Chapter 6 Discounted Cash Flow Valuation
Chapter 06 Quiz A Student Name _________________________
Student ID ____________
________ 1.
You are able to pay mortgage payments of $675 a month for thirty years. The interest rate is 9.5 percent,
compounded monthly. What price house can you afford to buy if you have $5,000 cash available as a down
payment?
a. $72,712.50
b. $75,275.51
c. $80,275.51
d. $85,275.51
________ 2.
You are going to receive $6,000 at the end of each quarter for the next five years. What is the net
present value of these payments at a discount rate of 7 percent, compounded quarterly?
a. $63,564.09
b. $100,517.29 c. $102,276.34 d. $103,011.96
________ 3.
You want to retire on the day you have $1,000,000 in your savings account. You expect to earn 4 percent,
compounded monthly, on your money during your retirement. Your plan is to withdraw $4,500 a month as
retirement income from this account. How many years can you be retired until you run out of money?
a. 33.80
b. 69.56
c. 202.34
d. 405.65
________ 4.
A preferred stock pays annual dividends of $1.75. How much are you willing to pay today to buy one share
of this stock if you want to earn a 12.5 percent rate of return?
a. $6.00
b. $14.00
c. $24.00
d. $72.00
________ 5.
A project will produce cash flows of $6,000, $7,500, $9,000, and $11,000 a year for the next four years,
respectively. What is the value of these cash flows today at a discount rate of 8.5 percent?
a. $24,588.74
b. $26,884.36
c. $27,559.03
d. $37,257.92
________ 6.
Today you are opening a savings account and depositing an initial $1,000 into it. You plan to deposit $4,000
into the account one year from today and deposit another $4,000 two years from today. How much will you
have in your account ten years from today if you earn an 8 percent rate of return?
a. $6,008.85
b. $12,220.96
c. $17,558.66
d. $19,430.32
________ 7.
What is the effective annual rate of 10.75 percent compounded continuously?
a. 11.04 percent
b. 11.19 percent c. 11.30 percent d. 11.35 percent
________ 8.
What is the effective annual rate of 14.5 percent compounded semiannually?
a. 15.03 percent
b. 15.31 percent c. 15.50 percent d. 15.82 percent
________ 9.
You borrow $135,000 for twenty years at 9 percent. This is an amortized loan with monthly payments. How
much of the first payment goes to the principle balance of the loan? Assume that one month is equal to 1/12
of a year.
a. $84.38
b. $87.50
c. $193.09
d. $202.13
________ 10. You just purchased a 15-year annuity at a cost of $70,000. The annuity will pay you $1,050 at the end of each
month, starting with this month. What rate of return are you earning on this investment?
a. 15.42 percent
b. 15.52 percent c. 16.45 percent d. 16.74 percent
6-1
Chapter 6 Discounted Cash Flow Valuation
Chapter 06 Quiz A
1.
Answers
d
   .095 3012  
1  1 / 1 


12 
  
 
APV $675  

.095


12




 $675  118.92668
 $80,275.51
Enter
3012
N
9.5/12
I/Y
Solve for
PV
80,275.51
-675
PMT
FV
Price of house = $80,275.51 + $5,000 = $85,275.51
2.
b
   .07 54  
1  1 / 1 
 
4   
  
APV  $6,000  

.07


4




 $6,000 16.7528813
 $100,517.29
Enter
Solve for
54
N
7/4
I/Y
6,000
PV
PMT
-100,517.29
FV
6-2
Chapter 6 Discounted Cash Flow Valuation
3.
a
  .04  t 
1  1 / 1 

12  
 

$1,000,000  $4,500 
.04
12
  .04  t 
1  1 / 1 

12  
 

222.222222 
.04
12
  .04  t 
.74074074  1  1 / 1 

12  
 
t
 .04 
.25925926  1 / 1 

12 

3.857142846  1.003333333t
ln 3.857142846  t ln1.003333 333
1.349926714  .00332779t
t  405.65 months  33.80 years
Enter
4/12 -1,000,000 4,500
N
I/Y
PV
PMT
Solve for 405.65
Number of years = 405.65 / 12 = 33.80 years
4.
b
5.
b
PV 
FV
$1.75
 $14.00
.125

