Financial Math Answers

If a 10-year, R1 000 par, zero coupon bond were issued at a price which gave investors a 10 percent rate of return, and if interest rates then dropped to the point where rd = YTM = 5%, we could be sure that the bond would sell at a discount below its R1 000 par value.

Marie Snell recently inherited some bonds (face value R100 000) from her father, and soon thereafter she became engaged to Sam Spade, a University of Florida marketing graduate. Sam wants Marie to cash in the bonds so the two of them can use the money to "live like royalty" for two years in Monte Carlo. The 2 percent annual coupon bonds mature on January 1, 2024, and it is now January 1, 2004. Interest on these bonds is paid annually on December 31 of each year, and new annual coupon bonds with similar risk and maturity are currently yielding 12 percent. If Marie sells her bonds now and puts the proceeds into an account which pays 10 percent compounded annually, what would be the largest equal annual amounts she could withdraw for two years, beginning today?

Recently, Midrand Hospitals Inc. filed for bankruptcy. The firm was reorganized as American Hospitals Inc., and the court permitted a new indenture on an outstanding bond issue to be put into effect. The issue has 10 years to maturity and a coupon rate of 10 percent, paid annually. The new agreement allows the firm to pay no interest for 5 years. Then, interest payments will be resumed for the next 5 years. Finally, at maturity (Year 10), the principal plus the interest that was not paid during the first 5 years will be paid. However, no interest will be paid on the deferred interest. If the required annual return is 20 percent, what should the bonds sell for in the market today?

13. Tina invests $42 000 at 12% p.a. for 4 years with interest compounded quarterly. The value of the investment on maturity is (correct to the nearest dollar)?
14. The price of a new car is $45 000. The value of the car depreciates by 15% p.a. The value of the car after 3 years is?
15. Kerry borrows $5200 in a personal loan to be repaid over 1 year. The interest rate charged is 12% p.a. If Kerry is to repay the loan in 52 weekly instalments, the amount of each repayment is?

8. A $30 000 loan is taken out to be repaid over 4 years at a flat interest rate of 15% p.a. The total amount that is to be repaid on the loan is?
9. If $150 000 is invested for 8 months at 4.8% p.a. simple interest, the amount to which the investment grows is?
10. After selling her apartment and paying off the mortgage, Ann has $400 000 to invest. She plans to invest it at 6.75% with interest compounding annually. The value of the investment will first exceed $550 000 after?
11. Successive discounts of 12% and 10% are equivalent to a single discount of?
12. A tennis racquet has a marked price of $480. The store offers a discount of 10% to account customers and a further 2.5% discount for accounts that are settled within 7 days. Calculate the price paid for the tennis racquet by an account customer who settles her account within 7 days.

1.The simple interest on a loan of $16 000 at 9% p.a. over 4 years is?
2. Successive discounts of 15% and 7% are equivalent to a single discount of?
3. Farming equipment that is valued at $150 000 depreciates at a rate of 10% p.a. The number of years that it will take for the value of the equipment to fall below $50 000 will be?
4. A laptop has a marked price of $980. The store offers a discount of 5% to account customers and a further 5% discount for accounts that are settled within 7 days. Calculate the price paid for the laptop by an account customer who settles her account within 7 days.
5. The price of a new car is $22 500. The value of the car depreciates by 20% p.a. The value of the car after 4 years is?
6. Terry invests $34 000 at 11% p.a. for 3 years with interest compounded quarterly. The value of the investment on maturity is (correct to the nearest dollar)?
7. A sum of money is to be invested for a 6-year period. Which of the following investments will give the greatest return?

The simple interest on a loan of $16 000 at 9% p.a. over 4 years is?

The number of bank accounts randomly opened per month by a Zanaco customers in Lusaka is represented by the probability distribution below.
X
19
20
21
22
P(X = x)
0.4
0.25
0.2
0.15
i. Find the expected number of accounts opened per month.
ii. Suppose opening an account incurs a fixed monthly costs of K100 and an additional handling cost of k5 per account. Find the expected monthly cost of opening bank accounts by Zanaco customers.

The company has a target D/E ratio of 0.45 which it intends to revert to as soon as possible, while its current D/E ratio is 0.50. Currently, the company has a beta of 1.5. The tax rate is 28%, the risk free rate 7% and the market risk premium, 6%. A very similar company recently issued bonds with a YTM of 10%. The company has R15 000 in total assets, R5000 in total liabilities with a book cost of 5% and has R10 000 in equity. The company currently has EBIT of R1000 which it expects to stay the same for the foreseeable future. R5000 will be raised, either by debt or equity. If debt is raised, the company expects to issue bonds at a market related YTM with a coupon rate of 10%. What would the return on equity be if the debt option was chosen?

The company has a target D/E ratio of 0.45 which it intends to revert to as soon as possible, while its current D/E ratio is 0.50. Currently, the company has a beta of 1.5. The tax rate is 28%, the risk free rate 7% and the market risk premium, 6%. A very similar company recently issued bonds with a YTM of 10%. The company has R15 000 in total assets, R5000 in total liabilities with a book cost of 5% and has R10 000 in equity. The company currently has EBIT of R1000 which it expects to stay the same for the foreseeable future. R5000 will be raised, either by debt or equity. If debt is raised, the company expects to issue bonds at a market related YTM with a coupon rate of 10%. if the company chose to use debt financing, what would it’s WACC be?