPV(hr)• Where: = 0 is the NPV when cash • flows are discounted at• IRR.

Payback Reciprocal

• Is a reasonable estimate of the IRR, provided that the following conditions are met:

• 1. The economic life of the project is at least twice the payback period.

• 2. The net annual cash inflows are constant throughout the life of the project.

• Payback Reciprocal:• Net Annual Cash Inflows/Investments• Or 1/ Payback Period

Cost of Capital

• Also called as Cut-Off Rate, Minimum Desired Rate or Hurdle Rate.

• The Cost of Capital serves as the standard rate with which selection from different alternatives is made.

• The Cost of Capital is the cost of using funds.• Funds can be sourced from bonds/long-tem debts,

preferred stocks, common stocks or even from retained earnings of the business.

• When the funds come from a combination of various sources, the weighted average cost of capital (WACC) must be computed, the weight being the percentage component of each item in the firm’s capital structure.

Cost of Capital

• Cost of capital are computed as follows:• For Bonds/Long-Term Debts:• -After tax rate of interest• For Preferred Stocks:• -Dividend per share divided by the present

market price of the stock.• For Common Stock and Retained Earnings:• -Earnings per share (after tax and preferred

dividend) divided by the current market price of the common stock.

Cost of Capital Problem

• Assumed data:• Capital structure:• % of Total• Bonds Payable, 10% P 500,000 50%• Preferred Stocks, 8%,• P100 par value 100,000 10%• Common Stocks, • 100,000 shares 300,000 30%• } 40%• Retained Earnings 100,000 10%• ‘T o t a l P1,000,000 100%

Cost of Capital Problem

• Other Data:• Income before tax P200,000• Less: Tax (35%) 70,000• Net Income P130,000• Less: Preferred Dividends• (P100,000 x 8%) 8,000• Balance for Common Stocks P122,000• divided by Number of Shares 100,000• Earning Per Share P 1.22 • Current Market Prices:• Common Stocks P 5/share• Preferred Stocks 160/share

Computation of Cost of Capital

• Bonds Payable:

• 10% (1 - 0.35) = 6.5%

• Preferred Stocks:

• P100 x 8%/P160 = P8/P160 = 5%

• Common Stocks:

• P1.22/P5 = 24.4%

Weighted Cost of Capital (WACC)

• Sources Cost of Weighted• of Funds Weights Capital Cost• Bonds 50% 6.5% 3.25%• Pref. Stocks 10% 5.0% 0.50%• Common• Stocks & 40% 24.4% 9.76% • Ret. Earnings• WACC 13.51% • Note: Funds of the company should be invested • into projects that would generate a rate of return • not lower than 13.51%.

Capital Structure

• Is that mix of debt and equity which maximizes the price of the firm’s stock.

• Optimal Capital Structure

• Is the one that strikes a balance between risk and return so as to maximize the price of the stock.

Factors that Influence the Capital Structure Decisions

• 1. Business Risk

• 2. Tax Implication

• 3. Financial Flexibility

• 4. Managerial Conservatism or Aggressiveness.

Dimensions of Risk

• 1. Business Risk

• The risk on the business’ operation if it uses no debt.

• 2. Financial Risk

• The additional risk placed on the common stockholders as a result of the firm’s decision to use debt.

Capital Structure

• What is the optimal (best) debt-equity ratio?

• Example:

• You need P100 million for a project, should all this money be raised by issuing stocks or 50% from stocks and 50% from debts?

Approaches to Valuation of Capital Structure(Market Value of the Firm)• 1.Net Operating Income Approach

• The net operating income is capitalized at an over all capitalization rate to obtain the total market value of the firm. The market value of the stocks is deducted from the total market value to obtain the market value of the debt.

Leverage Approach

• Degree of Operating Leverage (DOL)

• The percentage change in operating income (EBIT) associated with a given percentage change in sale.

• Formula:

• DOL = Percentage change in EBIT

• Percentage change in Sales

Degree of Financial Leverage (DFL)

• Shows how changes in operating income (EBIT) affect earning per share (EPS)

• Formula:

• DFL= Percentage change in EPS

• Percentage change in EBIT

Degree of Total Leverage (DTL)

• Shows the percentage change in EPS brought about by a given percentage change in sales. DTL shows the effects of both operating leverage and financial leverage.

