Question 1

Mr. Kiwat borrowed GH200,000 from his bankers to buy his dream house. Repayment is over 4 years and first payment is due one year from hence. He will make equal payments to amortize both the principal and interest, which is calculated on a reducing balance basis. The bank will charge 5% above its current base rate of 20% per annum.

Required:

Calculate Mr Bruce's annual payments

Show a table on how the annual payment will liquidate the loan and interest.

Cross Ltd has bought an asset with a life span of 4 years. At the end of the 4 years, replacement of the asset will cost GH12,000. In this direction, the company has decided to provide for the future commitment by setting up a sinking fund account into which equal annual investment will be made at the end of each year. Interest rate on the investment will be 12% per annum.

Required:

Calculate the annual instalments

Draw up the sinking fund schedule to show the growth fund

Assuming the first payments will be made now and 12 months thereafter, what are the annual payments?

Draw up the sinking fund schedule under (c)

Question 2

A father is planning a savings program to put his daughter through university. His daughter is now 13 year old. She plans to enroll at the university in 5 years, and it should take her 4 years to complete her education. Currently, the cost per year (for everything - her food, clothing, tuition, books, transportation, and so forth) is GH 12,000 per year. This cost is expected to remain constant throughout the four-year university education. The daughter recently received GH 7,500 from her grandfathers, estate; this money will be invested at a rate of 8% to help meet the costs of the daughter's education. The rest of the costs will be met by money the father will deposit in a savings account which also earns 8 percent compound interest per year. He will make 5 equal deposits into the account, one deposit per annum starting one year from now until his daughter starts university. These deposits will begin one year from now. (Assume that school fees are paid at the beginning of the year)

What will be the present value of the cost of 4 years of education at the time the daughter turns 18?

What will be value of the GH 7,500 that the daughter received from her grandfather's estate when she starts college at 18?

If the father is planning to make the first of 5 deposits one year from now, how large must each deposit be for him to able to put his daughter through college?

Question 3

Your company will generate GH 55,000 in annual revenue each year for the next eight years from a new information database. The computer system needed to set up the database costs GH 250,000. If you can borrow the money to buy the computer system at 7.5 percent annual interest, can you afford the new system?

An investment offers GH 2,250 per year for 15 years, with the first payment occurring one year from now. If the required return is 10 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever?

You want to have GH 50,000 in your savings account five years from now, and you're prepared to make equal annual deposits into the account at the end of each year. If the account pays 9.5 percent interest, what amount must you deposit each year?

First National Bank charges 7.5 percent compounded quarterly on its business loans. First United Bank charges 7.5 percent compounded semiannually. As a potential borrower, which bank would you go to for a new loan?

Question 4

It is now January 1. You plan to make a deposit of GH100 each, one every 6 months, with the first payment being made today. The bank pays a nominal interest rate of 12% but uses semiannual compounding. You plan to leave the money in the bank for 10 years. How much will be in your account after 10 years?

At the end of 10 years, how much is a GH100 initial deposit worth, assuming an annual interest rate of 10 percent compounded (i) annually? (ii) semiannually? (iii) quarterly

Question 5

a.Set up an amortization schedule for a GH 25,000 loan to be repaid in equal installments at the end of each of the next 5 years. The interest rate is 10%.

b. How large must each annual payment be if the loan is for GH 50,000? Assume that the interest rate remains at 10% and that the loan is still paid off over 5 years.

c. How large must each payment be if the loan is for GH 50,000, the interest rate is 10%, and the loan is paid off in equal installments at the end of each of the next 10 years? This loan is for the same amount as the loan in part b, but the payments are spread out over twice as many periods. Why are these payments not half as large as the payments on the loan in part b?

Question 6

Assume that your father is now 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retiresthat is, until age 85. He wants his first retirement payment to have the same purchasing power at the time he retires as GH 40,000 has today. He wants all of his subsequent retirement payments to be equal to his first retirement payment. (Do not let the retirement payments grow with inflation: Your father realizes that the real value of his retirement income will decline year by year after he retires.) His retirement income will begin the day he retires, 10 years from today, and he will then receive 24 additional annual payments.

