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Chapter 5 Discounted Cash Flow Valuation

Chapter 5 Discounted Cash Flow Valuation. Finding the rate Perpetuities Effective interest Loan amortization. FV of annuities PV of annuities PV of unequal cash flows Finding the payment Finding the # of payments. FV of annuities.

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Chapter 5 Discounted Cash Flow Valuation

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  1. Chapter 5Discounted Cash Flow Valuation • Finding the rate • Perpetuities • Effective interest • Loan amortization FV of annuities PV of annuities PV of unequal cash flows Finding the payment Finding the # of payments Chapter 5: Discounted Cash Flow Valuation

  2. FV of annuities • If I invest $100 at the end of each year for 3 years at an interest rate of 10%, what will the value of my investment be at the end of 3 years? • What if I invest the $100 at the beginning of each year for 3 years? (annuity due) Chapter 5: Discounted Cash Flow Valuation

  3. FV of annuities(ordinary annuity) • If I invest $100 at the end of each year for 3 years at an interest rate of 10%, what will the value of my investment be at the end of 3 years? Chapter 5: Discounted Cash Flow Valuation

  4. FV of annuities(annuity due) • What if I invest the $100 at the beginning of each year for 3 years? (annuity due) Chapter 5: Discounted Cash Flow Valuation

  5. PV of annuities • I win a $10,000 “mini-lottery”! But I get $1,000 per year starting now for 10 payments. The appropriate interest rate for this cash flow is 6%. What is the present value of the lottery proceeds? Chapter 5: Discounted Cash Flow Valuation

  6. PV of annuities • I win a $10,000 “mini-lottery”! But I get $1,000 per year starting now for 10 payments. The appropriate interest rate for this cash flow is 6%. Chapter 5: Discounted Cash Flow Valuation

  7. Annuity formulae • FV(annuity) • PV(annuity) Chapter 5: Discounted Cash Flow Valuation

  8. Clicker Question(finding the payment amount) How much should I save at the end of each year to accumulate $100,000 at the end of 10 years if interest rates are 9%? A. $ 6,582 B. $ 7,749 C. $ 9,534 D. $10,000 E. $12,000 Chapter 5: Discounted Cash Flow Valuation

  9. Clicker Question(finding the number of payments) If I save $2,000 per year (end of year), how many years will I need to save $20,000 if I receive interest of 6.3%? A. 7 years B. 8 years C. 9 years D. 10 years Chapter 5: Discounted Cash Flow Valuation

  10. Clicker Question(finding the interest rate) What return is required to obtain a future value of $200,000 in 20 years given $3,000 payments per year? (beginning of each year) A. 8.43% B. 9.79% C. 10.46% D. 11.33% Chapter 5: Discounted Cash Flow Valuation

  11. Clicker Question What has a higher future value in 3 years, if interest rates are 8% (not a calculator question)? A. $100 payments, 3 year ordinary annuity B. $100 payments, 3 year annuity due C. $200 lump sum received today D. $300 lump sum received in 3 years E. all answers produce the same future value Chapter 5: Discounted Cash Flow Valuation

  12. Perpetuities • What is the value of a $6 annual payment in perpetuity if the relevant interest rate is 12%? Chapter 5: Discounted Cash Flow Valuation

  13. PV of unequal cash flows • A real estate investment will generate the following cash flows (end of year): • Year 1: -$500 • Year 2: $500 • Year 3: $1,000 • Year 4: $50,000 If the opportunity cost of funds is 12%, what is the present value of this investment? Chapter 5: Discounted Cash Flow Valuation

  14. Clicker Question What is the net present value (NPV) today of the following cash flows if interest rates are 8%? year 1: $500 year 2: $1,000 year 3: $1,500 A. $1,235 B. $2,511 C. $2,999 D. $3,163 E. $6,945 Chapter 5: Discounted Cash Flow Valuation

  15. Clicker Question What is the net future value (NFV) today of the following cash flows if interest rates are 8%? year 1: $500 year 2: $1,000 year 3: $1,500 A. $1,235 B. $2,511 C. $2,999 D. $3,163 E. $6,945 Chapter 5: Discounted Cash Flow Valuation

  16. Effective interest • Stated/quoted interest rates versus effective annual rates (EAR): Is 1% interest per month the same as 12% interest per year? • Example 1 • I invest $1,000 for 10 years at 12% per year • I invest $1,000 for 10 years at 1% per month • Example 2 • A bank pays 12% per year (compounded monthly) on an account; what is the effective annual rate paid? Chapter 5: Discounted Cash Flow Valuation

  17. Effective interest • Example 1 • I invest $1,000 for 10 years at 12% per year • I invest $1,000 for 10 years at 1% per month Chapter 5: Discounted Cash Flow Valuation