 
 

1
1
1
NPV  $6,000 
 $7,500 
 $9,000 
1
2
3
(1  .085)  
(1  .085) 
1  .085  



1
 $11,000 
4
1  .085 

 $5,529.954  $6,370.915  $7,046.173  $7,937.317
 $26,884.36
Enter
1
N
8.5
I/Y
2
N
8.5
I/Y
3
N
8.5
I/Y
4
N
8.5
I/Y
Solve for
Enter
Solve for
Enter
Solve for
Enter
PV
-5,529.954
PMT
6,000
FV
PV
-6,370.915
PMT
7,500
FV
PV
-7,046.173
PMT
9,000
FV
PMT
11,000
FV
PV
6-3
Chapter 6 Discounted Cash Flow Valuation
Solve for
-7,937.317
NPV = $5,529.954 + $6,370.915 + $7,046.173 + $7,937.317 = 26,884.36
6.
c

 
 
FV  $1,000  (1  .08)10  $4,000  (1  .08)9  $4,000  (1  .08)8
 $2,158.92  $7,996.02  $7,403.72
 $17,558.66
Enter
10
N
8
I/Y
-1,000
PV
PMT
FV
2,158.92
9
N
8
I/Y
-4,000
PV
PMT
FV
7,996.02
8
N
8
I/Y
-4,000
PV
PMT
FV
7,403.72
Solve for
Enter
Solve for
Enter
Solve for
FV = $2,158.92 + $7,996.02 + $7,403.72 = $17,558.66
7.
d
EAR = e.1075 − 1 = 2.71828.1075 − 1 = .11349 = 11.35 percent
Input for Texas Instruments BA II plus
.1075, 2nd, ex, -1, =; EAR = 11.35 percent
2
8.
a
  .145 
EAR  1  
  1 = .15026 = 15.03 percent
  2 
Enter
14.5
NOM
Solve for
9.
EFF
15.03
2
C/Y
d
   .09  2012  
1  1 / 1 


   12 
 
$135,000 C  

.09


12




$135,000  111.144954C
C  $1,214.63
Enter
2012
N
Solve for
Interest1  $135,000 
9/12 135,000
I/Y
PV
PMT
FV
-1,214.63
.09
 $1,012.50
12
First month’s principle = $1,214.63 – $1,012.50 = $202.13
6-4

Chapter 6 Discounted Cash Flow Valuation
10.
c
1512
  

r 
1

1
/
1

  


   12 
  ; This cannot be solved directly, so it’s easiest to just use the
$70,000  $1,050  

