Tutorial Five
Problems
1. Periodic Interest Rates. In the following table, fill in the periodic rates and the effective annual
rates.
Semiannual
10%
2
Quarterly
12%
4
Monthly
9%
12
Daily
5.25%
365
2. Periodic Interest Rates. You have a savings account in which you leave the funds for one year
without adding or withdrawing from the account. What would you rather have: a daily compounded
rate of 0.045%, a weekly compounded rate of 0.305%, a monthly compounded rate of 1.5%, a
quarterly compounded rate of 4.5%, a semiannually compounded rate of 9.75%, or an annually
compounded rate of 19%?
3. EAR. What is the effective annual rate of a mortgage rate that is advertised at 7.25% (APR) over
the next twenty years and paid with quarterly payments?
4. EAR. What is the effective rate of a monthly car loan that is advertised at 10% (APR)?
5.
Present value with periodic rates. Let’s follow up with Sam Hinds, the dentist, from Chapter
4 and his remodeling project (Problem 12). The cost of the equipment for the project is $18,000, and
the purchase will be financed with a 7.5% loan over six years. Originally, the loan called for annual
payments. Redo the payments based on quarterly payments (four per year) and monthly payments
(twelve per year). Compare the annual cash outflow of the two payments. Why does the monthly
payment plan have less total cash outflow each year?
6.
Present value with periodic rates. Cooley Landscaping needs to borrow $30,000 for a new
front-end dirt loader. The bank is willing to loan the money at 8.5% interest for the next ten years
with annual, semiannual, quarterly, or monthly payments. What are the different payments that
Cooley Landscaping could choose for these different payment plans?
7. Future Value with Periodic Rates. Matt Johnson delivers newspapers and is putting away $20.00
every month from his paper route collections. Matt is thirteen years old and will use the money
when he goes to college in five years. What will be the value of Matt’s account in five years with his
monthly payments if he is earning 6% (APR), 8% (APR), or 12% (APR)?
8.
Future value with periodic rates. We return to Denise, our hopeful millionaire from Chapter
4 (Example 4.3) and this chapter (Example 5.2). In Chapter 4, Denise was putting away $5,000 per
year at the end of each year at 6% interest, with the expectation that in forty-four years she would
be a millionaire. If Denise switches to a monthly savings plan and puts one-twelfth of the $5,000
away each month ($416.66), how much will she have in forty-four years at the 6% APR? Why is it
more than the $1,000,000 goal? In this chapter, Denise was putting away $546.23 for thirty years at
9% to become a millionaire. Why does it take more per month when she is putting money away at
9% than when she was earning a lower rate of 6% over the forty-four years? Hint: what interest rate
would she need for the 30 years putting away $416.66 to match the future value when she started
fourteen years earlier at 6%?
So Denise would have to find an investment rate of 10.62% for the next 30 years if she wanted to
match the same future value. If she can only get 9%, she will need to increase her monthly
contributions to reach the same $1,076,759.95 future value.
9.
Payments with periodic rates. What payment does Denise (from problem 8) need to make
at the end of each month over the coming forty-four years at 6% to reach her retirement goal of
$1,000,000?
10. Savings with Periodic Rates. What investment per month does Patrick need to make at the end
of each month into his savings account over the coming eighteen months to reach his vacation goal
of $8,000 if he is getting 5% APR on his account?
Tutorial Six
Problems
Bond Prices: Use the following table for problems 1 through 4.
Par Value
Coupon Rate
Years to
Maturity
Yield to
Maturity
Price
$1,000.00
8%
10
6%
?
$1,000.00
6%
10
8%
?
$5,000.00
9%
20
7%
?
$5,000.00
12%
30
5%
?
1.
Price the bonds from the above table with annual coupon payments.
2.
Price the bonds from the above table with semiannual coupon payments.
