# Problem set fm 1

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.

## future value

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