r


12




calculator method to get an answer. You can then use the calculator answer taken to several decimal places as the
rate in the formula just to verify that your answer is correct.
Enter
1512
N
/12 -70,000 1,050
I/Y
PV
PMT
FV
Solve for
16.45
With more decimals, the answer is 16.44722824 percent.
6-5
Chapter 6 Discounted Cash Flow Valuation
Chapter 06 Quiz B Student Name _________________________
Student ID ____________
________ 1.
You want to pay mortgage payments of $750 a month for twenty-five years. The interest rate is 6.5 percent,
compounded monthly. What price house can you afford to buy if you have $7,500 cash available as a down
payment?
a. $103,577.02
b. $104,178.69 c. $111,077.02 d. $118,577.02
________ 2.
You are going to receive $7,000 at the end of each quarter for the next eight years. What is the net
present value of these payments at a discount rate of 9 percent, compounded quarterly?
a. $158,463.72
b. $162,029.15 c. $477,809.07 d. $481,392.64
________ 3.
You want to retire on the day you have $800,000 in your savings account. You expect to earn 5 percent,
compounded monthly, on your money during your retirement. Your plan is to withdraw $5,000 a month as
retirement income from this account. How many years can you be retired until you run out of money?
a. 21.85
b. 22.02
c. 262.23
d. 264.22
________ 4.
A preferred stock pays annual dividends of $3.65. How much are you willing to pay today to buy one share
of this stock if you want to earn an 11 percent rate of return?
a. $17.73
b. $23.64
c. $33.18
d. $59.09
________ 5.
A project will produce cash flows of $4,000, $4,500, $6,500, and $8,000 a year for the next four years,
respectively. What is the value of these cash flows today at a discount rate of 7.5 percent?
a. $18,837.57
b. $19,286.85
c. $23,915.49
d. $25,156.99
________ 6.
Today you are opening a savings account and depositing an initial $2,000 into it. You plan to deposit $3,000
into the account three years from today and deposit another $5,000 four years from today. How much will
you have in your account five years from today if you earn a 10 percent rate of return?
a. $11,857.02
b. $12,351.02
c. $14,526.10
d. $16,105.10
________ 7.
What is the effective annual rate of 12.5 percent compounded monthly?
a. 12.50 percent
b. 13.10 percent c. 13.24 percent d. 13.31 percent
________ 8.
What is the effective annual rate of 14.7 percent compounded daily?
a. 15.24 percent
b. 15.53 percent c. 15.73 percent d. 15.83 percent
________ 9.
You borrow $155,000 for thirty-five years at 7 percent. This is an amortized loan with monthly payments.
How much of the first payment goes to the principle balance of the loan? Assume that one month is equal to
1/12 of a year.
a. $80.31
b. $86.06
c. $984.48
d. $990.23
________ 10. You just purchased a 25-year annuity at a cost of $80,000. The annuity will pay you $1,200 at the end of each
month, starting with this month. What rate of return are you earning on this investment?
a. 17.78 percent
b. 17.82 percent c. 18.06 percent d. 18.10 percent
6-6
Chapter 6 Discounted Cash Flow Valuation
Chapter 06 Quiz B
1.
Answers
d
   .065  2512  
1  1 / 1 


12 
  
 
APV $750  

.065


12




 $750 148.1026946
 $111,077.02
Enter
2512
N
6.5/12
I/Y
Solve for
-750
PV
PMT
111,077.02
FV
Home price = $111,077.02 + $7,500 = $118,577.02
2.
a
   .09 84  
1  1 / 1 
 
4   
  
APV  $7,000  

.09


4




 $7,000  22.63767419
 $158,463.72
Enter
Solve for
3.
84
N
9/4
I/Y
7,000
PV
PMT
-158,463.72
FV
b
6-7
Chapter 6 Discounted Cash Flow Valuation
   .05  t  
1  1 / 1 
 
12   
  
$800,000  $5,000  

.05


12




   .05  t  
1  1 / 1 
 
12   
  
160  

.05


12




  .05  t 
.666666667  1  1 / 1 

12  
 
t
 .05 
.333333333  1 / 1 

12 

3  .995850622 t
ln 3  t ln1.004166 667
1.098612289  .00415801t
t  264.22 months
Enter
Solve for
N
264.22
5/12
I/Y
-800,000 5,000
PV
PMT
FV
Number of years = 264.22 / 12 = 22.02 years
4.
c
5.
a
PV 
$3.65
 $33.18
.11

 
 

1
1
1
NPV  $4,000 
 $4,500 
 $6,500 
1
2
3
(1  .075)  
(1  .075) 
1  .075  



1
 $8,000 
4
1  .075 

 $3,720.93  $3,894.00  $5,232.24  $5,990.40
 $18,837.57
Enter
1
N
7.5
I/Y
2
N
7.5
I/Y
3
N
7.5
I/Y
4
7.5
Solve for
Enter
Solve for
Enter
Solve for
Enter
PV
-3,720.93
PMT
4,000
FV
PV
-3,894.00
PMT
4,500
FV
PV
-5,232.24
PMT
6,500
FV
8,000
6-8
Chapter 6 Discounted Cash Flow Valuation
N
I/Y
Solve for
PV
-5,990.40
PMT
FV
NPV = $3,720.93 + $3,894.00 + $5,232.24 + $5,990.40 = 18,837.57
6.
b

 
 
