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Future Value Calculations

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Problem 1

Bret borrows $500,000 from bank to buy a new house. The loan is repayable in monthly installments over 20 years. The nominal interest rate is 10% per annum. What is the monthly repayment? After 5 years have passed, the bank increases the interest rate to 12% per annum and Bret is given the option of either increasing the monthly repayment or extending the terms of the loan. What would be the new monthly repayment if Bret chooses to keep the original loan term unchanged? What would be the new loan term if Bret wishes to keep the original monthly repayment unchanged?

Problem 2

You are considering the purchase of an apartment complex that currently generates a net cash flow of $500,000 per year. You normally demand a 10% rate of return on such investments. Future cash flows are expected to grow with inflation at 4% per year from today’s level.
(a) How much would you be willing to pay for the complex if it:
(i) Will produce cash flows forever?
(ii) Will have to be torn down in 20 years? Assume that the site will be worth $5 million at that time net of demolition costs (the $5 million includes 20 years’ inflation).
(b) Calculate the real discount rate corresponding to the 10% nominal rate. Redo the calculation for parts (i) and (ii) using real cash flows. (Hint: your answers should be the same)

Problem 3

Newcastle Ltd is all-equity financed and has a cost of capital of 15 percent. A consultant suggests that Newcastle could easily borrow up to 50% of the value of its assets at an interest rate of 10% and achieve a rating for its debt of A+ or better. He argues that raising new capital by borrowing would lower the company’s cost of capital, and increase the NPV of some projects that were recently rejected. Use a numerical example to illustrate the consultant’s argument. Is his argument correct? Explain and justify your answer.

Problem 4

Study the capital structures of two companies, a bank and a manufacturing company, from the S&P/ASX 200 index in Australia over the past three years. Identify the discernible differences in the capital structures of these two companies and explain the differences you have identified. You should provide summary information about the companies, including the names, stock codes, brief financial data (assets, liabilities, etc.) and capital structure over the past three years.
(Hint: the name list of the component companies for S&P/ASX 200 index can be found on: http://au.finance.yahoo.com/q/cp?s=%5EAXJO )

Case Study

Ten years ago, in 1998, Rebel Cole founded a small mail-order company selling high-quality sports equipment. Since those early days, Cole Sports has grown steadily and has been consistently profitable. The company has issued 2 million shares, all of which are owned by Rebel Cole and his five children.

For some months Rebel has been wondering whether the time has come to take the company public. This would allow him to cash in on part of his investment and would make it easier for the firm to raise capital, should it wish to expand in the future.

But how much are the shares worth? Rebel’s first instinct is to look at the firm’s balance sheet, which shows that the book value of the equity is $26.34 million, or $13.17 per share. A share price of $13.17 would put the stock on a Price/Earning ratio of 6.6, which is much lower than the 13.1 P/E ratio of Rebel’s larger rival, Molly Sports.

Rebel suspects that book value is not necessarily a good guide to a share’s market value. He thinks of his daughter Jenny, who works in an investment bank. She would undoubtedly know what the shares are worth. He decides to phone her after she finishes her work that day at 9pm or before she starts the next day at 6am.

Before phoning, Rebel writes down some basic data on the company’s profitability. After recovering from its early losses, the company has earned a return that is higher than its estimated 10% cost of capital. Rebel is fairly confident that the company could continue to grow steadily for the next 6 to 8 years. In fact he feels that the company’s growth has been somewhat held back in the last few years by the demands from two of the children for the company to make large dividend payments. Perhaps, if the company went public, it could hold back on dividends and plow more money back into the business.

There are some clouds on the horizon. Competition is increasing and only that morning Molly Sports announced plans to form a mail-order division. Rebel is worried that beyond the next six or so years it might become difficult to find worthwhile investment opportunities.

Rebel realizes that Jenny will need to know much more about the prospects for the business before she can put a final figure on the value of Cole Sports, but he hopes that the information is sufficient for her to give a preliminary indication of the value of the shares.

   1999   2000   2001   2002   2003   2004   2005   2006   2007   2008(E)
EPS($)   -2.1   -0.70   0.23   0.81   1.10   1.30   1.52   1.64   2.00   2.03
Div ($)   0.00   0.00   0.00   0.20   0.20   0.30   0.30   0.60   0.60   0.80
BV ($)   9.80   7.70   7.00   7.61   8.51   9.51   10.73   11.77   13.17   14.40
ROE(%)   -27.0   -7.1   3.0   11.6   14.5   15.3   16.0   15.3   17.0   15.4
Note: EPS = earnings per share, Div = dividends per share, BV= book value per share
ROE = return on equity. The figures of 2008 are based on estimates.

Questions:

a) Help Jenny forecast dividend payments for Cole Sports and to estimate the value of the stock. You do not need to provide a single figure. For example, you may wish to calculate two figures, one on the assumption that the opportunity for further profitable investment is reduced in year 6 and another on the assumption that it is reduced in year 8.

b) How much of your estimate of the value of Cole’s stock comes from the present value of growth opportunities?
(Hint: you can make your assumptions and change the estimated inputs, but make sure that your assumptions are consistent with the information provided and with the theories you have learned from this course)

Solution

The answers to all the questions are included in the solution along with detailed calculations.

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