Solution sketches, Test 2

Ordering of the problems is the same as in Version D

Investment portfolio Your investment portfolio has annual

returns of 20%, 30%, 10%, and 48% over each of four years. What is the geometric average annual return over this four-year period? Take the product of 1.2, 1.3, 1.1, and

1.48 2.53968

Take the fourth root and subtract 1: 0.2623935 about 26%

A two-stock portfolio You have a two-stock portfolio: You own

50 shares of Macrosoft stock, priced at $30 per share today. You own 40 shares of Baskin Ribbon stock, priced at $100 per share today. If you expect Macrosoft stock to go up by 10% over the next year and Baskin Ribbon stock to go up by 6% over the next year, what is your expected return over the next year of this portfolio?

A two-stock portfolio Total value of Macrosoft stock

50 times $30 = $1500 Total value of Baskin Ribbon stock

40 times $100 = $4000 Total value of portfolio: $5500 Expected return is the weighted

average of the two stock’s returns 0.10 (1500/5500) + 0.06 (4000/5500) =

0.070909 Pick 7%

Two stocks that are perfectly negatively correlated on their returns

You find two stocks that are perfectly negatively correlated on their returns. One stock’s returns have a standard deviation of 10% and the other has a standard deviation of 30%. If you can make a portfolio mixing these two stocks in any combination you want, the lowest possible standard deviation portfolio possible has a standard deviation of _____.

Two stocks that are perfectly negatively correlated on their returns

See Figure 11.4 The minimum variance point is 0 Minimum variance of 0 minimum

standard deviation is 0

Equivalent annual cost

If you buy Machine A, you have to pay $1,650 today (year 0), and maintenance costs of $220 in year 1. Machine A lasts two years. The effective annual discount rate is 10%. What is the equivalent annual cost of Machine A?

Equivalent annual cost

PV of costs: $1650 + $220 / 1.1 = $1850

EAC calculation X / 1.1 + X / 1.12 = 1850 X =

$1065.98 You could have also used the annuity

formula

Compounding problem

You invest $1,000 into an account that pays a 12% stated annual interest rate. Interest is compounded monthly. How much money will be in the account after 14 years? $1,000 (1.01)12×14 = $5,320.97

Dividend in 6 years

You buy a stock that pays a $1 dividend payment today. The dividend will go up by 10% each of the next three years, and by 5% for each of the three following years. How much will the dividend be six years from today? $1 (1.1)3 (1.05)3 = $1.5408

Stock valuation A stock has a dividend payment of

$2 later today, and the dividend goes up by $0.20 for each of the next five years. After the dividend payment five years from today, the company goes out of business and does not pay anything else to stock holders. How much is this stock worth if your effective annual discount rate is 3%?

Stock valuation Add the following

$2.00 $2.20/1.03 $2.40/1.032

$2.60/1.033

$2.80/1.034

$3.00/1.035

Total is about $13.85

Finding an annual growth rate You buy a stock today for $50. The next

dividend payment will be made one year from now, and you expect the growth rate (as a percentage) of the yearly dividend to be constant forever. Assume the dividend paid earlier today was $1 and the effective annual discount rate is 8%. What is the annual growth rate of the stock based on these assumptions?

Finding an annual growth rate

Use the growing perpetuity formula, we get 50 = (1 + g) / (0.08 – g) Note the next dividend is 1 + g

Solving for g gives us 0.05882 Pick 5.9%

Calculating standard deviation of a sample Four stocks have annual returns of

0.1, 0.2, 0.3, and 0.4. The standard deviation of this sample is _____. Average return is 0.25 Sum of squared deviations is 0.05 Variance is 0.05/3 Standard deviation is the square root

of variance About 12.910% (Pick 13%)

Using beta to calculate expected return

The risk-free rate of return is 4%. For a particular security, assume that the beta is 1.3. The market return of a well-diversified portfolio is 17%. What is the return for this security? R = 4% + 1.3(17% - 4%) R = 20.9%

PV of a stream of payments You will receive $500 every six months,

starting one year from now. If your effective annual interest rate is 5%, what is the present value of this stream of payments? First payment is two 6-month blocks from now

We remove the first payment if we view this as a perpetuity

r every six months is sqrt(1.05) – 1 = 2.4695% PV of the stream of payments is

500/0.024695 – 500/1.024695 = $19,759

IRR Bill Loney has just invested in a new

lunch meat. He spent $100,000 today in the development of the new meat, and will receive $150,000 six years from now. His annual discount rate is 4%. What is his annual internal rate of return for this project? Pick a discount rate such that the NPV is 0

0 = -100,000 + 150,000/(1+IRR)6

IRR = 0.06991 (pick 7%)

Yield to maturity

You buy a zero coupon bond today that will mature five years from today. If the bond has a $700 face value and you buy it for $523 today, what is the yield to maturity? No annual interest payments 523(1 + r)5 = 700 r = 0.06003 (pick

6%)

Return of the bond over the next year

A bond pays coupons once per year. You buy a bond today that makes its last coupon payment of $60 one year from today. The face value of the bond is $2,000. If the bond sells for $1,500 today, what is the return on the bond over the next year? 1500 (1 + r) = 2060 r = 37.33%

Balloon payment Shannon takes out a 30-year, fixed-

rate mortgage for $300,000. The stated annual interest rate is 4.8% for this loan, compounded monthly. You will only make payments of $1,500 per month, and you will pay off the remaining balance in the form of a balloon payment at the end of the loan. How large will the balloon payment be?

Balloon payment Monthly r = 0.004 PV of payments is

(1500/0.004)(1 – (1/1.004)360) = $285,896.52

PV of remaining balance is $300,000 – $285,896.52 = $14,103.48

FV of remaining balance is $14,103.48 (1.004)360 = $59,355.76

Two states of the world

There are two states of the world, each with 50% probability of occurring: Good and Bad. When times are Good, Stock P has a rate of return of 10%, and stock Q has a rate of return of 15%. When times are Bad, Stock P has a rate of return of 5%, and stock Q has a rate of return 12%.

Part (a)

What is the expected return for each company? P: .5(10%) + .5(5%) = 7.5% Q: .5(15%) + .5(12%) = 13.5%

Part (b)

What is the variance of Stock P’s return? [(.1-.075)2 + (.05-.075)2]/2 =

0.000625

Part (c)

What is the covariance of the two stocks? ½ [(.1-.075)(.15-.135) + (.05-.075)

(.12-.135)] 0.000375