HEALTHCARE FINANCIAL MANAGEMENT Chapter 9 -- Time Value Analysis PROBLEM 1 Find the following values for a lump sum assuming annual, semiannual, and quarterly compounding: ANSWER Amount Annual Interest Rate Semi-Annual Interest Rate Quarterly Interest Rate Time Period (annual compounding) Time Period (semi-annual compounding) Time Period (quarterly compounding) Annual Compounding Semiannual Compounding Quarterly Compounding a. Future Value $500.00 8% 1 b. Future Value $500.00 8% 5 c. Present Value $500.00 8% 1 d. Present Value $500.00 8% 5

PROBLEM 2 What is the effective annual rate (EAR) if the stated rate is 8 percent and compounding occurs: Compounding Frequency Interest Rate Time Period EAR a. Semiannually b. Quarterly

PROBLEM 3 Find the following values assuming a regular, or ordinary, annuity and then repeat assuming the annuities are annuities due: Amount Annual Interest Rate Time Period (annual compounding) Ordinary Annuity Annuity Due a. Present Value $400.00 10% 10 b. Future Value $400.00 10% 10 c. Present Value $200.00 5% 5 d. Future Value $200.00 5% 5

Chapter 9 -- Time Value Analysis PROBLEM 4 Consider the following uneven cash flow stream: a. What is the present (Year 0) value of the following cash flow stream: Year Cash Flow Opporutnity Cost Rate 0 $0 10% PV= PV= $1,715.87 1 $250 2 $400 3 $500 4 $600 5 $600 b. Now we add an outflow (or cost) of $1,000 at Year 0. What is the present value (or net present value) of the stream? Year Cash Flow Opporutnity Cost Rate 0 ($1,000) 10% PV= 1 $250 2 $400 3 $500 4 $600 5 $600 c. Time value analysis involves either discounting or compounding cash flows.Many healthcare financial management decisions---such as bond refunding, capital investment, and lease versus buy---involve discounting projected future cash flows. What factors must executives consider when choosing a discount rate to apply to forecasted cash flows. ANSWER:

PROBLEM 5 (a) What is the present value of the following perpetuity: PMT= $100.00 Discount rate = 7% PV= (b) Suppose that interest rates double in the economy and the appropriate discount rate is now 14 percent. What would happen to the present value of the perpetuity? PMT= $100.00 Discount rate = 14% PV=

Chapter 9 -- Time Value Analysis PROBLEM 6 Epitome Healthcare has just borrowed $1,000,000 on a five-year, annual payment term loan at a 15 percent rate.The first payment is due one year from now. Complete the amortization schedule for this loan. Total cost of loan $1,000,000 interest rate (APR) 15% time (years) 5 Payment Payment Interest Principal Payment Remaining Balance Beginning Balance Year 1 Year 2 Year 3 Year 4 Year 5 Totals

1 2 3 4 5 6 7 8 A B C D HEALTHCARE FINANCIAL MANAGEMENT F G H Chapter 9 -- Time Value Analysis PROBLEM 1 Find the following values for a lump sum assuming annual, semiannual, and quarterly compounding: 9 10 11 12 13 14 15 16 17 18 19 20 21 22 E a. b. c. d. Future Value Future Value Present Value Present Value $ $ $ $ Amount 500.00 500.00 500.00 500.00 Annual Interest Rate 8% 8% 8% 8% Semi-Annual Interest Rate Quarterly Interest Rate Time Period Time Period (annual (semi-annual compounding) compounding) 1 5 1 5 When you have a compounding frequency other than annual you need to adjust both the interest and time period. For interest you divide by the compounding frequency and for time you multiply by the compounding frequency. For semi-annual the compounding frequency is two. You will pay/receive two payments of interest a year. Therefore, on a one year investment you will receive two payments of interest, on a five year investment ten payments, and so on. However, you will not receive the full amount of interest but rather an equivalent reduction. So if the interest is 8% annual you will pay/received 4% semi annually. The same concepts apply to quarterly compounding except the multiplier/divisor is four. See the adjustments to the formula in the grey shaded boxes. Please let me know if you need further guidance on understanding this concept as it flows throughout the remainder of the course. I J K 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 L ANSWER Time Period (quarterly compounding) Annual Compounding Semiannual Compounding 1 2 3 4 5 6 7 A B C D HEALTHCARE FINANCIAL MANAGEMENT F G H Chapter 9 -- Time Value Analysis PROBLEM 2 What is the effective annual rate (EAR) if the stated rate is 8 percent and compounding occurs: 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 E a. b. Compounding Frequency Semiannually Quarterly Interest Rate Time Period EAR Use the =EFFECT function express your results as a p I 1 2 3 4 5 6 7 Use the =EFFECT function within Excel to simplify your calculation ans express8your results as a percentage. 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 1 2 3 4 5 6 A B C D E HEALTHCARE FINANCIAL MANAGEMENT Chapter 9 -- Time Value Analysis PROBLEM 3 Find the following values assuming a regular, or ordinary, annuity and then repeat assuming the annuities are annuities 1 2 3 4 5 6 7 8 9 A B C D HEALTHCARE FINANCIAL MANAGEMENT F G H I Chapter 9 -- Time Value Analysis PROBLEM 4 Consider the following uneven cash flow stream: a. What is the present (Year 0) value of the following cash flow stream: 10 11 12 13 14 15 16 17 18 19 E Year 0 1 2 3 4 5 Cash Flow $0 $250 $400 $500 $600 $600 Opporutnity Cost Rate 10% PV= PV= b. Now we add an outflow (or cost) of $1,000 at Year 0. What is the present value (or net present value) of the stream? 20 Year 0 1 2 3 4 5 21 22 23 24 25 26 27 Cash Flow ($1,000) $250 $400 $500 $600 $600 Opporutnity Cost Rate 10% PV= 28 c. Time value analysis involves either discounting or compounding cash flows. Many healthcare financial management decisions---such as bond refunding, capital investment, and lease versus buy---involve discounting projected future cash flows. What factors must executives consider when choosing a discount rate to apply to forecasted cash flows. 29 ANSWER: 30 31 32 33 34 35 36 37 A 38 39 40 41 42 B C D E F G H I 1 2 3 4 5 6 7 A B C D HEALTHCARE FINANCIAL MANAGEMENT E Chapter 9 -- Time Value Analysis PROBLEM 5 (a) What is the present value of the following perpetuity: F G H I A 1 2 3 4 5 6 B C D HEALTHCARE FINANCIAL MANAGEMENT E F G Chapter 9 -- Time Value Analysis PROBLEM 6 Epitome Healthcare has just borrowed $1,000,000 on a five-year, annual payment term loan at a 15 percent rate. The fir is due one year from now. H I 1 2 3 4 5 erm loan at a 15 percent rate. The first payment 6