ANSWER
Price = $1,000.00 × 1/(1.03)20 + $40.00 (1 – 1/(1.03)20)/ 0.03
Price = $1,000.00 × 0.5537 + $40.00 × 14.8775
Price = $553.67 + $595.10 = $1,148.77
Price = $1,000.00 × 1/(1.04)20 + $30.00 (1 – 1/(1.04)20)/ 0.04
Price = $1,000.00 × 0.4564 + $30.00 × 13.5903
Price = $456.39 + $407.71 = $864.10
Price = $5,000.00 × 1/(1.035)40 + $225.00 (1 – 1/(1.035)40)/ 0.035
Price = $5,000.00 × 0.2526 + $225.00 × 21.3551
Price = $1,262.86 + $4,804.90 = $6,067.75
Price = $5,000.00 × 1/(1.025)60 + $300.00 (1 – 1/(1.025)60)/ 0.025
Price = $5,000.00 × 0.2273 + $300.00 × 30.9087
Price = $1,136.41 + $9,272.60 = $10,409.01
3.
Price the bonds from the above table with quarterly coupon payments.
ANSWER
Price = $1,000.00 × 1/(1.015)40 + $20.00 (1 – 1/(1.015)40)/ 0.015
Price = $1,000.00 × 0.5584 + $20.00 × 7.3601
Price = $558.39 + $588.81 = $1,085.84
Price = $1,000.00 × 1/(1.02)40 + $15.00 (1 – 1/(1.02)40)/ 0.02
Price = $1,000.00 × 0.4632 + $15.00 × 6.7101
Price = $463.19 + $402.60 = $863.22
Price = $5,000.00 × 1/(1.0175)80 + $75.00 (1 – 1/(1.0175)80)/ 0.0175
Price = $5,000.00 × 0.2584 + $75.00 × 10.5940
Price = $1,292.10 + $3,178.20 = $4,464
Price = $5,000.00 × 1/(1.0125)120 + $150.00 (1 – 1/(1.0125)120)/ 0.0125
Price = $5,000.00 × 0.2314 + $150.00 × 15.3725
Price = $1,156.89 + $9,223.47 = $10,423.50
4.
Price the bonds from the above table with monthly coupon payments.
ANSWER
Price = $1,000.00 × 1/(1.005)120 + $6.67 (1 – 1/(1.005)120)/ 0.005
Price = $1,000.00 × 0.5584 + $6.67 × 7.3601
Price = $558.39 + $588.81 = $1,150.42
Price = $1,000.00 × 1/(1.0067)120 + $5.00 (1 – 1/(1.0067)120)/ 0.0067
Price = $1,000.00 × 0.4632 + $5.00 × 6.7101
Price = $463.19 + $402.60 = $860.13
Price = $5,000.00 × 1/(1.0058)240 + $37.50 (1 – 1/(1.0058)240)/ 0.0058
Price = $5,000.00 × 0.2476 + $37.50 × 128.98
Price = $1,238.01 + $4,836.84 = $6,074.85
Price = $5,000.00 × 1/(1.0042)360 + $50.00 (1 – 1/(1.0042)360)/ 0.0042
Price = $5,000.00 × 0.2314 + $50.00 × 15.3725
Price = $1,156.89 + $9,223.47 = 10,377.65
Yield-to-Maturity: Use the following table for problems 5 through 8.
Par Value
Coupon Rate
Years to Maturity
Yield to Maturity
Price
$1,000.00
8%
10
?
$1000.00
$1,000.00
6%
10
?
$850.00
$5,000.00
9%
20
?
$5,400.00
$5,000.00
12%
30
?
$4,300.00
5.
What is the yield of the above bonds if interest (coupon) is paid annually?
ANSWER
(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1
INPUT 10
?
-1000.00
80.00 1000.00
KEYS
I/Y
PV
FV
N
CPT
PMT
8.0
(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1
INPUT 10
?
-850.00 60.00 1000.00
KEYS
I/Y
PV
N
CPT
PMT
FV
8.2619
(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1
INPUT 20
?
-5400.00
450.00 5000.00
KEYS
I/Y
PV
FV
N
CPT
PMT
8.1746
(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1
INPUT 30
?
