**Unformatted text preview: **How long will it take $ 100 to grow to $225.22 at 7 NPER PV
FV
i
12.0000552 -100
225.22
0.07 2. Suppose that the NASDAQ Composite index h
In February of 1992 it was at a level of 4,696. What was th
period?
PV
FV
n
I = FV/PV ^1/nIntRate -4696
2052
8
#NUM! -9.83%
Rate formula In February of 2000 the NASDAQ Composite index peaked at a level of 4,680 (j 2,004. The NASDAQ index has historically grown at an average annual rate of
many years will it take for the index to grow from its F NPER PV
-4680
FV
2004
I
0.08
-11.020549 11 years 4.What interest rate makes $100 gr
pv
FV
n
Rate -100
161.05
5
10.00% 5. Suppose you'll inherit 8,500 in 21 years but need some money now. On the timeline, show how much you can
of 4.2% per annum (compounded annually) on its loan. The timeline starts at Period 0 and ends at Period 21. T
PV0=? i=4.2
FV
i
n PV 6.You want to withdraw 8,000 from your bank account in 2 years and 3,000 the following year. How
FV1
FV2
i
add PVs
PV1
PV2
sum 7.You want to have a balance in your bank account of 100 in 8 years. Your bank offers an interest rate of 8% (per ann
FV
i
n
PV 100
0.04
16
($53.39) 8. Maria expects to receive a payment of
what is the present
FV
n
i
PV 34000
8
0.15
($11,114.66) 9. You have $460 in an account which pays 4.5% compounded annually. How man account PV
i1
n
Difference FVFV1
FV2
Difference 460
0.045
8
($654.17)
($761.30)
($107.13) 10. Today you invested 15,600 in an investment that pays 6% and will mature in 3 years. Once the investm 10. Today you invested 15,600 in an investment that pays 6% and will mature in 3 years. Once the investm PV
i
n NPER -15600 fV of first 3
0.06 I
3n
fv of 6 -9.25498533 Suppose you win the lottery. The winnings consist of 20 equal annual p
earns 8% p
n
pmt
i
FV 20
50000
0.08
($2,288,098.21) You hope to retire in 35 years and you need $1,000,000 in the bank to live the life n
i
fv
PMT 35
0.07
1000000
($7,233.96) 3. You have been offered an investment opportunity that will pay you $5,000 per year for 6 years. What is the valu
n
pmt
i
FV OA
FV AD 6
5000
0.07
($35,766.45)
($38,270.11) Homer plans to deposit $275 in the bank in one year. He plans to make the same deposit two Homer plans to deposit $275 in the bank in one year. He plans to make the same deposit two
pmt
i
n
fv 275
0.052
3
($913.81) Sabrina deposits 800 in an account at the beginning of each year for 5 yea
pmt
n
i 800
5
0.02
($4,246.50) You've graduated from college and landed a good job. You want to replace your car, but don't want to
earn 9%. If the market performs as you're hopin
$30,000? Ign
n=?
fv
I
pmt 50,000
0.12
600 Uriah Heep celebrated his 18th birthday by opening a savings account at the Thames River Bank and depositing $
Uriah decided to abandon his savings plan. He never saved again, but he left the accumulated savings in the bank a
ad
n
pmt
FV 13
4700
($85,947.95)
85947.95 A young couple wishes to accumulate $13,000 at the end of 4 years so that they can make a down payment o n
i
FV
PMT 4
0.05
13,000
($3,016.15) You won the lottery! The prize is $100 paid at the end of each of the next 4 years. Wha n
pmt
i
PV 4
100
0.1
($316.99) Let's look at the retirement question from another viewpoint. Suppose you hav
n
pv
pmt
RATE 30
562889
50000
8% You won the lottery! The prize is $100 paid at the beginning of each of the next 4 years (sta
pmt
n
i
pv Suppose we want to determine the present value of the dividends paid by a share of preferred stock.