Inflation is expected to be 5% per year from today forward. He currently has GH 100,000 saved up; and he expects to earn a return on his savings of 8% per year with annual compounding. To the nearest dollar, how much must he save during each of the next 10 years (with equal deposits being made at the end of each year, beginning a year from today) to meet his retirement goal? (Note: Neither the amount he saves nor the amount he withdraws upon retirement is a growing annuity.)

Question 7

As the Head of Business Development of Fidelity Venture Capital, a client has presented a business plan that has the following projected returns for your consideration;

Stock A Stock B

State of the Economy Returns Prob Returns Prob

Excellent 32% 0.4 40% 0.2

Worse -5% 0.4 8% 0.3

Normal 21. % 0.2 25% 0.5

Required:

Calculate the expected return for each stock

Calculate the total risk of the client's business for each stock

If your client plans investing equally in each stock, with a correlation coefficient of -0.8, what is the portfolio return and portfolio risk?

If the beta of the client's business is 0.9 and the risk free rate is 22%, calculate the required rate of investment if the market risk premium is 4%.

Question 8

The earnings, dividends and stock price of Carpetto Technologies Inc. are expected to grow at 7% per year in the future. Carpetto's common stock sells for GH 23 per share, its last dividend was GH 2, and the company will pay a dividend of GH 2.14 at the end of the current year.

Using the discounted cash flow approach, what is its cost of common equity?

If the firm's beta is 1.6, the risk-free rate is 9%, and the average return on the market is 13%, what is the firm's cost of common equity using CAPM approach?

If the firm's bond earns a return of 12%, what will the cost of equity be using the bond-yield-plus-risk-premium approach? Use a risk premium of 4%

On the basis of the results of parts a through c, what would you estimate Capetto's cost of cost of common equity to be?

Question 9

Consider the following information about three stocks:

Returns

State of Economy Prob A B

Boom 0.3 0.2 0.25

Normal 0.45 0.15 0.11

Bust 0.25 0.01 -0.15

If your portfolio is invested 70 percent in A and 30 percent in B, what is the portfolio expected return? The variance? The standard deviation?

If the expected T-bill rate is 3.80 percent, what is the expected risk premium on the portfolio?

If the expected inflation rate is 3.50 percent, what are the approximate and exact expected real returns on the portfolio? What are the approximate and exact expected real risk premiums on the portfolio?

Question 10

Based on the following information, calculate the expected return and standard deviation for each of the following stocks. What are the covariance and correlation between the returns of the two stocks? Calculate the portfolio return and portfolio standard deviation if you invest equally in each asset.

Returns

State of Economy Prob J K

Recession 0.25 -0.02 0.034

Normal 0.6 0.138 0.062

Boom 0.15 0.218 0.092

A portfolio that combines the risk-free asset and the market portfolio has an expected return of 7 percent and a standard deviation of 10 percent. The risk-free rate is 4 percent, and the expected return on the market portfolio is 12 percent. Assume the capital asset pricing model holds. What expected rate of return would a security earn if it had a .45 correlation with the market portfolio and a standard deviation of 55 percent?

Suppose the risk-free rate is 4.2 percent and the market portfolio has an expected return of 10.9 percent. The market portfolio has a variance of .0382. Portfolio Z has a correlation coefficient with the market of .28 and a variance of .3285. According to the capital asset pricing model, what is the expected return on Portfolio Z?

Question 11

Consider the following information about Stocks A and B:

Returns

State of Economy Prob A B

Recession 0.15 0.11 -0.25

Normal 0.55 0.18 0.11

Irrational Exuberance 0.3 0.08 0.31

The market risk premium is 7.5 percent, and the risk-free rate is 4 percent. Which stock has the most systematic risk? Which one has the most unsystematic risk? Which stock is "riskier"? Explain.