-4300.00
600.00 5000.00
KEYS
I/Y
PV
FV
N
CPT
6.
PMT
13.9991
What is the yield of the above bonds if interest (coupon) is paid semiannually?
ANSWER
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT 20
?
-1000.00
40.00 1000.00
KEYS
I/Y
PV
FV
CPT
N
PMT
8.0
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT 20
?
-850.00 30.00 1000.00
KEYS
I/Y
PV
N
CPT
PMT
FV
8.2300
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT 40
?
-5400.00
225.00 5000.00
KEYS
I/Y
PV
FV
N
CPT
PMT
8.1807
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT 60
?
-4300.00
300.00 5000.00
KEYS
I/Y
PV
FV
N
CPT
7.
PMT
13.9936
What is the yield of the above bonds if interest (coupon) is paid quarterly?
ANSWER
(TVM Keys) Set Calculator to P/Y = 4 and C/Y = 4
INPUT 40
?
-1000.00
20.00 1000.00
KEYS
N
I/Y
PV
FV
CPT
8.0
PMT
(TVM Keys) Set Calculator to P/Y = 4 and C/Y = 4
INPUT 40
?
-850.00 15.00 1000.00
KEYS
N
I/Y
PV
CPT
8.2140
PMT
FV
(TVM Keys) Set Calculator to P/Y = 4 and C/Y = 4
INPUT 80
?
-5400.00
112.50 5000.00
KEYS
N
I/Y
PV
FV
CPT
8.1838
PMT
(TVM Keys) Set Calculator to P/Y = 4 and C/Y = 4
INPUT 120
?
-4300.00
150.00 5000.00
KEYS
N
I/Y
PV
FV
CPT
13.9909
8.
What is the yield of the above bonds if interest (coupon) is paid monthly?
PMT
ANSWER
(TVM Keys) Set Calculator to P/Y = 12 and C/Y = 12
INPUT 120
?
-1000.00
6.67
KEYS
I/Y
PV
FV
N
CPT
PMT
1000.00
8.0
(TVM Keys) Set Calculator to P/Y = 12 and C/Y = 12
INPUT 120
?
-850.00 30.00 1000.00
KEYS
I/Y
PV
N
CPT
PMT
FV
8.2033
(TVM Keys) Set Calculator to P/Y = 12 and C/Y = 12
INPUT 240
?
-5400.00
37.50 5000.00
KEYS
I/Y
PV
FV
N
CPT
PMT
8.1859
(TVM Keys) Set Calculator to P/Y = 12 and C/Y = 12
INPUT 360
?
-4300.00
50.00 5000.00
KEYS
I/Y
PV
FV
N
CPT
PMT
13.9891
Tutorial Seven
1.
Anderson Motors Inc. has just set the company dividend policy at $0.80 per year. The
company plans to be in business forever. What is the price of this stock if
a. An investor wants a 5% return?
b. An investor wants an 8% return?
c. An investor wants a 10% return?
d. An investor wants a 12.5% return?
e. An investor wants a 20% return?
ANSWER
Use the constant dividend infinite dividend stream model:
r
a.
b.
c.
0
d.
e.
2.
Diettreich Electronics wants its shareholders to earn a 16% return on their investment in the
company. At what price would the stock need to be priced today if Diettreich had a
a. $0.40 constant annual dividend forever?
b. $1.00 constant annual dividend forever?
c. $1.80 constant annual dividend forever?
d. $2.40 constant annual dividend forever?
ANSWER
Use the constant dividend with infinite horizon model:
r
a.
b.
c.
d.
3.
Singing Fish Fine Foods has a current annual cash dividend policy of $2.25. The price of the
stock is set to yield a 12% return. What is the price of this stock if the dividend will be paid
a.
for 10 years?
b.
for 15 years?
c.
for 40 years?
d.
for 60 years?
e.
for 100 years?
f.
forever?
