Principles of Accounting II Chapter 14: Time Value of Money What Is Accounting? Process of,, and information To facilitate informed. Accounting is the of. Operating, Investing, Financing Businesses plan for which activity? Which activity occurs first in a company? Which activity is important? Equation Fun(damentals) Profit + Expenses = Assets - Owners Equity = Contributions + Profit - Dividends = 1
Financial Statements Which statement provides a of the business s financial health at a point in time? Which statement contains,, and activities in separate sections? revenue is on which statement? Determine Cash and Accrual Basis Income TJ shipped CDs to customers and billed them $. TJ deposited $ he received from customers into his bank account. TJ incurred $ in operating costs. TJ wrote checks to cover operating costs in the amount of $. Determine Cash Receipts Billie s cash basis income for the month was $. She wrote checks for $ to pay operating expenses this month. 2
Determine Accrual Revenue Nancy incurred $ operating expenses. She wrote checks for $ in operating expenses and deposited $ from customer payments. Her accrual basis income was $. How much did she bill her customers? Principles I vs. Principles II In Principles I, we focused on the business. In Principles II, we will focus on and activities. Return of Investment vs. Return on Investment Return of investment is. Return on investment is. Rate of Return Rate of return = ----------------------------------------------- 3
Calculate Rate of Return You invest $ in a certificate of deposit. Later, you receive $. What is the rate of return? You Can t Lose in Real Estate Now assume you invest $ in a tract of raw land. One year later, you sell the land to your brother-in-law for $. What is the rate of return? Using Rate of Return You invest $ in a bank account earning a % annual rate of return. At the end of year 1, what do you expect to have in the account? How about at the end of year 2? 4
Interest = Principal x Rate x Time i 1 = p 1 + i 1 = i 2 = p 2 + i 2 = This illustrates. Advantage of Compounding What does it mean to compound? What is the result of more compounding? Why? 5
Semiannual Compounding Power! Principal Interest Date Amount Income Balance 1/1/x1 $ 2,000.00 6/1/x1 $ 2,000.00 12/31/x1 6/1/x2 12/31/x2 How was the $ interest computed? When compounding interest more than once a year, use the. 6
Try This One Jimbob deposits $ in a savings account on 1/1/x1 and earns % annual interest. Quarterly Compounding: Principal Interest Date Amount Income Balance 1/1/x1 $ 5,000.00 3/1/x1 $ 5,000.00 6/1/x1 9/1/x1 12/31/x1 Semiannual Compounding: Principal Interest Date Amount Income Balance 1/1/x1 $ 5,000.00 6/1/x1 $ 5,000.00 12/31/x1 What is his balance on 6/1/x1 and 12/31/x1 if interest is compounded? What is his balance on 6/1/x1 and 12/31/x1 if interest is compounded? 7
Future Value of $1 Future value is. Let s prove our answer for the $ we invested for a year at % with quarterly and semiannual compounding. We need: o interest rate per period (not year) o # of periods Go to the Future Value of $1 table on page 922. Quarterly: $5,000 x = $ [same as $5,000 x x x x ] Semiannually: $5,000 x = $ [same as $5,000 x x ] Present Value of $1 In computing FV, we knew the ( ), the interest rate, and the length of time. Sometimes we know the, the interest rate, and the length of time but wish to compute the. Present value is. 8
Decision Involving Present Value Customer Blanche will pay $ today. Customer Bob will pay $ in a year. Assuming both Bob and Blanche are reliable credit risks, which customer do you prefer assuming an effective interest rate of %? Key: Compare the payments of both customers on a basis. $5,000 x = $, which is than Blanche s current $ payment. Could the two payments have been compared on a basis instead? Would the decision differ? Learning Insights Compare dollar amounts on either a or basis. comparisons are generally better. The PV is always than the FV. 9
Try Working These How much would you have to invest today at % compounded semiannually to accumulate $ at the end of years? $ x = $ How much can you spend on a new car if you invest the $ you have now for years at % compounded quarterly? $ x = $ Introduction to Annuities We have calculated the value of a known current amount. We have calculated the value of a known future amount. Annuities involve a known of payments. One can determine either the present or future value of annuities. Future Value of an Annuity Distinguish between a - and an. Which one of these is an annuity? $20,000 compounded annually at 18% for 8 years $200 per month for 48 months at annual 18% Jot down your guesstimate of the annuity s future value. 10
Calculating Annuity s Future Value How many periods does the annuity involve? What is the annuity s interest rate per period? What is the annuity s table factor? Apply the table factor to the annuity payment. Does your answer make sense? Calculating Annuity s Present Value You wish to retire and receive $ a year for life. You expect to live years after retirement and earn interest of % per year. How much must you save by the day you retire to ensure that level of annual income? Is this an annuity? What is the annuity payment? How many periods does the annuity involve? What is the annuity s interest rate per period? What is the annuity s table factor? Apply the table factor to the annuity payment. Does the answer make sense? 11
Time Value Concepts in a Nutshell Do the involve a dollar amount or a of dollar amounts? Does the require knowledge of a or dollar amount? Find the Annuity Payment If you had $ saved for college, how much could you spend each year to make it last for years assuming an investment rate of %. PVA = Factor x Payments 12