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FNAN 301
Solutions to lab problems – 2/11/2011
Group lab problem
You own a bowling alley that is expected to make annual cash flows forever.
The cost of capital
is 12.5%.
The next annual cash flow is expected in one year from today and all subsequent cash
flows are expected to grow annually by 2.5%.
What is the value of the bowling alley if you
know that the cash flow in 5 years from today is expected to be $100,000?
Time
0
1
2
3
4
5
…
Cash flow
0
C
1
C
1
× (1.025)
C
1
× (1.025)
2
C
1
× (1.025)
3
C
1
× (1.025)
4
…
Cash flow
0
C
1
C
1
× (1.025)
C
1
× (1.025)
2
C
1
× (1.025)
3
$100,000
…
Present value
?
Approach:
1) find the expected cash flow in 1 year
2) use the expected cash flow in 1 year to find the value today
1) find the expected cash flow in 1 year
The cash flows reflect a growing perpetuity
We know that C
5
= C
1
× (1+g)
4
C
5
= 100,000
g = .025
100,000 = C
1
× (1.025)
4
So C
1
= 100,000 / (1.025)
4
= $90,595.06
2) use the expected cash flow in 1 year to find the value today
The cash flows reflect a growing perpetuity
We know that PV = C
1
/ (r – g)
C
1
= $90,595.06
r = .125
g = .025
PV = 90,595.06
/ (.125 – .025)
= 90,595.06 / .100
= $905,950
1
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Solutions to lab problems – 2/11/2011
Group lab problem
What is the value of a night club that is expected to generate fixed cash flows of $170,000 with
the first cash flow in 4 years and the last cash flow in 9 years if the appropriate discount rate is
13.5 percent?
The value can be found in 2 steps.
1) Find the value of the night club as of one year before the first payment is made
2) Find the present value (as of today) of the night club
Time
0
1
2
3
4
5
6
7
8
9
Pmt #
1
2
3
4
5
6
CF
0
0
0
0
170k
170k
170k
170k
170k
170k
1) The first of a series of 6 fixed payments occurs in 4 years, so we can find the value of the
night club as of 3 years from now as an ordinary annuity.
The 6 fixed payments occur in 4,
5, 6, 7, 8, and 9 years from now.
END Mode
Enter
6
13.5
170,000
0
N
I%
PV
PMT
FV
Solve for
670,226
The night club is expected to be worth $670,226 in 3 years
2) The value today of something worth 670,226 in 3 years can be found as
PV
0
= PV
3
/ (1+r)
3
PV
3
= 670,226
r = .135
PV
0
= 670,226 / (1.135)
3
= $458,388
Mode is not relevant, since PMT = 0
Enter
3
13.5
0
670,226
N
I%
PV
PMT
FV
Solve for
458,388
Today, the value of the night club is $458,388
Note: the following 3 cash flow patterns have the same present value when r = 13.5%
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This note was uploaded on 02/16/2011 for the course FINANCE 301 taught by Professor Murray during the Spring '09 term at George Mason.
 Spring '09
 MURRAY
 Cost Of Capital

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