1. You are considering two annuities, both of which make total annuity payments of
$10,000 over their life. Which would be worth more today, annuity A which pays
$1,000 at the end of each year for the next 10 years, or annuity B which pays $775 at
the end of the first year, but the annuity payment grows by $50 each year, reaching
$1,225 at the end of the 10th year? Are there any circumstances in which the two
would be equal? Explain your reasoning. The second annuity weights its payments
more toward the back of the period, rather than the front, making it less valuable
unless the discount rate is zero. At 0% they are equal.
2. ABC Corporation’s common stock dividend yield is 2.1%, it just paid a dividend of
$1 and is expected to pay a dividend of $1.07 one year from now, and dividends are
expected to grow at this same rate indefinitely. What is the required rate of return on
ABC’s stock? r = .07+.021 = 9.1%
3. Given the opportunity to invest in one of the three bonds listed below, which would
you purchase? Why? Assume a market interest rate of 7%.
Bond
Face Value
Coupon Rate
Maturity
Price
$1,000
4%
1 year
$990
A
$1,000
7.5%
17 years
$990
B
$1,000
8.5%
15 years
$990
C
Compute the intrinsic price and compare to the selling price. BondA=$971.96,
BondB=$1,048.81, BondC=$1,136.62. Bond C is the best buy as it should be priced at
$1,136 and is selling for $990. Or compute the YTM's based on the given price:
BondA=5.05%, BondB=7.6%, BondC=8.62%. Bond C has the highest YTM. Or you
know that B and C should be selling at premiums since the market rate is lower than the
coupon rate. C is better than B because of a higher coupon over a shorter period.
4. Use the following financial statements to answer the three questions: (15 points)
ABC, Inc.
Balance Sheet
Cash
Accts. Rec.
Inventory
Total CA
Net fixed assets
Total assets
2002
100
240
480
820
760
2003
120
320
450
890
830
2002
Accts. Payable
180
Notes Payable
150
Total CL
330
Long term debt
200
Common Stock
50
Retained Earnings
1000
Total claims
$1,580
$1,580 $1,720
ABC, Inc.
Income Statement
2002
Sales
$2,100
Cost of goods sold
1,550
Gross Profit
550
Operating expenses
350
2003
$2,300
1,530
770
400
2003
190
50
240
350
70
1060
$1,720
Depreciation
EBIT
Interest
EBT
Taxes
Net Income
40
160
25
135
46
$89
50
320
35
285
97
$188
a. Compute operating cash flow for 2003.
OCF = EBIT + Depreciation - Taxes = 320 + 50 - 97 = $273
b. Compute cash flow to bondholders for ABC, Inc. for 2003.
CF(B) = 35 - 150 = -$115
c. Compute cash flow to stockholders for ABC, Inc. for 2003.
CF(S) = 128 -20 = $108
Dividends = Net Income - Retained Earnings = 188-60 = 128
d. Compute the cash flow from assets for ABC, Inc.
CFA = 108 + (-115) = 273-120-160= -7
5. (15 points)You and your spouse have found your dream home in Rapid City, South
Dakota. The selling price is $120,000; you will put $20,000 down and obtain a 30-year
fixed-rate mortgage at 8.25% for the rest. Assume monthly payments begin in one
month.
a. What will each payment be?
PV = 100,000; I = 8.25%/12 = .68875; n = 30*12 = 360; PMT = $751.27
b. How much interest will you pay (in dollars) over the life of the loan?
751.27*360 = 270,457.20 - 100,000 = $170,457.20
c. If you plan to prepay the loan by making an additional payment each month along
with your regular payment, how much extra must you pay each month if you wish to pay
off the loan in 20 years?
PMT on a 20 year loan is $852.07. Therefore, the extra each month is 852.07751.21=$100.80
6. Floyd Clymer is the CFO of Mid-America Mustang, a manufacturer of parts for classic
automobiles. Floyd is considering the purchase of a 2-ton press which will allow the firm
to stamp out auto fenders. The equipment costs $250,000. The project is expected to
produce after-tax cash flows of $60,000 the first year, and increase by $10,000 annually;
the after-tax cash flow in year 5 will reach $100,000. Liquidation of the equipment will
net the firm $10,000 in cash at the end of 5 years, making the total cash flow in year five
$110,000. Assume a required return of 15 percent. (25 points)
a. What is the payback period for the proposed investment? 3.444 years
b. What is the project’s discounted payback period? 4.7467 years
d. What is the project’s net present value? $13,852.25
e. Assuming the required return is 15%, what is the project’s profitability index? 1.0554
Time Cash
Flow
0
-250
1
60
2
70
3
80
4
90
Discounted CF
5
54.6894
Add this column and
subtract 250 to get NPV.
Add this column and divide
by 250 to get PI
110
52.1739
52.9301
52.6013
51.4578
Payback: After 3 years 40 remains to be
paid back. 40/90=.4444
Discounted Payback: After 4 years
40.8369 remains to be paid back.
40.8369/54.6894 = 0.7467
7. You are 35 years old today and are considering your retirement needs. You expect to
retire at age 65, and your actuarial tables suggest that you will live to be 100. You want
to move to the Bahamas when you retire. You estimate that it will cost you $300,000 to
make the move (on your sixty-fifth birthday) and that your living expenses will be
$30,000 a year (starting at the end of year 66 and continuing through the end of year 100)
after that. You expect to earn 8% on your money. (15 points)
a. How much will you need to have saved by your retirement date to be able to afford
this course of action?
PV of the $30,000 payments (at age 65) = 349,637
Total needs at age 65 = 300,000 (for the move) + 349,637 = 649,637
b. You already have $50,000 in savings. How much would you need to save each year
for the next 30 years to be able to afford this retirement plan?
FV of the 50,000 = 503,132.84 (n=30, i=8%)
To be funded by payments = 649,637-503,133 = 146,504
n=30, I=8%, FV= 146,504, PMT = ? = 1293.25
or
PV of the 649,637 = 64559.19 (n=30, I-8%)
64559 - 50000 = 14,559 to be funded by the payments.
PV = 14559, I=8%, n=30, PMT = ? = 1293.25
c. If you did not have any current savings and do not expect to be able to start saving
money for the next five years, how much would you have to set aside each year after that
to be able to afford this retirement plan?
FV=649,637, n=25, I=8%, PMT = ? = 8,886