Managerial Finance

Net Present Value (NPV)Week 5

Some assumptions for project

• Bank wants at least 8% (unless you have other information from an acceptable source)

• Bank will not fund more than 70% of capital investment

• Tax rate come from Hotel I/S• Shareholders usually require upwards of

15% return

Today’s Topics

• Product & Economic Lifecycles (Evaluating Your Project Over Time)

• Depreciation• Cash Flow• Time Value and Discount Rate• Risk• Inflation

What’s in the future ?

Period 1 Period 2 Period 3 Period 4 Period 5Revenuesless Expenses (net of Depreciation AND Interest)less Depreciation equals Earnings Before Taxes and Interestless Taxes @ 35%plus Depreciation Cash Flow for calculating NPVwhen using WACC as discountfactor

How will these numbers change over the years?

What factors will affect them?

What’s in the future ?

•Product Life Cycle

•Economic Life Cycle

•Inflation

The Role of Time Value in Finance

• Most financial decisions involve costs & benefits that are spread out over time.

• Understanding the Time Value of Money allows comparison of cash flows from different periods.

•Question: Your father has offered to give you some money and asks that you choose one of the following two alternatives:

•€10.000 today, or•€13.310 three years from now.

•What do you do?

Time Line

                                                                                                                        

         

Simple Interest• With simple interest, you don’t earn interest on

interest.

• Year 1: 5% of $100 = $5 + $100 = $105

• Year 2: 5% of $100 = $5 + $105 = $110

• Year 3: 5% of $100 = $5 + $110 = $115

• Year 4: 5% of $100 = $5 + $115 = $120

• Year 5: 5% of $100 = $5 + $120 = $125

Compound Interest• With compound interest, a depositor earns interest on interest!

• Year 1: 5% of $100.00 = $5.00 + $100.00 = $105.00

• Year 2: 5% of $105.00 = $5.25 + $105.00 = $110.25

• Year 3: 5% of $110.25 = $5 .51+ $110.25 = $115.76

• Year 4: 5% of $115.76 = $5.79 + $115.76 = $121.55

• Year 5: 5% of $121.55 = $6.08 + $121.55 = $127.63

Compounding andDiscounting

$100 x (1.08)1 = $100 x (1.08) $100 x 1.08 = $108

Future Value of a Single Amount

• If Andreas places $100 in a savings account paying 8% interest compounded annually, how much will he have in the account at the end of one year?

FV5 = €800 X (1 + 0.06)5 = $800 X (1.338) = €1,070.40

Future Value of a Single Amount: The Equation for Future Value

• Tobias places €800 in a savings account paying 6% interest compounded annually. He wants to know how much money will be in the account at the end of five years.

Future Value of a Single Amount:A Graphical View of Future Value

Future Value Relationship

$300 x [1/(1+i)n] = $300 x [1/(1.06)1]

= $300 x 0.9434

= $283.02

Present Value of a Single Amount

• Luisa has an opportunity to receive $300 one year from now. If she can earn 6% on her investments, what is the most she should pay now for this opportunity?

Money is worthmore

today than tomorrowThe Time Value of Money

                                                                                                                        

         

PV = FV/(1+i)n

= $1,700/(1 + 0.08)8 = $1,700/1.851 = $918.42

Present Value of a Single Amount: The Equation for Future Value

• Feline wishes to find the present value of $1,700 that will be received 8 years from now. Feline’s opportunity cost is 8%.

Present Value of a Single Amount: A Graphical View of Present Value

Present ValueRelationship

Present Value of a Mixed Stream

• Kings Island Team has been offered an opportunity to receive the following mixed stream of cash flows over the next 5 years.

Present Value of a Mixed Stream

• If the firm must earn at least 9% on its investments, what is the most it should pay for this opportunity?

Calculate your project’s relevant cash flows

Period 1 Period 2 Period 3 Period 4 Period 5Revenuesless Expenses (net of Depreciation AND Interest)less Depreciation equals Earnings Before Taxes and Interestless Taxes @ 25%plus Depreciation Cash Flow for calculating NPVwhen using WACC as discountfactor

How will these numbers change over the years?

What factors will affect them?

Excluding Interest, because WACC is the discount factor!!!

WACC

rWACC = Equity + Debt

Equity × rEquity + Equity + Debt

Debt × rDebt ×(1 – Tx)

BUT WHAT ABOUT INFLATION????Already captured in returns on debt/equity

WACC = 12%PLC = 3 Years

Investment = € 100,000Year 0 Year 1 Year 2 Year 3

Net Cash Flow (€100,000) € 50,000 € 51,000 € 48,000

1 + WACC (n) ÷ 1.12 ÷ 1.12 2 ÷ 1.12 3

Discounted Cash Flow (€100,000) € 50,000 € 40,657 34,165

WACC = 12%PLC = 3 Years

Investment = € 100,000Year 0 Year 1 Year 2 Year 3

Net Cash Flow (€100,000) € 50,000 € 51,000 € 48,000

1 + WACC (n) ÷ 1.12 ÷ 1.12 2 ÷ 1.12 3

Discounted Cash Flow (€100,000) € 50,000 € 40,657 34,165

WACC = 12%PLC = 3 Years

Investment = € 100,000Year 0 Year 1 Year 2 Year 3

Net Cash Flow (€100,000) € 50,000 € 51,000 € 48,000

1 + WACC (n) ÷ 1.12 ÷ 1.12 2 ÷ 1.12 3

Discounted Cash Flow (€100,000) € 50,000 € 40,657 34,165

WACC = 12%PLC = 3 Years

Investment = € 100,000Year 0 Year 1 Year 2 Year 3

Net Cash Flow (€100,000) € 50,000 € 51,000 € 48,000

1 + WACC (n) ÷ 1.12 ÷ 1.12 2 ÷ 1.12 3

Discounted Cash Flow (€100,000) € 44,643 € 40,657 € 34,165

Year 0 Year 1 Year 2 Year 3

Net Cash Flow (€100,000) € 50,000 € 51,000 € 48,000

1 + WACC (n) ÷ 1.12 ÷ 1.12 2 ÷ 1.12 3

Discounted Cash Flow (€100,000) € 44,643 + 40,657 + 34,165

Sum = Present Value€ 119,465

Present Value

Year 0 Year 1 Year 2 Year 3

Net Cash Flow (€100,000) € 50,000 € 51,000 € 48,000

1 + WACC (n) ÷ 1.12 ÷ 1.12 2 ÷ 1.12 3

Discounted Cash Flow (€100,000) + 44,643 + 40,657 + 34,165

Sum = Net Present Value€ 19,465

NET Present Value

PV & NPV

Present Value of Cash Flow € 119,465Minus Investment (100,000)Net Present Value (NPV) € 19,465

PI & PP

• Profitability Index • Payback Period• Limitations of these methods• Decision criteria

Good luck!