FV  $2,000  (1  .10) 5  $3,000  (1  .10) 2  $5,000  (1  .10)1
 $3,221.02  $3,630.00  $5,500.00
 $12,351.02
Enter
5
N
10
I/Y
-2,000
PV
PMT
FV
3,221.02
2
N
10
I/Y
-3,000
PV
PMT
FV
3,630.00
1
N
10
I/Y
-5,000
PV
PMT
FV
5,500.00
Solve for
Enter
Solve for
Enter
Solve for
FV = $3,221.02 + $3,630.00 + $5,500.00 = $12,351.02
12
7.
c
  .125 
EAR  1  
  1  .1324  13.24 percent
  12 
Enter
12.5
NOM
Solve for
8.
12
C/Y
d
  .147 
EAR  1  

  365 
Enter
14.7
NOM
Solve for
9.
EFF
13.24
365
 1  .1583  15.83 percent
EFF
15.83
365
C/Y
b
   .07  3512  
1  1 / 1 


12 
  
 
$155,000 C  

.
07


12




$155,000  C  156.5297092
C  $990.23
Enter
Solve for
3512
N
7/12
I/Y
155,000
PV
PMT
-990.23
FV
6-9

Chapter 6 Discounted Cash Flow Valuation
Interest 1  $155,000 
.07
 $904.17
12
First month’s principle = $990.23 – $904.17 = $86.06
10.
a
2512
  

r 
1  1 / 1  

   12 
  ; This cannot be solved directly, so it’s easiest to just use the
$80,000  $1,200  

r


12




calculator method to get an answer. You can then use the calculator answer taken to several decimal places as the
rate in the formula just to verify that your answer is correct.
Enter
2512
N
/12 -80,000
1,200
I/Y
PV
PMT
FV
Solve for
17.78
With more decimals, the answer is 17.7818277 percent.
6-10
Chapter 6 Discounted Cash Flow Valuation
Chapter 06 Quiz C Student Name _________________________
Student ID ____________
________ 1.
You want to retire on the day you have $900,000 in your savings account. You expect to earn 6 percent,
compounded monthly, on your money during your retirement. Your plan is to withdraw $5,750 a month as
retirement income from this account. How many years can you be retired until you run out of money?
a. 24.75
b. 24.91
c. 25.20
d. 25.50
________ 2.
Today you are opening a savings account and depositing an initial $5,000 into it. You plan to deposit $6,500
into the account two years from today and deposit another $8,000 four years from today. How much will you
have in your account five years from today if you earn an 11 percent rate of return?
a. $25,314.60
b. $26,194.89
c. $32,858.63
d. $29,602.37
________ 3.
You want to pay mortgage payments of $700 a month for thirty-five years. The interest rate is 3.8 percent,
compounded monthly. What price house can you afford to buy if you have $10,000 cash available as a down
payment?
a. $172,466.25
b. $182,980.73 c. $186,466.25 d. $186,980.73
________ 4.
A preferred stock pays annual dividends of $1.20. How much are you willing to pay today to buy one share
of this stock if you want to earn a 12 percent rate of return?
a. $10.00
b. $20.00
c. $40.00
d. $120.00
________ 5.
A project will produce cash flows of $1,000, $1,500, $3,000, and $5,000 a year for the next four years,
respectively. What is the value of these cash flows today at a discount rate of 9.5 percent?
a. $7,927.09
b. $8,013.85
c. $12,013.85
d. $15,095.44
________ 6.
You are going to receive $9,000 at the end of each quarter for the next six years. What is the net
present value of these payments at a discount rate of 11 percent, compounded quarterly?
a. $49,161.30
b. $98,776.25
c. $156,607.17 d. $160,913.87
________ 7.
What is the effective annual rate of 10.20 percent compounded weekly?
a. 10.20 percent
b. 10.60 percent c. 10.69 percent d. 10.73 percent
________ 8.
What is the effective annual rate of 15.25 percent compounded continuously?
a. 16.36 percent
b. 16.45 percent c. 16.47 percent d. 16.50 percent
________ 9.
You borrow $300,000 for forty years at 8 percent. This is an amortized loan. How much of the first payment
goes to the principle balance of the loan? Assume that one month is equal to 1/12th of a year.
a. $72.12
b. $85.94
c. $2,072.12
d. $2,085.94
________ 10. You just purchased a 20-year annuity at a cost of $75,000. The annuity will pay you $1,100 at the end of each
month, starting with this month. What rate of return are you earning on this investment?
a. 14.67 percent
b. 17.00 percent c. 17.28 percent d. 17.60 percent
6-11
Chapter 6 Discounted Cash Flow Valuation
Chapter 06 Quiz C
1.
Answers
d
   .06  t  
1  1 / 1 
 
