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Stocks, bonds options and futures calculation problems

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1. How much will you have after 6 years if you invest \$15,000 at 8% per year compounded annually? Quarterly?

2. How much you need to invest now at 8% interest rate compounded semiannually in order to have \$10,000 in 5 years from now?

3. Find the present value of \$12,000 due four years from now if rate of interest is 6.0% per year and compounded quarterly ?

4. What is the market value of a 60-day \$5,000,000 commercial paper if rate of interest is 6.5% and compounded monthly?

4. You borrow \$10,000 for one year with the nominal interest of 6.9% per year compounded monthly. You are required to pay the lender the principle and interest after one year. What is the APR of this loan if the lender charges \$350 application and processing fee and you agree that \$350 to be added to your loan? What is the APR if you withdraw \$350.00 from your saving account, which pays 3.5%, and pay the charge up front?

5.Assume you buy a \$5000 corporate bond with 6.0 percent coupon rate of \$4850. This bond will mature in three years. If you hold the bond till maturity, what will be the yield to maturity? What is the bonds current yield? What is the average annual rate of return on investment?

6.The conversion ratio for XYZ convertible debenture is 20. You buy a \$1000 of this bond at \$100 premium. What is the parity price of XYZ stock?

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Solution Preview

1. How much will you have after 6 years if you invest \$15,000 at 8% per year compounded annually? Quarterly?

FV = PV (1+R)N where PV is the present value
R is the interest rate
N is the period

Annually

FV = 15,000(1.08)6
= 15,000(1.5869)
= 23,803.50

Quarterly

FV = 15,000(1.02)6x4
= 15,000(1.6804)
= 25,206

2. How much you need to invest now at 8% interest rate compounded semiannually in order to have \$10,000 in 5 years from now?

FV = PV (1+R)N where PV is the present value
R is the interest rate
N is the period

10,000 = PV (1.04)5x2
10,000 = PV (1.4802)
PV = 6,755.84

3. Find the present value of \$12,000 due four years from now if rate of interest is 6.0% per year and compounded quarterly?

12,000 = PV (1.015)4x4
12,000 = PV (1.2690)
PV = 9,456.26

4. What is the ...

Solution Summary

This solution is comprised of a detailed explanation to solve stocks, bonds options and futures calculation problems.

\$2.19

Rates of Return on Convertible Bond Investments

Fondren Exploration, Ltd., has 1,000 convertible bonds (\$1,000 par value) outstanding, each of which may be converted to 50 shares. The \$1 million worth of bonds has 25 years to maturity. The current price of the stock is \$26 per share. The firm's net income in the most recent fiscal year was \$270,000. The bonds pay 12 percent interest. The corporation has 150,000 shares of common stock outstanding. Current market rates on long-term nonconvertible bonds of equal quality are 14 percent. A 35 percent tax rate is assumed.

a.Compute diluted earnings per share.

b.Assume the bonds currently sell at a 5 percent conversion premium over conversion value (based on a stock price of \$26). However, as the price of the stock increases from \$26 to \$37 due to new events, there will be an increase in the bond price, and a zero conversion premium. Under these circumstances, determine the rate of return on a convertible bond investment that is part of this price change, based on the appreciation in value.

c.Now assume the stock price is \$16 per share because a competitor introduced a new product. Would the conversion value be greater than the pure bond value, based on the interest rates stated above? (See Table 16-3 in Chapter 16 to get the bond value without having to go through the actual computation.)

d.Referring to part c, if the convertible traded at a 15 percent premium over the conversion value, would the convertible be priced above the pure bond value?

e. If long-term interest rates in the market go down to 10 percent while the stock price is at \$23, with a 6 percent conversion premium, what would the difference be between the market price of the convertible bond and the pure bond value? Assume 25 years to maturity, and once again use Table 16-3 for part of your answer.

Table 16-3
Interest Rates and Bond Prices (the bond pays 12% interest)
------------------------------------------------------------------------------
Rate in the Market (%) - Yield to Maturity*
Years to Maturity 8% 10% 12% 14% 16%
1 1038.16 1018.54 1000 981.48 963.98
15 1345.52 1153.32 1000 875.54 774.48
25 1429.92 1182.36 1000 862.06 754.98