There are two stocks in the market, Stock A and Stock B . The price of Stock A today is GH 75. The price of Stock A next year will be GH64 if the economy is in a recession, GH 87 if the economy is normal, and GH97 if the economy is expanding. The probabilities of recession, normal times, and expansion are 0.2, 0.6, and 0.2, respectively. Stock A pays no dividends and has a correlation of 0.7 with the market portfolio. Stock B has an expected return of 14 percent, a standard deviation of 34 percent, a correlation with the market portfolio of 0.24, and a correlation with Stock A of 0.36. The market portfolio has a standard deviation of 18 percent. Assume the CAPM holds.

If you are a typical, risk-averse investor with a well-diversified portfolio, which stock would you prefer? Why?

What are the expected return and standard deviation of a portfolio consisting of 70 percent of Stock A and 30 percent of Stock B ?

What is the beta of the portfolio in part (b)?

Question 12

Robert and Mabel are using the CAPM for making recommendations to their clients. Their research department has developed the information shown in the following table.

Forecasted returns, Standard deviations and Betas

Stock Forecasted Return Standard Deviation Betas

X 14% 36% 0.8

Y 17% 25% 1.5

Market Index 14% 15% 1.0

Risk Free rate 5%

Calculate the expected return using the CAPM for each stock.

Estimate the alpha (difference between expected return and market actual return) for each stock.

Identify and justify which stock would be more appropriate for an investor.

Question 13

Corbett and Sullivan Enterprises (CSE) use the Modified Internal Rate of Return (MIRR) when evaluating projects. CSE's cost of capital is 9.5%. What is the MIRR of a project if the initial costs are GH10,200,000 and the project lasts seven years, with each year producing the same after-tax cash inflows of GH1,900,000?

Assume that both Apple and Yahoo plot on the SML. Apple has a beta of 2.6 and an expected return of 21.2%. Yahoo has a beta of 0.90 and an expected return of 9.3%. The expected return on the market portfolio is 10% and the risk-free rate is 3%. See table below. If you wish to hold a portfolio consisting of Apple and Yahoo and have a portfolio beta equal to 1.5,

What proportion of the portfolio must be in Apple?

ii) What is the expected return on the portfolio?

Apple Yahoo Market Portfolio Risk-free Asset

Beta 2.6 0.9 1.0 0.0

Expected Return 21.2% 9.3% 10.0% 3.0%

Question 14

Cronox Industries and Zealous Incorporated share prices and dividends are shown below for the period 1995 - 2000.

CronoxIndustries Zealous Incorporated

Year Stock price Dividend (GH) Stock price Dividend(GH)

2005 7.62 0.85 55.75 2.00

2006 12 0.90 60.00 2.25

2007 10.75 0.95 57.25 2.50

2008 17 1.00 48.75 2.75

2009 15.75 1.06 52.30 2.90

2010 17.25 1.15 48.75 3.00

Use the data given to calculate annual returns for Cronox, and Zealous.

Compute average return (Arithmetic Average) over the five year period (2006-2010)

Calculate the risk (standard deviation of returns) for both Cronox and Zealous.

Calculate the coefficient of variation for both companies

Compare the two companies in terms of risk and returns.

Calculate the correlation coefficient between the two stock

Calculate the portfolio risk and return assuming the assets are equally weighted.

Assuming Kweku invested GH20,000 in the stocks of Cronox Industries and GH30,000 in that of Zealous Incorporated with a correlation coefficient between the two firms of 0.8, what is the portfolio risk and return?

Question 15

Suppose you invest 60% of your portfolio in ABC and 40% in KDS.The expected dollar return on your ABC stock is 20% and on KDS is 30%. The standard deviations of their annualized daily returns are 36% and 47%, respectively. Assume a correlation coefficient of 0.8 and calculate the portfolio standard deviation and portfolio expected return.

Glory Ltd is a stock listed on the Ghana Stock exchange which has a beta of 1.8. The rate on Government of Ghana traded treasury bills is 11% and the market risk premium for the Ghana Stock Exchange is 20%. Calculate the expected return on the stock.