Fight Finance

Question 96  bond pricing, zero coupon bond, term structure of interest rates, forward interest rate

An Australian company just issued two bonds paying semi-annual coupons:

• 1 year zero coupon bond at a yield of 8% pa, and a
• 2 year zero coupon bond at a yield of 10% pa.

What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.

(a) 6.01%

(b) 6.02%

(c) 9.20%

(d) 12.02%

(e) 18.40%

Question 177  implicit interest rate in wholesale credit

A furniture distributor offers credit to its customers. Customers are given 25 days to pay for their goods, but if they pay immediately they will get a 1% discount.

What is the effective interest rate implicit in the discount being offered? Assume 365 days in a year and that all customers pay either immediately or on the 25th day. All rates given below are effective annual rates.

(a) 0.0004

(b) 0.1301

(c) 0.1365

(d) 0.1460

(e) 0.1580

Question 229  bond pricing

An investor bought two fixed-coupon bonds issued by the same company, a zero-coupon bond and a 7% pa semi-annual coupon bond. Both bonds have a face value of $1,000, mature in 10 years, and had a yield at the time of purchase of 8% pa.

A few years later, yields fell to 6% pa. Which of the following statements is correct? Note that a capital gain is an increase in price.

(a) The zero-coupon bond and the 7% semi-annual coupon bond were both discount bonds but now they are both premium bonds.

(b) The zero-coupon bond and the 7% semi-annual coupon bond were both premium bonds but now they are both discount bonds.

(c) When yields fell, the investor made a capital loss on both bonds.

(d) When yields fell, the investor made a capital gain on both bonds.

(e) When yields fell, the investor made a capital gain on the zero coupon bond but a loss on the 7% semi-annual coupon bond.

Question 296  CFFA, interest tax shield

Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant?

Remember:

###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - ΔNWC+IntExp###

(a) An increase in revenue (##Rev##).

(b) An decrease in revenue (##Rev##).

(c) An increase in rent expense (part of fixed costs, ##FC##).

(d) An increase in interest expense (##IntExp##).

(e) An increase in dividends.

Question 297  implicit interest rate in wholesale credit

You just bought $100,000 worth of inventory from a wholesale supplier. You are given the option of paying within 5 days and receiving a 2% discount, or paying the full price within 60 days.

You actually don't have the cash to pay within 5 days, but you could borrow it from the bank (as an overdraft) at 10% pa, given as an effective annual rate.

In 60 days you will have enough money to pay the full cost without having to borrow from the bank.

What is the implicit interest rate charged by the wholesale supplier, given as an effective annual rate? Also, should you borrow from the bank in 5 days to pay the supplier and receive the discount? Or just pay the full price on the last possible date?

Assume that there are 365 days per year.

(a) 0.143476 is the implicit rate. The buying firm should borrow from the bank and pay at day 5.

(b) 0.130771 is the implicit rate. The buying firm should NOT borrow from the bank and just pay at day 60.

(c) 0.125473 is the implicit rate. The buying firm should borrow from the bank and pay at day 5.

(d) 0.120131 is the implicit rate. The buying firm should NOT borrow from the bank and just pay at day 60.

(e) 0.020408 is the implicit rate. The buying firm should borrow from the bank and pay at day 5.

Question 352  income and capital returns, DDM, real estate

Two years ago Fred bought a house for $300,000.

Now it's worth $500,000, based on recent similar sales in the area.

Fred's residential property has an expected total return of 8% pa.

He rents his house out for $2,000 per month, paid in advance. Every 12 months he plans to increase the rental payments.

The present value of 12 months of rental payments is $23,173.86.

The future value of 12 months of rental payments one year ahead is $25,027.77.

What is the expected annual growth rate of the rental payments? In other words, by what percentage increase will Fred have to raise the monthly rent by each year to sustain the expected annual total return of 8%?

(a) -0.3426%

(b) 0%

(c) 0.2754%

(d) 2.9944%

(e) 3.3652%

Question 373  debt terminology

Which of the following statements is NOT correct? Lenders:

(a) Are long debt.

(b) Invest in debt.

(c) Are owed money.

(d) Provide debt funding.

(e) Have debt liabilities.

Question 505  equivalent annual cash flow

A low-quality second-hand car can be bought now for $1,000 and will last for 1 year before it will be scrapped for nothing.

A high-quality second-hand car can be bought now for $4,900 and it will last for 5 years before it will be scrapped for nothing.

What is the equivalent annual cost of each car? Assume a discount rate of 10% pa, given as an effective annual rate.

The answer choices are given as the equivalent annual cost of the low-quality car and then the high quality car.

(a) $100,   $490

(b) $909.09,   $608.5

(c) $1,000,   $980

(d) $1,000,   $1578.3

(e) $1,100,   $1,292.61

Question 790  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate, log-normal distribution, VaR, confidence interval

A risk manager has identified that their hedge fund’s continuously compounded portfolio returns are normally distributed with a mean of 10% pa and a standard deviation of 30% pa. The hedge fund’s portfolio is currently valued at $100 million. Assume that there is no estimation error in these figures and that the normal cumulative density function at 1.644853627 is 95%.

Which of the following statements is NOT correct? All answers are rounded to the nearest dollar.

(a) Future portfolio values have a log-normal distribution. The mean (expected or arithmetic average) portfolio value in one year is $115,603,957.

(b) The median (50th percentile) portfolio value in one year is $115,603,957.

(c) The 90% confidence interval of continuously compounded portfolio returns over the next year ##(r_{0 \rightarrow 1})## is ##-39.3456088\% < r_{0 \rightarrow 1} < 59.3456088\%##.

(d) The 90% confidence interval of portfolio values in one year ##(V_1)## is ##\$67,472,095 < V_1 < \$181,023,395##.

(e) The annual 95% relative VaR is $48,131,863 and the absolute VaR is $32,527,905.

Question 817  expected and historical returns, income and capital returns

Over the last year, a constant-dividend-paying stock's price fell, while it's future expected dividends and profit remained the same. Assume that:

• Now is ##t=0##, last year is ##t=-1## and next year is ##t=1##;
• The dividend is paid at the end of each year, the last dividend was just paid today ##(C_0)## and the next dividend will be paid next year ##(C_1)##;
• Markets are efficient and the dividend discount model is suitable for valuing the stock.

Which of the following statements is NOT correct? The stock's:

(a) Historical capital return last year was negative ##\left( \dfrac{P_0 - P_{-1}}{P_{-1}} < 0 \right)##.

(b) Historical dividend yield last year was negative ##\left( \dfrac{C_0}{P_{-1}} < 0 \right)##.

(c) Expected future capital return next year is positive ##\left( \dfrac{P_1 - P_0}{P_0} > 0 \right)##.

(d) Expected future dividend yield next year is positive ##\left( \dfrac{C_1}{P_0} > 0 \right)##.

(e) Expected future total return next year is positive ##\left( \dfrac{P_1 - P_0 + C_1}{P_0} > 0 \right)##.