ANSWER
Use the finite constant dividend model except with f (use infinite constant dividend model)
Price = Dividend × (1 – 1/(1+r)n) / r
a.
Price = $2.25 × (1 – 1/(1.12)10 / 0.12 = $2.25 × 5.6502 = $12.71
b.
Price = $2.25 × (1 – 1/(1.12)15 / 0.12 = $2.25 × 6.8109 = $15.32
c.
Price = $2.25 × (1 – 1/(1.12)40 / 0.12 = $2.25 × 8.2438 = $18.54
d.
Price = $2.25 × (1 – 1/(1.12)60 / 0.12 = $2.25 × 8.3240 = $18.73
e.
Price = $2.25 × (1 – 1/(1.12)100 / 0.12 = $2.25 × 8.3332 = $18.75
f.
Price = $2.25 / 0.12 = $18.75
4.
Pfender Guitars has a current annual cash dividend policy of $4.00. The price of the stock is
set to yield an 8% return. What is the price of this stock if the dividend will be paid
a.
for 10 years and then a liquidating or final dividend of $25.00?
b.
for 15 years and then a liquidating or final dividend of $25.00?
c.
for 40 years and then a liquidating or final dividend of $25.00?
d.
for 60 years and then a liquidating or final dividend of $25.00?
e.
for 100 years and then a liquidating or final dividend of $25.00?
f.
forever with no liquidating dividend?
ANSWER
Use the finite constant dividend model liquidating dividend except with f (use infinite constant
dividend model)
Price = Dividend × (1 – 1/(1 + r)n) / r + Liquidating Dividend × (1/(1 + r)n)
a.
Price = $4.00 × (1 – 1/(1.08)10 / 0.08 + $25.00 × 1/1.0810
= $4.00 × 6.7101 + $25 × 0.4632 = $26.84 + $11.58 = $38.42
b.
Price = $4.00 × (1 – 1/(1.08)15 / 0.08 + $25.00 × 1/1.0815
= $4.00 × 8.5595 + $25 × 0.3152 = $34.24 + $7.88 = $42.12
c.
Price = $4.00 × (1 – 1/(1.08)40 / 0.08 + $25.00 × 1/1.0840
= $4.00 × 11.9246 + $25 × 0.0460 = $47.70 + $1.15 = $48.85
d.
Price = $4.00 × (1 – 1/(1.08)60 / 0.08 + $25.00 × 1/1.0860
= $4.00 × 12.3766 + $25 × 0.0099 = $49.51 + $0.24 = $49.75
e.
Price = $4.00 × (1 – 1/(1.08)100 / 0.08 + $25.00 × 1/1.08100
= $4.00 × 12.4943 + $25 × 0.0005 = $49.98 + $0.01 = $49.99
f.
Price = $4.00 / 0.08 = $50.00
5.
King Waterbeds has an annual cash dividend policy that raises the dividend each year by 4%.
Last year’s dividend was $0.50 per share. What is the price of this stock if
a. an investor wants a 6% return?
b. an investor wants an 9% return?
c. an investor wants a 10% return?
d. an investor wants a 14% return?
e. an investor wants a 20% return?
ANSWER
Use the constant growth dividend model with infinite horizon:
g)/(r
a.
b.
c.
g)
d.
e.
6.
Seitz Glassware is trying to determine its growth rate for an annual cash dividend. Last year’s
dividend was $0.35 per share. The target return rate for the stock is 12%. What is the price of
this stock if
a. the annual growth rate is 2%?
b. the annual growth rate is 4%?
c. the annual growth rate is 5%?
d. the annual growth rate is 8%?
e. the annual growth rate is 10%?
ANSWER
Use the constant growth dividend model with infinite horizon:
g)/(r
g)
a.
b.
c.
d.
e.
7.
Miles Hardware has an annual cash dividend policy that raises the dividend each year by 3%.
