1 / 37

Mastering Cash Flow Valuation Techniques

This chapter covers discounted cash flow valuation methods, perpetual payments, effective interest rates, loan amortization, and annuity calculations. Learn to find rates, payment amounts, and number of payments efficiently. Explore the present value of unequal cash flows and future value and present value of annuities. Clicker questions challenge your understanding through practical scenarios. Dive into loan amortization tables and effective interest rate calculations for comprehensive financial analysis.

chartley
Download Presentation

Mastering Cash Flow Valuation Techniques

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related