that
Perpetuity
PMT
i
Perpetuity
pmt/i Homer expects to receive $250 next year. He also expects to receive $250 in two years a
i
pmt
n
PV
PV of 2 years + 25 You are 62 and planning your retirement. If you retire immediately, then your Canadian Pension Plan (CPP) benefi
should you retire and start claiming retirement benefits? Since the benefits are certain as long as you live, the appr
rate. The real risk free rate is 3.5% per annum. Assume that benefits are collected at the end of each month. Expre
early from the future v
age 62
$1927 now
age 67
$2,338
real rate
0.035 Age 62
n
i
FV 28
0.035
-1927 Age 67
n
I=
FV 23
0.035
-2338 You have been making $2,100 per-year contributions to your company retirement plan for 20 y
pmt
n
fv
Rate -2100
20
252000
16.33% An endowed faculty chair is created when a benefactor makes a donation of sufficient size that earnings from the d
endow a chair in your name if the salary and benefits were $81,000 and the interest rate wa PMT
i
Perpetuity 81000
0.07
$1,157,142.86 Suppose you have two 3-year annuities, one beginning one period from now (with $200 payments) and another b
annuities, and what is their combined PV? As
n
3
pmt
-200
i
0.1
pv
$497.37
Combined PV Congratulations! You won the lottery. You will receive two payments of $14,000 at the end of each of the next 2 yea
rate is 3%. What is the present va
PMT
n
i
NPV 14000
2
0.03
$66,468.41 You are 30 years old today. You want to retire at the age of 65. You expect to live until age 85. You would like to hav
working years in order to achieve your retirement goal? Assume end of period payments.
m
12 working
i/m
0.005 i
0.06
m*n
420 n
35
pmt
($1,694.35) You tried to sneak a cappuccino into the movie theatre. It spilled on your leg and scalded you. Your lawyer says th
catch is that the first payment won't ha
years. What is the present value of your settlemen You tried to sneak a cappuccino into the movie theatre. It spilled on your leg and scalded you. Your lawyer says th
catch is that the first payment won't ha
years. What is the present value of your settlemen
pmt
n
i
pv in 2 years
pv -9000
10
0.033
$78,104.81
($73,194.28) Your friend, Ernest Defraud, wants to borrow $1,000 for 3 years. Let's assume that you want to earn interest
pv
n
i
FV
interest earn -1000
3
0.05
$1,157.63 pmt
$157.63 You are going to borrow $104,000 to fund the start of your new restaurant. The bank wants to be repa
PV
n
i
FV -104000
3
0.08
$131,010.05 Your friend, Ernest Defraud, wants to borrow $1,000 for 3 years. He has proposed an amortized loan with payment
How much interest do you earn from reinvestment and how
PV
n
pmt
i
50 -1000
3
367.21
0.05
$1,157.63 7.2 Zero Coupon bonds Consider a zero coupon bond with a maturity in 2 years and a face value of $1,000. Assume that the price of the bo
the bond?
n
2
FV
100
Price
90.7
Yield
Err:502 A zero coupon bond with a maturity in 5 years and a maturity value of $100 trades for a price of $78.254. If
n
FV
Price
INTRATE If the 3-year spot rate is 4%, then what is the price of a 3-year U.S. gov If the 3-year spot rate is 4%, then what is the price of a 3-year U.S. gov
FV
i
n
PV What is the percentage change in price for a zero coupon bond if the yield changes from 7.5% to 8.5%? The bond
7.5%, as the base in the percen
i
n
FV
PV1
PV2 Based on the table of bond prices below, what is the shape of the yield curve?