Last year’s dividend was $1.00 per share. Investors want a 15% return on this stock. What is the
stock’s price if
a.
the company will be in business for 5 years and not have a liquidating dividend?
b.
the company will be in business for 15 years and not have a liquidating dividend?
c.
the company will be in business for 25 years and not have a liquidating dividend?
d.
the company will be in business for 35 years and not have a liquidating dividend?
e.
the company will be in business for 75 years and not have a liquidating dividend?
f.
forever?
ANSWER
Use the constant growth dividend model with a finite dividend stream:
Price = Last Dividend × (1 + g) / (r – g) × [1 – ((1+g) / (1+r))n]
a.
Price = $1.00 × (1.03) / (0.15 – 0.03) × [1 – ((1.03) / (1.15))5]
= $1.03 / 0.12 × [1 - 0.5764] = $8.58 × [0.4236] = $3.64
b.
Price = $1.00 × (1.03) / (0.15 – 0.03) × [1 – ((1.03) / (1.15))15]
= $1.03 / 0.12 × [1 - 0.1915] = $8.58 × [0.8085] = $6.94
c.
Price = $1.00 × (1.03) / (0.15 – 0.03) × [1 – ((1.03) / (1.15))25]
= $1.03 / 0.12 × [1 - 0.0636] = $8.58 × [0.9364] = $8.03
d.
Price = $1.00 × (1.03) / (0.15 – 0.03) × [1 – ((1.03) / (1.15))35]
= $1.03 / 0.12 × [1 - 0.0211] = $8.58 × [0.9789] = $8.40
e.
Price = $1.00 × (1.03) / (0.15 – 0.03) × [1 – ((1.03) / (1.15))75]
= $1.03 / 0.12 × [1 - 0.0003] = $8.58 × [0.9997] = $8.58
f.
Price = $1.00 × (1.03) / (0.15 – 0.03) = $1.03 / 0.12 = $8.58
8.
Sia Dance Studios has an annual cash dividend policy that raises the dividend each year by
2%. Last year’s dividend was $3.00 per share. The company will be in business for forty years with no
liquidating dividend. What is the price of this stock if
a.
an investor wants a 9% return?
b.
an investor wants an 11% return?
c.
an investor wants a 13% return?
d.
an investor wants a 15% return?
e.
an investor wants a 17% return?
ANSWER
Use the constant growth dividend model with a finite dividend stream:
Price = Last Dividend × (1 + g) / (r – g) × [1 – ((1+g) / (1+r))n]
a.
Price = $3.00 × (1.02) / (0.09 – 0.02) × [1 – ((1.02) / (1.09))40]
= $3.06 / 0.07 × [1 - 0.0703] = $43.71 × [0.9297] = $40.64
b.
Price = $3.00 × (1.02) / (0.11 – 0.02) × [1 – ((1.02) / (1.11))40]
= $3.06 / 0.09 × [1 - 0.0340] = $34.00 × [0.9660] = $32.85
c.
Price = $3.00 × (1.02) / (0.13 – 0.02) × [1 – ((1.02) / (1.13))40]
= $3.06 / 0.11 × [1 - 0.0166] = $27.82 × [0.9834] = $27.35
d.
Price = $3.00 × (1.02) / (0.15 – 0.02) × [1 – ((1.02) / (1.15))40]
= $3.06 / 0.13 × [1 - 0.0082] = $23.54 × [0.9918] = $23.35
e.
Price = $3.00 × (1.02) / (0.17 – 0.02) × [1 – ((1.02) / (1.17))40]
= $3.06 / 0.15 × [1 - 0.0041] = $20.40 × [0.9959] = $20.32
9.
Fey Fashions expects the following dividend pattern over the next seven years:
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
$1.00
$1.10
$1.21
$1.33
$1.46
$1.61
$1.77
Then the company will have a constant dividend of $2.00 forever. What is the price of this stock
today if an investor wants to earn
a.
15%?
b.
20%?
ANSWER
There are two dividend patterns here; the first is a constant growth pattern for the next seven years
and then a constant dividend forever. Solve each part separately and then add the two parts.
