23 Aug Please use excel functions to do the calculations on the worksheet for full credit! Note that there is more than one tab in this spreadsheet.Problemset1.xlsx
What would the future value of $100 be after 5 years at 10% compound interest?
N
5
I
10%
PV
$100
PMT
$0
FV=
Suppose you currently have $2,000 and plan to purchase a 3-year certificate of deposit (CD) that pays 4% interest compounded annually. How much will you have when the CD matures?
N
3
I
4%
PV
$2,000
PMT
$0
FV=
A company’s sales in 2009 were $100 million. If sales grow at 8%, what will they be 10 years later?
N
10
I
8%
PV ($M)
$100
PMT
$0
FV ($M)=
How much would $1, growing at 5% per year, be worth after 100 years?
N
100
I
5%
PV
$1
PMT
$0
FV=
What would FV be if the growth rate were 10%?
N
100
I
10%
PV
$1
PMT
$0
FV=
present value
Suppose a risk-free bond promises to pay $2,249.73 in 3 years. If the going risk-free interest rate is 4%, how much is the bond worth today?
N
3
I
4%
PMT
$0
FV
$2,249.73
PV=
How would your answer change if the bond matured in 5 rather than 3 years?
N
5
I
4%
PMT
$0
FV
$2,249.73
PV=
If the risk-free interest rate is 6% rather than 4%, how much is the 5-year bond worth today?
N
5
I
6%
PMT
$0
FV
$2,249.73
PV=
Interest rate
Suppose you can buy a U.S. Treasury bond which makes no payments until the bond matures 10 years from now, at which time it will pay you $1,000. What interest rate would you earn if you bought this bond for $585.43?
N
10
PMT
$0
PV
$585.43
FV
$1,000
I =
What rate would you earn if you could buy the bond for $550?
N
10
PMT
$0
PV
$550.00
FV
$1,000
I =
Microsoft earned $0.33 per share in 1997. Fourteen years later, in 2011, it earned $2.75. What was the growth rate in Microsoft’s earnings per share (EPS) over the 14-year period?
N
14
PMT
$0
PV
$0.33
FV
$2.75
I =
If EPS in 2011 had been $2.00 rather than $2.75 what would the growth rate have been?
N
14
PMT
$0
PV
$0.33
FV
$2.00
I =
Perpetuity
What is the present value of a perpetuity that pays ₤1,000 per year, beginning one year from now, if the appropriate interest rate is 5%?
PMT
£1,000
I
5%
PV=
What would the value be if the perpetuity began its payments immediately?
The perpetuity formula values payments 1 through infinity. If a payment is to be received immediately, it must be added to the formula result.
PMT
£1,000
I
5%
PV=
Annuity
What is the PVA of an ordinary annuity with 10 payments of $100 if the appropriate interest rate is 10%?
N
10
I
10%
PMT
-$100
FV
$0
PV=
What would the PVA be if the interest rate were 4%?
N
10
I
4%
PMT
-$100
FV
$0
PV=
What would the PVAs be if we were dealing with annuities due?
Part a
Part b
BEGIN MODE
BEGIN MODE
N
10
N
10
I
10%
I
4%
PMT
-$100
PMT
-$100
FV
$0
FV
$0
PV
PV
Assume that you are offered an annuity that pays $100 at the end of each year for 10 years. You could earn 8% on your money in other equally risky investments. What is the most you should pay for the annuity?
N
10
I
8%
PMT
-$100
FV
$0
PV=
If the payments began immediately, then how much would the annuity be worth?
BEGIN MODE
N
10
I
8%
PMT
-$100
FV
$0
PV=
NPV
What is the present value of a 5-year ordinary annuity of $100 plus an additional $500 at the end of Year 5 if the interest rate is 6%?
Interest rate
6%
Year
0
1
2
3
4
5
Ann Pmt
$0
$100
$100
$100
$100
$100
Lump Sum
$500
Total CFs
$0
$100
$100
$100
$100
$600
NPV
What is the present value of the following uneven cash flow stream: $0 at Time 0, $100 at the end of Year 1 (or at Time 1), $200 at the end of Year 2, $0 at the end of Year 3, and $400 at the end of Year 4, assuming the interest rate is 8%?
Interest rate
8%
Year
0
1
2
3
4
CFs
$0
$100
$200
$0
$400
NPV
IRR
An investment costs $465 now and is expected to produce cash flows of $100 at the end of each of the next 4 years, plus an extra lump sum payment of $200 at the end of the 4th year. What is the expected rate of return on this investment?
Year
0
1
2
3
4
Ann Pmt
-$465
$100
$100
$100
$100
Lump Sum
$200
Total CFs
-$465
$100
$100
$100
$300
IRR
An investment costs $465 and is expected to produce cash flows of $100 at the end Year 1, $200 at the end of Year 2, and $300 at the end of Year 3. What is the expected rate of return on this investment?
Year
0
1
2
3
CFs
-$465
$100
$200
$300
IRR
Value of bond
A bond that matures in six years has a par value of $1,000, an annual coupon payment of $80, and a market interest rate of 9%. What is its price?
Years to Maturity
6
Annual Payment
$80
Par value
$1,000
Going rate, rd
9%
Value of bond =
Last year a firm issued 30-year, 8% annual coupon bonds at a par value of $1,000. (1) Suppose that one year later the going rate drops to 6%. What is the new price of the bonds, assuming that they now have 29 years to maturity?
Years to Maturity
29
Coupon rate
8%
Annual Payment
$80
Par value
$1,000
Going rate, rd
6%
Value of bond =
Yield of bond
A bond currently sells for $850. It has an eight-year maturity, an annual coupon of $80, and a par value of $1,000. What is its yield to maturity? What is its current yield?
Years to Maturity
8
Annual Payment
$80.00
Current price
$850.00
Par value = FV
$1,000.00
Going rate, rd =YTM:
Annual Payment
$80.00
Current price
$850.00
Current yield:
A bond currently sells for $1,250. It pays a $110 annual coupon and has a 20-year maturity, but it can be called in 5 years at $1,110. What are its YTM and its YTC? Is it likely to be called if interest rates don't change?
Years to Maturity
20
Years to Call
5
Annual Payment
$110
Annual Payment
$110
Current price
$1,250
Current price
$1,250
Par value = FV
$1,000
Call price
$1,110
YTM
YTC
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