Zero coupon bond prices
Maturity
1
2
3
Rate1
rate 2
rate 3 The 2-year spot rate is 5.2%. What is the price of a zero coupon bond
n
i
FV
PV If the real rate is 10% and inflation is 5%, then what is th
kr Pie
kn =
kn= kr = if the nominal interest rate is 3.6% and inflation is expec
kn
0.036
pie
0.017
(1+.036)/(1+.017)
1.87% The market expects the 1-year spot rate (starting today) to be 4.6% and next year's 1-year spot rate
K=(1+k1)*(1+k2)^(1/2) -1 k1
k2
K= 0.046
0.098
7.72% What is the nominal rate of interest for a 10-year corporate bond if the real rate is 4.2%, expected inflation is 2.8%
3.1%
n
10
kr
0.042
INF
0.028
LRP
0.0038
DRP
0.016
MRP
0.031
YTM 0.121976
YTM = kr + INF + (kr *INF) + LRP + DRP + MRP The 6-year T-note has a Bloomberg price quote of 99-2
0.859375
0.765625 The timeline shows the face values for zero coupon bonds. A 1-year zero coupon bond has a face value of $C, where
is 1% (k1
Price at year 1 n
i
FV
PV
Bond price 1
0.01
-10
$9.901
$115.630 A 2-year coupon bond has a coupon rate of 5% and a face value of $1,000. The price of the
Fv
100
Price
103.875
i
0.05
Yield
2.9756% Suppose you found a bond in your great-great-aunt's attic. It has 2 years before it matures (it has been in that sho
interest is paid annually and the yield to maturity of the bond is 9%, then wha
n
2
FV
YTM
C
PV 1000
0.09
100
($1,017.59) Let us compute the price of a Chrysler bond. The bonds have a 10.95% coupon rate that is paid semi-annually, a $
compounding and that the yield to maturity is 1
m
2
i
0.1095
i/m
0.05475
FV
1000
n
20
n*m
40
C
54.75
YTM =
0.12
YTM semi
0.06
PV =
($921.01) Springfield Nuclear Energy Inc. bonds are currently trading at $1,116.54. The bonds have a face value of $1,000, a co
yield to maturity of the bonds
FV
i
Price
YIELD 7.00% What is the yield to maturity of a 9% semiannual coupon bond with a face value o
ytm
0.09
C
90
FV
100
Price
83.78
YIELD
0.119955450646 Beam Inc. bonds are trading today for a price of $1,122.91. The bond currently has 16 years until maturity and ha
coupon is due in one year, and the face value of the bond is $1,000. What
Price
n
YTM
FV
PMT= -1122.91
16
0.0302
1000
$40.00 Consider an annual coupon bond with a face value of $100, 11 years to maturity, and a price of $90. The coupon r
how much money do you have if you hold the b
FV
100
n
11
Price
90
($87.38)
Pmt
7
187.38 i 0.025 The Government of Canada has a 24-year bond that matures 24 ye
$1,000. The bond has a coupon rate of 3.5% per year, paid semiannually. The yield on the bond is 7%. If coupons
coupons over the life of the bond? Calculate the interest as a percentage of t
n
FV
r
yield
coupons 24
1000
0.035
0.07
0.04
0.02 Iron Maiden became the first heavy-metal band to sell bonds when it arranged a $30 million deal in February 1999.
of future royalties from the band's albums like "The Number of the Beast." Each bond in the issue had a f
The yield to maturity on the bond was 6.25%. At wh
FV
n
m
C
YTM coupon rTE=
FV=
K1= 0.053
53
1000
0.012 52.3715415 ($52.37) 1000
17
2
0.045
0.0625
0.03125 46
1000
0.011 K2=
K3= 0.019 ($103.05)
0.031 ($1,062.11)
($1,217.54)
1064.2564 0.018
0.03
1047.636838229 Plain Vanilla bonds have a face value of $1,000, pay an annual coupon of $41, have 19 years until maturity and hav
the price of the bond?
FV
C
n
YTM
PV 1000
41
19
0.0721
($683.56) Consider three annual coupon bonds each with a face value of $1,000 and 10 years remaining to maturity. The first
the third has a coupon rate of 12%. Assume that the yield to maturity of the bonds is 10%. Which bond trad
Bond 1
Bond 2
FV
1000
n
10
C
80 C
YTM
0.1
($877.11)
($1,000.00) Consider an annual coupon bond issued by Chrysler Corp. The bond has a 10.95% coupon rate, a $1,000 face value
you buy it today, hold it for 1 year, and sell it after the next coupon. Assume that interest rates do not change durin
you earn on the bon
First year
FV
CR
C
n YTM
Price
PV
Price Change
Return A newly issued Government of Canada bond matures in exactly 10 years. The coupon rate is 3.25% per year and cou