  18. Effective interest • Example 2 • A bank pays 12% per year (compounded monthly) on an account; what is the effective annual rate paid? Chapter 5: Discounted Cash Flow Valuation

  19. Effective interest • EAR Formula: Chapter 5: Discounted Cash Flow Valuation

  20. Loan amortization • Establish an amortization table for the following loan: • $10,000 loan for 3 years at 10% annual interest rate with annual repayment of principal and interest. • Step 1: establish payment amount • Step 2: develop amortization table Chapter 5: Discounted Cash Flow Valuation

  21. Clicker Question(amortization) What is the regular payment for a $10,000 loan for 3 years at 10% annual interest? A. $2,500 B. $3,333 C. $4,021 D. $5,000 Chapter 5: Discounted Cash Flow Valuation

  22. Loan Amortization Chapter 5: Discounted Cash Flow Valuation

  23. Clicker Question What is the monthly payment for this mortgage: $250,000 borrowed at 8% APR for 30 years amortized on a monthly basis. A. $ 416 B. $ 1,834 C. $ 2,765 D. $ 4,609 E. $ 22,207 Chapter 5: Discounted Cash Flow Valuation

  24. Clicker Question How much total interest will I pay on a $250,000 loan at 8% annual interest paid monthly over 30 years? Take a guess… A. $168,000 B. $264,000 C. $306,000 D. $410,000 Chapter 5: Discounted Cash Flow Valuation

  25. How much total interest will I pay on a $250,000 loan at 8% annual interest paid monthly over 30 years? Chapter 5: Discounted Cash Flow Valuation

  26. $250,000 loan at 8% annual interest paid monthly over 30 years Chapter 5: Discounted Cash Flow Valuation

  27. What if I pay $2,000 per month, rather than $1,834 on a $250,000 loan at 8% annual interest paid monthly? How more quickly will the loan be paid off? Chapter 5: Discounted Cash Flow Valuation

  28. Clicker Question I planned to save $5,000 per year for 30 years (at 7%). How much more would I have if I saved for 35 years? Take a guess….. A. $ 37,000 B. $ 85,000 C. $147,000 D. $220,000 Chapter 5: Discounted Cash Flow Valuation

  29. I planned to save $5,000 per year for 30 years (at 7%). How much more would I have if I saved for 35 years? Chapter 5: Discounted Cash Flow Valuation

  30. Clicker Question At what age do you want to retire (no longer have to work)? A. less than 55 years old B. 55 – 60 years old C. 60 – 65 years old D. 65 – 70 years old E. over 70 years old Chapter 4: Time Value of Money (lump sums)

  31. Clicker Question How much money do you plan to have saved (in today’s dollars) by the time you retire? A. less than $500,000 B. $500,000 - $750,000 C. $750,000 – $1 million D. $1 million – $1.5 million E. over $1.5 million Chapter 4: Time Value of Money (lump sums)

  32. Clicker Question What overall, long term return do you expect to get from your future investments? A. 3 – 7% B. 7 – 10% C. 10 – 13% D. 13 – 16% E. over 16% Chapter 4: Time Value of Money (lump sums)

  33. Clicker Question How long will it take to become a millionaire if you save $5,000 per year, starting next year, if your investment return is 9%? A. 21.5 years B. 28.7 years C. 31.5 years D. 34.2 years E. 44.9 years Chapter 5: Discounted Cash Flow Valuation

  34. Clicker Question When you retire in 35 years, your retirement account pays a fixed $90,000 per year (starting at retirement). If inflation is 3.5% between now and retirement, what is the purchasing power of the $90,000 payments today? A. $26,998 B. $36,452 C. $66,789 D. $78,962 E. $97,254 Chapter 5: Discounted Cash Flow Valuation

  35. Clicker Question When you retire in 35 years (60 years old) your retirement account pays a fixed $90,000 per year (starting at retirement). If inflation is 3.5% between and retirement, what is the purchasing power of the first $90,000 payment today? A. $ 26,998 B. $ 36,452 C. $ 66,789 D. $ 78,962 E. $ 97,254 Chapter 5: Discounted Cash Flow Valuation

  36. Keys to Savings Success • Start saving/investing EARLY • Save in tax sheltered vehicle • Get company match (401k) • Earn more---SAVE more • Leave savings ALONE • Save mostly in equities (stock funds) • Diversify to reduce risk Chapter 5: Discounted Cash Flow Valuation

  37. Chapter-end Homework Problems • Chapter 5 • Problems 1, 3, 5, 7, 9, 11, 19 Chapter 5: Discounted Cash Flow Valuation

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