Part one: Constant growth for seven years, first find growth rate and note that there are six changes
in the dividend stream over the seven years.
g = ($1.77 / $1.00)1/6 – 1 = 1.771/6 – 1 = 10%
Next, use the finite dividend growth model
Price = Dividend × (1 + g) / (r – g) × [1 – ((1+g) / (1+r))n]
Part two: Use the constant dividend (infinite period) model and then discount the price at period 7
back to the present
Price7 = Dividend8 / r
Price0 = Price7 / (1 + r)7
a.
Part One Price = $1.00 (1.10) / (0.15 – 0.10) × [ 1 – (1.10/1.15)7]
Part One Price = $22.00 × 0.2674 = $5.88
Part Two Price = ($2.00 / 0.15) / (1.15)7 = $13.33 / 2.66 = $5.01
Price = $5.88 + $5.01 = $10.89
b.
Part One Price = $1.00 (1.10) / (0.20 – 0.10) × [ 1 – (1.10/1.20)7]
Part One Price = $11.00 × 0.4561 = $5.02
Part Two Price = ($2.00 / 0.20) / (1.20)7 = $10.00 / 3.5832 = $2.79
Price = $5.02 + $2.79 = $7.81
10.
Staton-Smith Software is a new up-start company and will not pay dividends for the first five
years of operation. It will then institute an annual cash dividend policy of $2.50 with a constant
growth rate of 5% with the first dividend at the end of year six. The company will be in business for
25 years total. What is the price of this stock if an investor wants
a.
a 10% return?
b.
a 15% return?
c.
a 20% return?
d.
a 40% return?
ANSWER
Calculate the price at the beginning of the sixth year (end of the fifth year) with the finite constant
growth dividend model and then discount the price by five years to the present value.
a.
Price5 = $2.50 / (0.10 – 0.05) × [1 – (1.05/1.10)20]
Price5 = $50.00 × 0.6056 = $30.28
Price0 = $30.28 / 1.105 = $30.28 / 1.6105 = $18.80
b.
Price5 = $2.50 / (0.15 – 0.05) × [1 – (1.05/1.15)20]
Price5 = $25.00 × 0.8379 = $20.95
Price0 = $20.95 / 1.155 = $20.95 / 2.0114 = $10.41
c.
Price5 = $2.50 / (0.20 – 0.05) × [1 – (1.05/1.20)20]
Price5 = $16.67 × 0.9308 = $15.51
Price0 = $15.51 / 1.205 = $15.51 / 2.4883 = $6.23
d.
Price5 = $2.50 / (0.40 – 0.05) × [1 – (1.05/1.40)20]
Price5 = $7.14 × 0.9968 = $7.12
Price0 = $7.12 / 1.405 = $7.12 / 5.3782 = $1.32
Tutorial Eight
1.
Profits. What are the profits on the following investments?
Investment
Original Cost
or Invested $
Selling Price
of Investment
Distributions
Received $
CD
$500.00
$540.00
$0.00
Stock
$23.00
$34.00
$2.00
Bond
$1,040.00
$980.00
$80.00
Bike
$400.00
$220.00
$0.00
Dollar Profit
ANSWER
Investment
Original Cost
or Invested $
Selling Price of Distributions
Investment
Received $
Dollar Profit
CD
$500.00
$540.00
$0.00
$40
Stock
$23.00
$34.00
$2.00
$13
Bond
$1,040.00
$980.00
$80.00
$20
Bike
$400.00
$220.00
$0.00
-$180
CD Dollar Return = $540 + $0 – $500 = $40
Stock Dollar Return = $34 + $2 – $23 = $13
Bond Dollar Return = $980 + $80 – $1,040 = $20
Bike Dollar Return = $220 + $0 – $400 = -$180
2.
Profits. What are the profits on the following investments?