a recession. You expect that the monetary authorities will relax monetary policy which will cause interest rates to
from the inter
n
10
cr
0.0325
Price
104.85
Yields
0.0269
10 year yield fall 1.44%
0.0072 A bond has 5 years to maturity, a coupon rate of 7.3 %, and a face value of $ 1000. The yield to maturity is 13.8 %. A
of the bond when it has 4 years to maturity (one year from today) and what is the percentage increase/decrease in a. Current price of bond
Price
b. coupon yield on bond
C/price of bond
c. Capital gain yield
Cap gain yield = YTM - coupon yield
d. Price when 4 years to maturity
n
4
PV
$809.83
%inc/dec
4.39% n
cr
C
FV
YTM
PV=
775.77
9.41%
4.39% 5
0.073
-73
-1000
0.138
$775.77 HOMEWORK CHAPTER 7 The table below shows market prices for four zero coupon bonds with four different terms: one, two, three and four
graph the yield curve. What is the sha
Zero coupon bond prices
Term(years) Price($)
Yield
1
-934.58
7.00%
2
-857.34
8.00%
3
-772.18
9.00%
4
-683.01
10.00%
FV
1000 Cyberdyne Systems is issuing a series of zero coupon bonds to raise $500M to fund research and development at its
the bond is 4%. What is the fair price for one of C PV FV
N
Yield
($438.83) 1000
21
0.04 If the nominal rate of interest is 14.03 % and the real rate of intere
6.52% 0.065203176086 What is the price of a 5-year, 7.9% coupon rate, $1,000 face value bond that pays interest annu
n
5
FV
-1000
cr
0.079
C(PMT)
-79
YTM
0.066
$1,053.88 A Government of Canada bond with a 3-year maturity has a coupon rate o
The coupons are paid annually and the next coupon is due in one year. Using the Treasury spot rates giv
n
3
Treasury Spot Rates
cr
0.08
Term
C
-80
1 FV -1000 2
3
1099.97770005 A 10-year bond pays interest of $28.60 semiannually, has a face value of $1,000, and is selling fo
n
pmt
FV
Price
Rate 10
28.6
1000
-799.3
4.39%
0.087759233716 Consider an annual coupon bond with a face value of $100, 3 years to maturity, and a price of 92. T
annum, then how much money do you have if y
FV
n
Price
cr
C(PMT)
i 100
3
92
0.05
5
0.025
$15.38 annual coupon bond with a face value of $100, 3 years to maturity, and a price of 91. The coupon rate on the bond is 8%. If yo row to $225.22 at 7% interest (compounded annually)? Q Composite index hit a level of 2,052 in February of 2000.
f 4,696. What was the annual average compound growth rate over t
period? eaked at a level of 4,680 (just before the Tech Bubble popped). In February of 2006 it wa
level of
t an average annual rate of 8.0%. If the index continues to grow at its historic rate, then
he index to grow from its Feb 2006 level back to the Feb 2000 level? ate makes $100 grow to $161.05 over 5 years? he timeline, show how much you can borrow today from a bank if you promise your inheritance as repayment (interest and pri
ts at Period 0 and ends at Period 21. The timeline indicates that PV at Period 0 needs to be determined. At Period 21, F V is give
PV0=? i=4.2% FV21=$8,500 How much can you borrow today?
8500
0.042
21 ($3,582.59) years and 3,000 the following year. How much do you have to have in your bank account today in order to make those withdraw
8000 n
2
3000 n
3
0.09
($6,733.44)
($2,316.55)
($9,049.99) k offers an interest rate of 8% (per annum) with compounding 2 times per year. How much do you have to deposit in the accou ive a payment of 34,000 in 8 years. At a discount rate
hat is the present value of this payment? pounded annually. How many additional dollars of interest would you earn over 8 years if yo
account earning 6.5%? i2 0.065 will mature in 3 years. Once the investment matures, you will reinvest your funds for another 3 years in another investment tha
$18,579.85
0.08
3
($23,405.26) sist of 20 equal annual payments of $50,000. You decide to save all of this mo
earns 8% per year. What is the amount of your retirement nest e 00 in the bank to live the life you want after retirement. You can earn 7% per year on your i
goal? 0 per year for 6 years. What is the value of this stream of cash flows at the end of year 6 if you receive payments at the end of e
beginning of each year?
