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

2. Chapter 5: Discounted Cash Flow Valuation
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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)
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Chapter 5: Discounted Cash Flow Valuation

3. FV of annuities (ordinary annuity)
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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?
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Chapter 5: Discounted Cash Flow Valuation

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

5. Chapter 5: Discounted Cash Flow Valuation
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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?
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Chapter 5: Discounted Cash Flow Valuation

6. Chapter 5: Discounted Cash Flow Valuation
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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%.
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Chapter 5: Discounted Cash Flow Valuation

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

8. Clicker Question (finding the payment amount)
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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
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

9. Clicker Question (finding the number of payments)
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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 years
B years
C years
D. 10 years
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

10. Clicker Question (finding the interest rate)
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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 % D %
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

11. Chapter 5: Discounted Cash Flow Valuation
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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
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

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

13. PV of unequal cash flows
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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?
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Chapter 5: Discounted Cash Flow Valuation

14. Chapter 5: Discounted Cash Flow Valuation
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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
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

15. Chapter 5: Discounted Cash Flow Valuation
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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
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

16. Chapter 5: Discounted Cash Flow Valuation
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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?
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Chapter 5: Discounted Cash Flow Valuation

17. Chapter 5: Discounted Cash Flow Valuation
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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
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Chapter 5: Discounted Cash Flow Valuation

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

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

20. Chapter 5: Discounted Cash Flow Valuation
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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
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Chapter 5: Discounted Cash Flow Valuation

21. Clicker Question (amortization)
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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
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

22. Chapter 5: Discounted Cash Flow Valuation
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Loan Amortization
Period
Begin
Balance
Payment
Principal
(Payment – interest)
Interest 10%
(of begin balance)
Ending Balance
(Beg bal – principal) 1 2 3
Total
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Chapter 5: Discounted Cash Flow Valuation

23. Chapter 5: Discounted Cash Flow Valuation
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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
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

24. Chapter 5: Discounted Cash Flow Valuation
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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
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

25. Chapter 5: Discounted Cash Flow Valuation
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How much total interest will I pay on a $250,000 loan at 8% annual interest paid monthly over 30 years?
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

26. $250,000 loan at 8% annual interest paid monthly over 30 years
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$250,000 loan at 8% annual interest paid monthly over 30 years
Payment
Principal
Interest
Balance
1st
180th
270th
Total (360 pmts)
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

27. Chapter 5: Discounted Cash Flow Valuation
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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?
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

28. Chapter 5: Discounted Cash Flow Valuation
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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
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

29. Chapter 5: Discounted Cash Flow Valuation
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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?
Savings Length FV
Principal
Interest
30 years
35 years
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

30. Chapter 4: Time Value of Money (lump sums)
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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
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Chapter 4: Time Value of Money (lump sums)
Chapter 3: Working with Financial Statements

31. Chapter 4: Time Value of Money (lump sums)
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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
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Chapter 4: Time Value of Money (lump sums)
Chapter 3: Working with Financial Statements

32. Chapter 4: Time Value of Money (lump sums)
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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%
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Chapter 4: Time Value of Money (lump sums)
Chapter 3: Working with Financial Statements

33. Chapter 5: Discounted Cash Flow Valuation
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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 years
B years
C years
D years
E years
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

34. Chapter 5: Discounted Cash Flow Valuation
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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
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

35. Chapter 5: Discounted Cash Flow Valuation
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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
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

36. Keys to Savings Success
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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
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Chapter 5: Discounted Cash Flow Valuation
Chapter 3: Working with Financial Statements

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