# Fight Finance

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In Australia, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 2.83% pa.

The inflation rate is currently 2.2% pa, given as an APR compounding per quarter. The inflation rate is not expected to change over the next 2 years.

What is the real yield on these bonds, given as an APR compounding every 6 months?

A 2 year government bond yields 5% pa with a coupon rate of 6% pa, paid semi-annually.

Find the effective six month rate, effective annual rate and the effective daily rate. Assume that each month has 30 days and that there are 360 days in a year.

All answers are given in the same order:

$r_\text{eff semi-annual}$, $r_\text{eff yrly}$, $r_\text{eff daily}$.

A three year bond has a fixed coupon rate of 12% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value is $100. What is its price? For a bond that pays fixed semi-annual coupons, how is the annual coupon rate defined, and how is the bond's annual income yield from time 0 to 1 defined mathematically? Let: $P_0$ be the bond price now, $F_T$ be the bond's face value, $T$ be the bond's maturity in years, $r_\text{total}$ be the bond's total yield, $r_\text{income}$ be the bond's income yield, $r_\text{capital}$ be the bond's capital yield, and $C_t$ be the bond's coupon at time t in years. So $C_{0.5}$ is the coupon in 6 months, $C_1$ is the coupon in 1 year, and so on. You're the boss of an investment bank's equities research team. Your five analysts are each trying to find the expected total return over the next year of shares in a mining company. The mining firm: • Is regarded as a mature company since it's quite stable in size and was floated around 30 years ago. It is not a high-growth company; • Share price is very sensitive to changes in the price of the market portfolio, economic growth, the exchange rate and commodities prices. Due to this, its standard deviation of total returns is much higher than that of the market index; • Experienced tough times in the last 10 years due to unexpected falls in commodity prices. • Shares are traded in an active liquid market. Your team of analysts present their findings, and everyone has different views. While there's no definitive true answer, who's calculation of the expected total return is the most plausible? Assume that: • The analysts' source data is correct and true, but their inferences might be wrong; • All returns and yields are given as effective annual nominal rates. A 30 year Japanese government bond was just issued at par with a yield of 1.7% pa. The fixed coupon payments are semi-annual. The bond has a face value of$100.

Six months later, just after the first coupon is paid, the yield of the bond increases to 2% pa. What is the bond's new price?

The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.

$$p_0= \frac{c_1}{r-g}$$

Which expression is equal to the expected dividend return?

The financing decision primarily affects which part of a business?

A firm pays a fully franked cash dividend of \$70 to one of its Australian shareholders who has a personal marginal tax rate of 45%. The corporate tax rate is 30%.

What will be the shareholder's personal tax payable due to the dividend payment?

Which of the following is NOT a synonym of 'required return'?