9
19000
0.06
($218,335.00) e plans to make the same deposit two years from today and three years from today. How much will Homer have in the bank in e plans to make the same deposit two years from today and three years from today. How much will Homer have in the bank in at the beginning of each year for 5 years. If the account pays 2% interest annually, how much money will be in Sabrina's accoun t to replace your car, but don't want to take out a car loan. Instead, you decide to invest $300 per month in the stock market an
If the market performs as you're hoping, how many years will it take to accumulate
$30,000? Ignore taxes m
i/m 12
0.01
#REF! he Thames River Bank and depositing $4,700. He continued to deposit the same amount on every subsequent birthday until he
the accumulated savings in the bank account. The bank paid an interest rate of 5.5%. When Uriah turned 65, he withdrew the m n
i
FV 35
0.055
($559,849.91) that they can make a down payment on a house. What should their equal end-of-year deposits be to accumulate the $13,000, a he end of each of the next 4 years. What is the present value of the lottery annuity if the interest rate is 10%? m another viewpoint. Suppose you have saved $562,889 and want to withdraw $50,000 per year for 30 years. What rate of retu eginning of each of the next 4 years (starting today). What is the present value of the lottery annuity if the interest rate is 10%?
100
4
0.1
($164,456.29)
($348.69) nds paid by a share of preferred stock. We know that the stock promises to pay the holder an annual $100 dividend forever, an
that the first dividend will be paid in one year. 100
0.1
1000 16000
18
0.06
($173,241.66) o expects to receive $250 in two years and again in three years. What is the present value of those payments one year from tod
0.056
-250
2
$460.93 Plus 250
$710.93 ur Canadian Pension Plan (CPP) benefit is $1,927 per month. If you retire at age 67 then the benefit is $2,338 per month. If you
are certain as long as you live, the appropriate discount rate is the risk free rate. Since we are not incorporating inflation into the
lected at the end of each month. Express your answer as the difference in the future value of the benefits. That is, subtract the
early from the future value of benefits if you retire later. i/m 0.035
PV of age 62
PV of age 67 $1,861.84
$4,441.49 your company retirement plan for 20 years. It now has a balance of 252,000. What average compounded return have you earne sufficient size that earnings from the donation pay the salary and benefits of a professor forever. How much would have to be d
were $81,000 and the interest rate was 7%? Assume that the first salary (with benefits) is paid in one year's time. w (with $200 payments) and another beginning four periods from now (with $100 payments). What are the present values of ea
es, and what is their combined PV? Assume an interest rate of 10%.
n
3
pmt
-100
i
0.1
PV at 3 years
($248.69) pv
$186.84
$684.21 00 at the end of each of the next 2 years, followed by two more annual payments of $22,000 at the end of the following years. T
rate is 3%. What is the present value of your prize
22000
2 1 18333.3333
0.06
($17,295.60) live until age 85. You would like to have a monthly income of $14,000 per month in retirement. How much do you have to save
goal? Assume end of period payments. Assume an annual interest rate of 3.5% in retirement and 6% during your working life.
retirement
0.035 0.00291666667
20
240
PMT
-14000
pv
$2,413,960.76 g and scalded you. Your lawyer says that you can expect a payout from the coffee shop's insurance company of $9,000 per year
atch is that the first payment won't happen until the court case is over in 2
t is the present value of your settlement as of today? Assume an interest rate of 3.3%. 2
Annuity due assume that you want to earn interest at 5% compounded annually. What is the balloon payment? How much interest do you e restaurant. The bank wants to be repaid with a balloon payment in 3 years. They will charge 8% interest. How much will your pa posed an amortized loan with payments of $367.21. What is the future value of the payments if you can reinvest the first and se
o you earn from reinvestment and how much interest is included in the payments themselves? 1,000. Assume that the price of the bond is $907.03. If you buy the bond at that price and hold it until maturity, then what is th
the bond?
1000
1/1/2000
907.3
1/1/2002
5% RATE 5% of $100 trades for a price of $78.254. If you buy the bond and hold it for 5 years, then what is the yield on the bond?
5
100
1/1/2000
78.254
1/1/2005
0.055577989623534 RATE
5.03% n what is the price of a 3-year U.S. government zero coupon bond with a face value of $100? n what is the price of a 3-year U.S. government zero coupon bond with a face value of $100?
100
0.04
3
($88.90) changes from 7.5% to 8.5%? The bond has a face value of 1,000 and it matures in 19 years. Use the price determined from the fi
7.5%, as the base in the percentage calculation
0.075
19
-1000
$253.07
$212.24 0.085 -16.13% w, what is the shape of the yield curv...

View
Full Document