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Financial Planning Exercises
1. Ranking investments by expected returns. What makes for a good investment? Use the
approximate yield formula or a financial calculator to rank the following investments
according to their expected returns.
a. Buy a stock for $30 a share, hold it for three years, and then sell it for $60 a share (the
stock pays annual dividends of $2 a share).
Future price of- Current price
Average annual investment of investment
Current income + Number of years in investment period
b. Buy a security for $40, hold it for two years, and then sell it for $100 (current income on
this security is zero).
c. Buy a one-year, 5 percent note for $1,000 (assume that the note has a $1,000 par value
and that it will be held to maturity).
2. Calculating key financial ratios. Selected financial information about Backpacking
Resources, Inc., is as follows:
Total assets $20,000,000
Total liabilities $8,000,000
Total preferred stock $3,000,000
Total annual preferred stock dividends $240,000
Net profits after tax $2,500,000
Number of shares of common stock outstanding 500,000 shares
Current market price of common stock $50.00 a share
Annual common stock dividends $2.50 a share
Using the company’s financial information, compute the following:
a. The stock’s dividend yield
b. Book value per share
[Assets – liabilities – Preferred stock ] / number of stock outstanding
c. EPS
d. P/E ratio
3. Choosing appropriate stocks. Assume that you’ve just inherited $500,000 and have
decided to invest a big chunk of it ($350,000, to be exact) in common stocks. Your objective
is to build up as much capital as you can over the next 15 to 20 years, and you’re willing to
tolerate a “good deal’’ of risk.
a. What types of stocks (blue chips, income stocks, and so on) do you think you’d be most
interested in, and why? Select at least three types of stocks and briefly explain the rationale
for selecting each.
Answers can vary depending upon student’s interpretation of risk. A possible answer is:
One third, $70,000 in small cap stock; these companies have potential for growth.
b. Would your selections change if you were dealing with a smaller amount of money—say,
only $50,000? What if you were a more risk-averse investor?
4. Effectiveness of stock market timing. Discuss the evidence regarding the ability of most
investors to effectively time getting in and out of the stock market. How sensitive are
returns to being out of the market for just a few months of good stock market
performance?
Research shows that most investors are better off investing steadily than trying to time the
market. Because it is exceedingly difficult to buy consistently at market bottoms and sell at
market tops, there is a high potential cost of being out of the equity market during its best-
5. Calculating expected return on investment. An investor is thinking about buying some
shares of Health Monitoring, Inc., at $75 a share. She expects the price of the stock to rise
to $115 a share over the next three years. During that time, she also expects to receive
annual dividends of $4 per share. Given that the investor’s expectations (about the future
price of the stock and the dividends it pays) hold up, what rate of return can the investor
expect to earn on this investment? (Hint: Use either the approximate yield formula or a
financial calculator to solve this problem.)
See complete formula in answer 1a above.
6. Calculating book value. A company has total assets of $2.5 million, total liabilities of $1.8
million, and $200,000 worth of 8 percent preferred stock outstanding. What is the firm’s
total book value? What would its book value per share be if the firm had 50,000 shares of
common stock outstanding?
Total book value = A – L – PS dividend =2.5 -1.8 - .2 = $500,000
7. Calculating key stock performance metrics. The Morton Company recently reported net
profits after taxes of $15.8 million. It has 2.5 million shares of common stock outstanding
and pays preferred dividends of $1 million a year. The company’s stock currently trades at
$60 per share.
a. Compute the stock’s EPS.
b. What is the stock’s P/E ratio?
c. Determine what the stock’s dividend yield would be if it paid $1.75 per share to common
stockholders.
8. Calculating expected return on a stock. The price of Green Mountain Homes, Inc. is now
$85. The company pays no dividends. Sean Perth expects the price four years from now to
be $125 a share. Should Sean buy Garden Designs if he wants a 15 percent rate of return?
Explain.
Approximate yield = (0 + [(125 – 85)/4] ) / (85 + 125)/2 = 10 / 105 = 9.5%
Using the financial calculator set on 1 P/YR and End Mode:
9. Collect key data on actual stocks, bonds, and convertible bonds. Using the resources
available at your campus or public library, work the following problems. (Note: Show your
work for all your calculations.)
a. Select any two common stocks and then determine the dividend yield, EPS, and P/E ratio
for each.
b. Select any two bonds and then determine the current yield and yield to maturity of each.
c. Select any two convertible bonds and then determine the conversion ratio, conversion
value, and conversion premium for each.
10. Tax treatment of bond returns. An investor in the 28 percent tax bracket is trying to
decide which of two bonds to select: one is a 5.5 percent U.S. Treasury bond selling at par;
the other is a municipal bond with a 4.25 percent coupon, which is also selling at par.
Which of these two bonds should the investor select? Why?