   12   
$900,000  $5,750  

.06


12




   .06  t  
1  1 / 1 
 
   12   
156.5217391  

.06


12




  .06  t 
.782608696  1  1 / 1 

  12  
 .06 
.217391305  1 / 1 

 12 
4.599999997  1.005 t
t
ln 4.599999997  t ln1.005
1.526056303  .004987542t
t  305.97
Enter
Solve for
N
305.97
6/12
I/Y
-900,000 5,750
PV
PMT
FV
Number of years = 25.50
2.
b

 
 
FV  $5,000  (1  .11) 5  $6,500  (1  .11) 3  $8,000  (1  .11)1
 $8,425.29  $8,889.60  $8,880.00
 $26,194.89
Enter
5
N
11
I/Y
-5,000
PV
PMT
FV
8,425.29
3
N
11
I/Y
-6,500
PV
PMT
FV
8,889.60
1
N
11
I/Y
-8,000
PV
PMT
FV
8,880.00
Solve for
Enter
Solve for
Enter
Solve for
FV = $8,425.29 + $8,889.60 + $8,880.00 = $26,194.89
6-12

Chapter 6 Discounted Cash Flow Valuation
3.
a
   .038  3512  
1  1 / 1 


12 
  
 
APV $700  

.038


12




 $700  232.0946471
 $162,466.25
Enter
3512
N
Solve for
3.8/12
-700
I/Y
PV
PMT
162,466.25
FV
Home price = $162,466.25 + $10,000 = $172,466.25
4.
a
5.
a
PV 
$1.20
 $10.00
.12

 

 
 
1
1
1
1
NPV  $1,000 
 $1,500 
 $3,000 
 $5,000 
1
4
2
3
(1  .095)  
(1  .095)  
1  .095  
1  .095 

 $913.24  $1,251.02  $2,284.96  $3,477.87
 $7,927.09
Enter
1
N
9.5
I/Y
2
N
9.5
I/Y
3
N
9.5
I/Y
4
N
9.5
I/Y
Solve for
Enter
Solve for
Enter
Solve for
Enter
Solve for
PV
-913.24
PMT
1,000
FV
PV
-1,251.02
PMT
1,500
FV
PV
-2,284.96
PMT
3,000
FV
PV
-3,477.87
PMT
5,000
FV
NPV = $913.24 + $1,251.02 + $2,284.96 + $3,477.87 = $7,927.09
6.
c
   .11  64  
1  1 / 1 
 
4   
  
APV  $9,000  

.11


4




 $9,000  17.4007967
 $156,607.17
6-13
Chapter 6 Discounted Cash Flow Valuation
Enter
64
N
11/4
I/Y
Solve for
9,000
PV
PMT
-156,607.17
FV
52
7.
d
  .102 
EAR  1  
  1 ; EAR = 10.73 percent
  52 
Enter
10.20
NOM
Solve for
8.
c
EFF
10.73
52
C/Y
EAR = e.1525 − 1 = 2.71828.1525 − 1 =.16474 = 16.47 percent
Input for Texas Instruments BA II plus
.1525, 2nd, ex, −1 = 16.47 percent
9.
b
   .08  4012  
1  1 / 1 


   12 
 
$300,000 C  

.08


12




$300,000  C  143.8203923
C  $2,085.94
Enter
4012
N
8/12
I/Y
300,000
PV
Solve for
Interest 1  $300,000 
PMT
FV
-2,085.94
.08
 $2,000
12
First month’s principle = $2,085.94 – $2,000.00 = $85.94
10.
b
2012
  

r 
1  1 / 1  

   12 
  ; This cannot be solved directly, so it’s easiest to just use the
$75,000  $1,100  

r


12




calculator method to get an answer. You can then use the calculator answer taken to several decimal places as the
rate in the formula just to verify that your answer is correct.
Enter
2012
N
/12 -75,000
1,100
I/Y
PV
PMT
FV
Solve for
17.00
With more decimals, the answer is 16.99823943 percent.
6-14