• Formula:

• DTL = DOL x DFL

Modigliani & Miller Theory

• Develops the Tradeoff Theory of Capital Structure, where debt is useful because interest is TAX DEDUCTIBLE. But too much debt can hurt a company even with sound basic operations.

EPS Indifference Point (EIP)

• Is the level of sales at which EPS will be the same whether the firm uses debt or common stocks financing.

• Equity financing is preferred if the sales is below the EIP and debt financing is better is the sales is higher than the EIP.

Dividend Policy/Decision

• Dividends Defined• Are corporate earnings distributed to stockholders.

• 3 Relevant Dates Associated with Dividends• 1. Date of Declaration• 2. Date of Record• a. Cum Dividend• b. Ex-Dividend• 3. Date of Payment• •

Common Dividend Policies

• 1. Stable-Dividend –Per Share Policy

• 2. Constant Dividend-Payout Ratio

• 3. Residual Dividend Policy

• 4. Compromise/Combination Dividend Policy

Some Factors that Influence Dividend Policy

• 1. Growth Rate

• 2. Restrictive Covenants

• 3. Profitability

• 4. Earning Stability

• 5. Age and size

• 6. Penalties

Types of Dividends

• 1. Cash Dividends

• 2.. Stock Dividends

• 3. Non-Cash Dividends

• a. Scrip Dividends

• b. Property Dividends

Options Other than Dividends

• 1. Stocks Splits

• a. Split-Up

• b. Split-Down or Reverse Split

• c. Stock Repurchase (Treasury Stock)

Long-Term Financing• Bond• Is a long-term debt certificate indicating that the company has

borrowed a given sum of money and that it agrees to repay the same at a future time and subject to a fixed interest rate.

• Types of Bonds• 1. Debentures• 2. Subordinated Debentures• 3. Mortgage Bonds• 4. Collateral Trust Bonds• 5. Convertible Bonds• 6. Callable Bonds• 7. Guaranteed Bonds• 8. Serial Bonds• 9. Junk Bonds

Bonds Ratings

• Ratings used by Moody and Standard & Poors (U.S. financial advisory)

• Aaa - Prime Quality• Aa - High Quality• A - Upper Medium Grade• Bbb - Medium Grade• Bb - Lower Medium Grade• B - Speculative• Ccc/Cc - Very Speculative to near or in • default• C - Lowest Grade

Mergers and Acquisitions

• Merger• Is the combination of two or more

companies into one. Only the acquiring or dominant company retains its identity.

• Consolidation• When two or more companies are

combined to form a new company. In effect, the consolidating firms are dissolved and a new company is formed.

Rationale for Mergers or Business Combinations

• 1. Synergy

• 2. Diversification

• 3. Tax Consideration

• 4. Control

• 5. Purchase below Replacement Cost

Other Kinds of Business Combinations

• 1. Holding Company• 2. Parent Company/Subsidiary Company• 3. Joint Venture

• 3 Types of Mergers• 1. Vertical• 2. Horizontal• 3. Congeneric• 4. Conglomerate

Some Factors to Consider for Mergers

• 1. Earning Per Share (EPS)

• 2. Dividend Per Share

• 3. Market Per Share

• 4. Financial and Business Risk

• 5. Book Value Per Share

DIVESTITURES

• When a firm sells or closes one of its businesses resulting a permanent change in its scope of operations.

• Types of Divestitures:

• 1. Spin-Off

• 2. Leverage Buyout (LBO)

• 3. Going Private

• 4. Liquidation

Multinational Managerial Finance

• Multinational Corporation• A firm that operates in two or more countries.• Reasons for going “international”• 1. To seek new markets• 2. New sources of raw materials• 3. New Technology• 4. Production Efficiency• 5. Avoid (adverse) political and regulatory

hurdles.

International Monetary System

• 1. Positive/Deficit Trade Balance

• 2. Devaluation

• 3. Revaluation

• 4. Floating Exchange Rates