Municipal bond after tax is 4.25 * (1 - .05) = 4.04. Most states tax municipal bonds if issued by
another state; but do not tax Treasury bonds. If you assumed 5% tax rate, municipal bond is
11. Calculating current yield and yield to maturity. Describe and differentiate between a
bond’s (a) current yield and (b) yield to maturity. Why are these yield measures important
to the bond investor? Find the yield to maturity of a 20-year, 9 percent, $1,000 par value
bond trading at a price of $850. What’s the current yield on this bond?
a. The current yield is found by dividing the annual interest income by the market price of
b. The yield to maturity is the annual rate of return a bondholder would receive if he
or she held the bond to its maturity. This yield is approximated by adding the annual income to
These yield measures are important to bondholders because they are used to assess the
When using the financial calculator, set on 1 payment per year, End Mode, and assume that
Quote Current Yield
Yield to Maturity
Using Financial Calculator
9%, 20 yr., $850 $90/$850 = 10.6% 850 +/- PV
1000 FV
12. Calculating and comparing current yields. Which of these two bonds offers the highest
current yield? Which one has the highest yield to maturity?
a. A 6.55 percent, 22-year bond quoted at 52.000
b. A 10.25 percent, 27-year bond quoted at 103.625
Approximate yield = (102.5 + [(1000 – 1036.25)/27] ) / (1036.25 + 1000)/2 =
13. Calculating and interpreting current yield and yield to maturity. Find the current yield of
a 5.65 percent, 8-year bond that’s currently priced in the market at $853.75. Now, use a
financial calculator to find the yield to maturity on this bond (use annual compounding).
What’s the current yield and yield to maturity on this bond if it trades at $1,000? If it’s
priced at $750? Comment on your findings.
Current yield is (5.65% * 1,000) / 853.75 = 56.5/853.75 = 6.6%
Trades at $1,000, Approximate yield to maturity = (56.5 + [(1,000 – 1,000)/8] ) / (1,000 +
1,000)/2 = 56.5/ 1,000 = 5.65%
When using the financial calculator, set on 1 payment per year, End
Mode, and assume that interest payments are made twice a year.
Quote Current Yield
Yield to Maturity
Using Financial Calculator
a. 5.65%, 8 yr.,
$853.75
$56.50/$853.75 =
6.62%
853.75 +/- PV
1000 FV
b. 5.65%, 8 yr.,
$1,000
$56.50/$1,000 =
5.65%
1000 +/- PV
1000 FV
c. 5.65%, 8 yr., $750 $56.50/$750 =
7.53%
750 +/- PV
1000 FV
When the bond is trading at par, or at $1,000 per bond, the return is the face rate. If not trading
14. Calculating current yield and yield to maturity. A 25-year, zero coupon bond was recently
quoted at 6.500. Find the current yield and yield to maturity of this issue, given the bond
has a par value of $1,000. (Assume annual compounding for the yield to maturity measure.)
A zero coupon bond by definition pays no coupon or yearly interest, so investors profit only from
the capital gains. Zero coupon bonds are purchased at a deep discount and pay the investor par
Current yield = annual interest/current market price = 0
Trades at $65, Approximate yield to maturity = (0 + [(1,000 – 65)/25] ) / (1,000 + 65)/2 = 37.40/
532.5 = 7%
When using the financial calculator, set on 1 payment per year and End Mode.
15. Calculating current yield and return on investment. Assume that an investor pays $850
for a long-term bond that carries a 7.5 percent coupon. During the next 12 months, interest
rates drop sharply, and the investor sells the bond at a price of $962.50.
a. Find the current yield that existed on this bond at the beginning of the year. What was it
by the end of the one-year holding period?
b. Calculate the return on this investment using the approximate yield formula and a one-
year investment period.
Trades at $962.50, Approximate yield to maturity = (75 + [(962.5 – 850)/1 ) / (850 + 962.5)/2 =
When using the financial calculator, set on 1 payment per year, End Mode, and assume that
interest payments are made twice a year.
850 +/- PV
16. Calculating conversion value and conversion premium. Find the conversion value of a
convertible bond that carries a conversion ratio of 24, given that the market price of the
underlying common stock is $55 a share. Would there be any conversion premium if the
convertible bond had a market price of $1,500? If so, how much?
Conversion ratio of 24 means that the bond can be converted to 24 shares of stock. With a
If the convertible bond had a market price of $1,500, the conversion premium is the difference
17. Calculate current yield, conversion ratio, conversion price, and yield to maturity. A 6
percent convertible bond (maturing in 20 years) is convertible into 25 shares of the
company’s common stock. The bond has a par value of $1,000 and is currently trading at
$800; the stock (which pays a dividend of 95 cents a share) is currently trading in the
market at $35 a share. Use this information to answer the following questions:
a. What is the current yield on the convertible bond? What is the dividend yield on the
company’s common stock? Which provides more current income: the convertible bond or
the common stock? Explain.
Current dividend yield on the stock is dividend/price, $0.95 / $35 = 2.7%.
Convertible bond dividend income would be 25 * .95 = $23/75 in dividends if converted.
b. What is the bond’s conversion ratio? Its conversion price?
Bond’s conversion ratio if 25, that is 25 shares of stock for each bond.
c. What is the conversion value of this issue? Is there any conversion premium in this issue?
If so, how much?
Conversion value is the number of share times the current share price, 25 * 35 = $875.
d. What is the (approximate) yield to maturity on the convertible bond?
Trades at $800, Approximate yield to maturity = (60 + [(1,000 – 800)/20] ) / (1,000 + 800)/2 =
When using the financial calculator, set on 1 payment per year, End Mode, and assume that
800 +/- PV
18. Clean and dirty bond prices. You have decided to sell a 5 percent semiannual coupon
bond two months after the last coupon payment. The bond is currently selling for $951.25.
Answer the following questions about the bond:
a. What is the clean price of the bond?
b. What is the dirty (full) price of the bond?
The dirty (full) price of the bond adds the accrued interest. Interest of $25 is paid each six
c. Explain how the clean and dirty prices of the bond are relevant to the buyer of the bond.
Interest is earned with the passing of time. The seller is going to want their earned interest when