Investment
Original Cost or
Invested $
Selling Price of
Investment
Distributions
Received $
CD
$500.00
$525.00
$0.00
Stock
$34.00
$26.00
$2.00
Dollar Profits
Bond
$955.00
$1000.00
$240.00
Car
$42,000.00
$3,220.00
$0.00
Investment
Original Cost or
Invested $
Selling Price of
Investment
Distributions
Received $
Dollar Profits
CD
$500.00
$525.00
$0.00
$25
Stock
$34.00
$26.00
$2.00
-$6
Bond
$955.00
$1000.00
$240.00
$285
Car
$42,000.00
$3,220.00
$0.00
-$38,780
ANSWER
CD Dollar Return = $525 + $0 – $500 = $25
Stock Dollar Return = $26 + $2 – $34 = -$6
Bond Dollar Return = $1,000 + $240 – $955 = $285
Car Dollar Return = $3,220 + $0 – $42,000 = -$38,780
3.
Returns. What are the returns on the following investments?
Investment
Original Cost or
Invested $
Selling Price of
Investment
Distributions
Received $
CD
$500.00
$540.00
$0.00
Stock
$23.00
$34.00
$2.00
Bond
$1,040.00
$980.00
$80.00
Bike
$400.00
$220.00
$0.00
Investment
Original Cost or
Invested $
Selling Price of
Investment
Distributions
Received $
Percent Return
CD
$500.00
$540.00
$0.00
8.00%
Stock
$23.00
$34.00
$2.00
56.52%
Bond
$1,040.00
$980.00
$80.00
1.92%
Bike
$400.00
$220.00
$0.00
-45.00%
Percent Return
ANSWER
CD Percent Return = ($540 + $0 – $500) / $500 = 0.0500 or 8.00%
Stock Percent Return = ($34 + $2 – $23) / $23 = 0.565217 or 56.52%
Bond Percent Return = ($980 + $80 – $1040) / $1040 = 0.01923 or 1.92%
Bike Percent Return = ($220 + $0 – $400) / $400 = -0.45 or -45%
4.
Returns. What are the returns on the following investments?
Investment
Original Cost or
Invested $
Selling Price of
Investment
Distributions
Received $
CD
$500.00
$525.00
$0.00
Stock
$34.00
$2600
$2.00
Bond
$955.00
$1000.00
$240.00
Car
$42,000.00
$3,220.00
$0.00
Investment
Original Cost or
Invested $
Selling Price of
Investment
Distributions
Received $
Percent Return
CD
$500.00
$525.00
$0.00
5.00%
Stock
$34.00
$2600
$2.00
-17.65%
Bond
$955.00
$1000.00
$240.00
29.84%
Car
$42,000.00
$3,220.00
$0.00
-92.33%
Percent Return
ANSWER
CD Percent Return = ($525 + $0 – $500) / $500 = 0.0500 or 5.00%
Stock Percent Return = ($26 + $2 – $34) / $34 = -0.1765 or -17.65%
Bond Percent Return = ($1,000 + $240 – $955) / $955 = 0.2984 or 29.84%
Car Percent Return = ($3,220 + $0 – $42,000) / $42,000 = -0.9233 or -92.33%
5.Holding Period and Annual (Investment) Returns. Baker Baseball Cards Incorporated originally
purchased the rookie card of Hammerin’ Hank Aaron for $40.00. After holding the card for five
years, Baker Baseball Cards auctioned off the card for $200.00. What are the holding period return
and the annual return on this investment?
ANSWER
Annual Percentage retu
n
1/5
6.
Holding Period and Annual (Investment) Returns. Bohenick Classic Automobiles restores
and rebuilds old classic cars. The company purchased and restored a classic 1957 Thunderbird
convertible six years ago for $8,500. Today at auction, the car sold for $50,000. What are the holding
period return and the annual return on this investment?
ANSWER
Holding Period Return = ($50,000 – $8,500) / $8,500 = 4.8824 or 488.24%
APR = HPR/n = 488.24%/6 = 81.37%
EAR = (1 + 4.8824)1/6 – 1 = 1.3436 – 1 = 0.3436 or 34.36%
7.
Comparison of returns. Looking back at Problems 5 and 6, which investment had the higher
holding period return? Which had the higher annual return?
