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 1Period 2Period 3Period 4Period 5 Revenues less Expenses (net of Depreciation AND Interest) less Depreciation equals Earnings Before Taxes and Interest less 35% plus Depreciation Cash Flow for calculating NPV when using WACC as discount factor 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: € today, or € 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= $ $100.00= $ Year 2: 5% of $105.00= $ $105.00= $ Year 3: 5% of $ = $5.51+ $110.25= $ Year 4: 5% of $115.76= $ $115.76= $ Year 5: 5% of $121.55= $ $121.55= $127.63

Compounding and Discounting

$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?

FV 5 = €800 X ( ) 5 = $800 X (1.338) = €1, 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 = $ 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 worth more today than tomorrow The Time Value of Money

PV = FV/(1+i) n = $1,700/( ) 8 = $1,700/1.851 = $ 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 Value Relationship

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 1Period 2Period 3Period 4Period 5 Revenues less Expenses (net of Depreciation AND Interest) less Depreciation equals Earnings Before Taxes and Interest less 25% plus Depreciation Cash Flow for calculating NPV when using WACC as discount factor How will these numbers change over the years? What factors will affect them? Excluding Interest, because WACC is the discount factor!!!

WACC r WACC = Equity + Debt Equity × r Equity + Equity + Debt Debt × r Debt ×(1 – Tx) BUT WHAT ABOUT INFLATION???? Already captured in returns on debt/equity

WACC = 12% PLC = 3 Years Investment = € 100,000 Year 0Year 1Year 2Year 3 Net Cash Flow (€100,000)€ 50,000 € 51,000€ 48, WACC (n) ÷ 1.12 ÷ ÷ Discounted Cash Flow (€100,000)€ 50,000€ 40,65734,165

WACC = 12% PLC = 3 Years Investment = € 100,000 Year 0Year 1Year 2Year 3 Net Cash Flow (€100,000)€ 50,000 € 51,000€ 48, WACC (n) ÷ 1.12 ÷ ÷ Discounted Cash Flow (€100,000)€ 50,000€ 40,65734,165

WACC = 12% PLC = 3 Years Investment = € 100,000 Year 0Year 1Year 2Year 3 Net Cash Flow (€100,000)€ 50,000 € 51,000€ 48, WACC (n) ÷ 1.12 ÷ ÷ Discounted Cash Flow (€100,000)€ 50,000€ 40,65734,165

WACC = 12% PLC = 3 Years Investment = € 100,000 Year 0Year 1Year 2Year 3 Net Cash Flow (€100,000)€ 50,000 € 51,000€ 48, WACC (n) ÷ 1.12 ÷ ÷ Discounted Cash Flow (€100,000)€ 44,643€ 40,657€ 34,165

Year 0Year 1Year 2Year 3 Net Cash Flow (€100,000)€ 50,000 € 51,000€ 48, WACC (n) ÷ 1.12 ÷ ÷ Discounted Cash Flow (€100,000)€ 44, , ,165 Sum = Present Value € 119,465 Present Value

Year 0Year 1Year 2Year 3 Net Cash Flow (€100,000)€ 50,000 € 51,000€ 48, WACC (n) ÷ 1.12 ÷ ÷ Discounted Cash Flow (€100,000)+ 44, , ,165 Sum = Net Present Value € 19,465 NET Present Value

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

PI & PP Profitability Index Payback Period Limitations of these methods Decision criteria

Good luck!