Risk, Return, and the Time Value of Money Chapter 14

Relationship Between Risk and Return Risk – Uncertainty about the actual rate of return over the holding period Required rate of return Risk-free rate

Types of Risk Business risk (Changing Economy) Financial risk (Loan Default) Purchasing power risk (Inflation) Liquidity risk (Converting to Cash)

The Time Value of Money Money received today is worth more than money to be received in the future Interest Rates –Nominal Rates = Real Rates + Inflation Interest Rates are the rental cost of borrowing or the rental price charged for lending money Simple Interest – Interest on the initial value only (Not commonly used except for some construction loans) Compound Interest – Interest charged on Interest (Typical in Lending and Savings)

The Time Value of Money Present Value (PV) - a lump sum amount of money today Future Value (FV) - a lump sum amount of money in the future Payment (PMT) or Annuity - multiple sums of money paid/received on a regularly scheduled basis

The Six Financial Functions Future value of a lump sum invested today Compound Growth FV = PV(1+i) n PV=value today, i= interest rate, & n= time periods Example: where PV= $1, n=3, & i=10% –FV = $1 x (1+.10) x (1+.10) x (1+.10) –FV = $1 x –FV = $1.331

The Six Financial Functions Present Value of a Lump Sum Discounting –Process of finding present values from a future lump sum PV = FV [1/(1+i) n ] Example: where FV= $1, n=3, & i=10% –PV = $1 x [1/(1+.10) x (1+.10) x (1+.10)] –PV = $1 x [1/1.331] –PV = $1 x –PV = $0.7513

The Six Financial Functions Future Value of an Annuity –FVA = PMT[((1+i) n -1))/ i] –The future value of a stream of payments

The Six Financial Functions Present Value of an Annuity –PVA = PMT[(1-(1/(1+i) n ))/ i] –The present worth of a stream of payments

The Six Financial Functions Sinking Fund –SF PMT = FVA [ i / ((1+i) n -1))] –The payment necessary to accumulate a specific future value

The Six Financial Functions Mortgage Payments (Mortgage Constant) –MTG PMT = PVA [ i / ((1 - (1/(1+i) n )))] –The payment necessary to amortize (retire) a specific present value

Effect of Changing the Compounding Frequency –Interest Rates are quoted on an annual basis –Increasing the frequency of compounding increases the amount of interest earned –Increasing the frequency of payments for an amortizing loan decreases the amount of interest paid

Examples A Future Value Example: –You have just purchased a piece of residential land for $10,000. Based upon current and projected market conditions similar lots appreciate at 10% per year (annually). How much will your investment be worth in 10 years? How about 20 years. Is the effect of compounding 2 times greater?

Examples A Present Value Example: –You have been offered the option of purchasing a condo which will be sold for $150,000 at the end of 15 years. You need to make a reasonable offer for the investment so that you can purchase it today. You expect that similar investments would provide an 8% return per year (annually). How much should you be willing to pay (in one lump sum) today for this investment?

Examples Future Value of an Annuity Example: –You wish to save $2,000 per year over the 10 years you operate an apartment property. You can invest your savings at 8% per year (annually). How much money will you have in the account when you sell the investment?

Examples Present Value of an Annuity Example : –You will receive $5,000 per year over the next 30 years as equity income from a ground lease you wish to purchase. Investors require an 8% return for similar investments If you wish to buy this property, how much should you offer (in one lump sum) for the investment today?

Examples Sinking Fund Payment Example: –You wish to buy a house in 5 years. The down payment on a house, like you hope to purchase, will be $7,500. How much must you save every year to afford this down payment, given that you can invest the savings with the bank at 8%?

Examples Mortgage Payment Example: –You have negotiated the purchase of a condominium for $70,000. You will need a loan of $60,000, which the local bank has offered based on a 30 year term at 6% interest (annually). How much will your annual payment be for the condo? –Since nearly all mortgages are calculated on a monthly basis what is the monthly payment for the loan?

Net Present Value (NPV) Difference between how much an investment costs and how much it is worth to an investor NPV Decision Rule –If the NPV is equal to or greater than zero, we choose to invest

Net Present Value (NPV) PV inflows – PV outflows –NPV Formula:

Internal Rate of Return (IRR) The discount rate that makes the NPV equal to zero - the rate of return on the investment IRR Decision Rule –If the IRR is greater than or equal to our required rate of return, we choose to invest

Calculating Uneven Cash Flows Initial Cash Flow is the Cost of the Investment –Initial Cash Flow is Zero (0) if solving for PV Use the N j Key for Repeating Sequential Cash Flows