ANSWER
Holding Period Return for Trading Card = ($180 – $35) / $35 = 4.1429 or 414.29%
Holding Period Return for Classic Car = ($50,000 – $8,500) / $8,500 = 4.8824 or 488.24%
Trading Card HPR
< Classic Car HPR
Trading Card APR
= HPR/n = 414.29%/5 = 82.86%
Classic Car APR = HPR/n = 488.24%/6 = 81.37%
Trading Card APR
> Classic Car APR82.86%>81.37%
Trading Card EAR
= (1 + 4.1429)1/5 – 1 = 1.3875 – 1 = 0.3875 or 38.75%
Classic Car Annual Return
Trading Card EAR
= (1 + 4.8824)1/6 – 1 = 1.3436 – 1 = 0.3436 or 34.36%
> Classic Car EAR.
8.
Comparison of returns. WG Investors are looking at three different investment
opportunities. Investment One is a five-year investment with a cost of $125 and a promised payout
of $250 at maturity. Investment Two is a seven-year investment with a cost of $125 and a promised
payout of $350. Investment Three is a ten-year investment with a cost of $125 and a promised
payout of $550. WG Investors can only take on one of the three investments. Assuming all three
investment opportunities have the same level of risk, calculate the annual return for each
investment and select the best investment choice.
ANSWER
Holding Period Return for Investment One = ($250 – $125) / $125 = 1.00 or 100.00%
EAR-- Investment One = (1 + 1.00)1/5 – 1 = 1.1487 – 1 = 0.1487 or 14.87%
Holding Period Return for Investment Two = ($350 – $125) / $125 = 1.80 or 180.00%
EAR-- Investment Two = (1 + 1.80)1/7 – 1 = 1.1585 – 1 = 0.1585 or 15.85%
Holding Period Return for Investment Three= ($550 – $125) / $125 = 3.40 or 340.00%
EAR-- Investment Three = (1 + 3.40)1/10 – 1 = 1.15969 – 1 = 0.15967 or 15.97%
Investment Three has the highest annual return rate of the three choices. If all choices have the
same level of risk, choose Investment Three.
9.
Historical returns. Calculate the average return of the U.S. Treasury bills, long-term
government bonds, and large company stocks for 1990–1998 from Table 8.1. Which had the highest
and which had the lowest return?
ANSWER
Average Return U.S. Treasury Bill for 90s: 5.02%
Average Return U.S. Long-Term Government Bonds for 90s: 9.23%
Average Return U.S. Large Company Stocks for 90s: 18.99%
Highest was Large Company Stocks, Lowest was 3 Month T-Bills
10.
Historical returns. Calculate the average return of the U.S. Treasury bills, long-term
government bonds, and large company stocks for the 1950 to 1959, 1960 to 1969, 1970 to 1979, and
1980 to 1989 from Table 8.1. Which had the highest return? Which had the lowest return?
ANSWER
Answer from data is:
Average Return U.S. Treasury Bill for 50s: 1.87%
Average Return U.S. Long-Term Government Bonds for 50s: 0.35%
Average Return U.S. Large Company Stocks for 50s: 20.94%
Answer from data is:
Average Return U.S. Treasury Bill for 60s: 3.90%
Average Return U.S. Long-Term Government Bonds for 60s: 1.31%
Average Return U.S. Large Company Stocks for 60s: 8.74%
Answer from data is:
Average Return U.S. Treasury Bill for 70s: 6.31%
Average Return U.S. Long-Term Government Bonds for 70s: 6.80%
Average Return U.S. Large Company Stocks for 70s: 7.55%
Answer from data is:
Average Return U.S. Treasury Bill for 80s: 9.04%
Average Return U.S. Long-Term Government Bonds for 80s: 11.99%
Average Return U.S. Large Company Stocks for 80s: 18.24%
Highest Return was 20.94% in the 50s for Large Company Stocks and the lowest return was 0.35%
for Long-Term Government Bonds in the 50s.