Chapter 5 – Discounted Cash Flow Valuation
Unequal Cash Flows
Year 1
$
10,000
Year 2
$
15,000
Year 3
$
15,000
Year 5
$
20,000
Rate
10%
Year
Present value
1
$
10,000
$9,090.91
2
$
15,000
$12,396.69
On a Mac:
3
$
15,000
$11,269.72
COMMAND T = F4
4
$

$0.00
5
$
20,000
$12,418.43
Value today
$45,175.75
OR:
NPV function
Value today
$45,175.75
Suppose you are going to receive $10,000 in one year, $15,000 in two years and three years, and $20,0
the appropriate interest rate is 10 percent, what is the value of the cash flows today?
4
000 in five years. If
Perpetuities
Perpetuity payment
$
75,000
Interest rate
6%
Present value
$
1,250,000.00
Perpetuities
Perpetuity payment
$
75,000
Years until first pmt
9
< use 8, bc its always one period out
Interest rate
6%
Present value
$
1,250,000.00
Value today
$784,265.46
Growing Perpetuities
Perpetuity payment
$
10,000
Growth rate
2.50%
Interest rate
8%
Present value
$
181,818.18
Growing Perpetuities
You will receive $75,000 per year forever with the first payment occurring one year from today. If the
percent, what is the value of the perpetuity today?
Suppose the first perpetuity payment in the previous problem is exactly 9 years from today. What is th
flows today
You will receive perpetuity with a payment of $10,000 next year. The payment will grow by 2.5 perce
If the appropriate discount rate is 8 percent, what is the value of the cash flows today?
Perpetuity payment
$
1,000,000
Growth rate
8.00%
Interest rate
13%
Present value
$
4,761,904.76
You want to buy a song catalog. The royalties next year will be $1 million, and are expected to decrea
year indefinitely. If you want a 13 percent return, what is the most you should pay for the catalog?
e discount rate is 6
he value of the cash
ent per year forever.
ase by 8 percent per
Annuities
Payment
$
10,000
Years
3
Rate
10%
Year
Present value
1
$
10,000
$9,090.91
2
$
10,000
$8,264.46
3
$
10,000
$7,513.15
Value today
$
24,868.52
< present value will always be lower than f
Or with Excel:
Value today
$24,868.52
Take value today and invest:
Year 1
Year 2
Year 3
Start
$24,868.52 $
17,355.37 $
9,090.91
Interest
2,486.85
1,735.54
909.09
Total
$
27,355.37 $
19,090.91 $
10,000.00
Withdrawal
(10,000.00)
(10,000.00)
(10,000.00)
Amount left
$
17,355.37 $
9,090.91 $

Annuity due
Suppose the annuity payments of $10,000 begin today. What is the value of the cash flows now?
Suppose you are offered $10,000 per year for three years. If the discount rate is 10 percent, what is the
flows today?
Payment
$
10,000
Years
3
Rate
10%
Value today
$27,355.37
< add 1 in "type" it makes it an annuity due
Future Value of Annuities
Payment
$
5,000
Years
30
Rate
11%
Future value
$995,104.39
Future Value of Annuities Due
Suppose the first payment on the previous annuity is today. What is the value of your retirement accou
Payment
$
5,000
Years
30
Rate
11%
Future value
$1,104,565.87
< future value of AD is always higher than future value of A
Annuities
You are planning to save $5,000 per year for the next 30 years toward retirement with the first paymen
year from today. If you can earn an 11 percent interest rate, what will the value of your retirement port
You will receive $50,000 per year for 10 years with the first payment occurring 7 years from today. If
discount rate is 9 percent, what is the value of the cash flows today?
Payment
$
50,000
Number of payments
10
Years until first payment
7
Interest rate
9%
Value at beginning of annuity
$320,882.89
present va
Value today
$191,331.98
present value is one period before the first pa
Annuity payments
Years
40
Future value
$
1,500,000
Interest rate
11%
Amount of deposit
$2,578.09
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 Spring '14
 JoeSmolira