Chapter 3PrinciplesPrinciples ofof CorporateCorporate FinanceFinanceNinth EditionHow To Calculate Present Values3- 2 Topics CoveredValuing Long-Lived Assets Looking for Shortcuts Perpetuities and Annuities More Shortcuts Growing Perpetuities and Annuities3- 3Present ValuesDiscount Factors can be used to compute the present value of any cash flow.3- 4Present ValuesExample You just bought a new computer for $3,000. The payment terms are 2 years same as cash. If you can earn 8% on your money, how much money should you set aside today in order to make the payment when due in two years?3- 5Present ValuesReplacing “1” with “t” allows the formula to be used for cash flows that exist at any point in time3- 6Present ValuesExample You will receive $200 risk free in two years. If the annual rate of interest on a two year treasury note is 7.7%, what is the present value of the $200?Example You will receive $200 risk free in two years. If the annual rate of interest on a two year treasury note is 7.7%, what is the present value of the $200?Example You will receive $200 risk free in two years. If the annual rate of interest on a two year treasury note is 7.7%, what is the present value of the $200?Example You will receive $200 risk free in two years. If the annual rate of interest on a two year treasury note is 7.7%, what is the present value of the $200?3- 7Example You are considering an investment that will pay you $100 in one year and $200 in two years. If you want to earn 7% on your money in the first year and 7.7 % in the 2nd year, how much would you be willing to pay?3- 8Present ValuesPVs can be added together to evaluate multiple cash flows.3- 9Present ValuesPVs can be added together to evaluate multiple cash flows.3- 10Present ValuesPresent ValueYear 0100/1.07200/1.0772Total= $93.46= $172.42= $265.88$100$200Year 0 123- 11Present ValuesExample Assume that the cash flows from the construction and sale of an office building is as follows. Given a 5% required rate of return, create a present value worksheet and show the net present value.3- 12Present ValuesExample - continuedAssume that the cash flows from the construction and sale of an office building is as follows. Given a 5% required rate of return, create a present value worksheet and show the net present value.3- 13Present ValuesPresent ValueYear 0-170,000-100,000/1.05320,000/1.052Total = NPV-$170,000= -$170,000= $95,238= $290,249= $25,011 -$100,000+$320,000Year 0 12Example - continuedAssume that the cash flows from the construction and sale of an office building is as follows. Given a 5% required rate of return, create a present value worksheet and show the net present value.3- 14Short CutsSometimes there are shortcuts that make it very easy to calculate the present value of an asset that pays off in different periods. These tools allow us to cut through the calculations quickly.3- 15Short CutsPerpetuity - Financial concept in which a cash flow is theoretically received forever. See p166.3- 16Short CutsPerpetuity - Financial concept in which a cash flow is theoretically received forever. 3- 17Present ValuesExample What is the present value of $1 billion every year, for all eternity, if you estimate the perpetual discount rate to be 10%?3- 18Short CutsAnnuity - An asset that pays a fixed sum each year for a specified number of years.Perpetuity (first payment in year 1)Perpetuity (first payment in year t + 1)Annuity from year 1 to year tAssetYear of Payment1 2.t t + 1Present Value3- 19Short CutsAnnuity - An asset that pays a fixed sum each year for a specified number of years.3- 20Example Tiburon Autos offers you “easy payments” of $5,000 per year, at the end of each year for 5 years. If interest rates are 7%, per year, what is the cost of the car? Present Values5,000 Year 0 1 2 3 4 5 5,0005,0005,0005,000Present Value at year 03- 21Annuity Short CutExample You agree to lease a car for 4 years at $300 per month. You are not required to pay any money up front or at the end of your agreement. If your opportunity cost of capital is 0.5% per month, what is the cost of the lease?3- 22Annuity Short CutExample - continued You agree to lease a car for 4 years at $300 per month. You are not required to pay any money up front or at the end of your agreement. If your opportunity cost of capital is 0.5% per month, what is the cost of the lease?3- 23Annuity Short CutExample The state lottery advertises a jackpot prize of $295.7 million, paid in 25 installments over 25 years of $11.828 million per year, at the end of each year. If interest rates are 5.9% what is the true value of the lottery prize?3- 24FV Annuity Short CutFuture Value of an Annuity The future value of an asset that pays a fixed sum each year for a specified number of years.3- 25Annuity Short CutExample What is the future val