Fight Finance

Question 132  bill pricing, simple interest rate

A 90-day Bank Accepted Bill (BAB) has a face value of $1,000,000. The simple interest rate is 10% pa and there are 365 days in the year. What is its price now?

(a) $10,000,000.00

(b) $8,021,978.02

(c) $976,772.86

(d) $975,935.83

(e) $100,000.00

Question 140  IRR, NPV, profitability index

A project has an internal rate of return (IRR) which is greater than its required return. Select the most correct statement.

(a) The NPV will be negative and the profitability index will be less than 1.

(b) The NPV will be positive and the profitability index will be more than 1.

(c) The payback period will be positive and the Accounting Rate of Return will be more than the target return.

(d) The NPV will be positive and the profitability index will be negative.

(e) The NPV will be negative and the profitability index will be positive.

Question 192  NPV, APR

Harvey Norman the large retailer often runs sales advertising 2 years interest free when you purchase its products. This offer can be seen as a free personal loan from Harvey Norman to its customers.

Assume that banks charge an interest rate on personal loans of 12% pa given as an APR compounding per month. This is the interest rate that Harvey Norman deserves on the 2 year loan it extends to its customers. Therefore Harvey Norman must implicitly include the cost of this loan in the advertised sale price of its goods.

If you were a customer buying from Harvey Norman, and you were paying immediately, not in 2 years, what is the minimum percentage discount to the advertised sale price that you would insist on? (Hint: if it makes it easier, assume that you’re buying a product with an advertised price of $100).

(a) 79.72%

(b) 24.00%

(c) 21.24%

(d) 20.28%

(e) 12.00%

Question 207  income and capital returns, bond pricing, coupon rate, no explanation

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.

(a) coupon rate = ##\dfrac{C_{0.5}+C_{1}}{F_T}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}(1+r_\text{total})^{0.5}+C_{1}}{P_0}##

(b) coupon rate = ##\dfrac{2 \times C_{0.5}}{F_T}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}(1+r_\text{capital})^{0.5}+C_{1}}{P_0}##

(c) coupon rate = ##\dfrac{2 \times C_{1}}{P_0}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}+C_{1}}{P_0}##

(d) coupon rate = ##\dfrac{2 \times C_{1}}{P_0}##, ##r_\text{income, 0 to 1}=\dfrac{2 \times C_{1}}{P_0}##

(e) coupon rate = ##\dfrac{2 \times C_{1}}{F_T}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}(1+r_\text{total})^{0.5}+C_{1}}{F_T}##

Question 414  PE ratio, pay back period, no explanation

A mature firm has constant expected future earnings and dividends. Both amounts are equal. So earnings and dividends are expected to be equal and unchanging.

Which of the following statements is NOT correct?

(a) This firm's expected capital return equals zero.

(b) This firm's expected total return and income return are equal.

(c) This firm's forward looking PE ratio will equal the inverse of the firm's expected income return.

(d) This firm's forward looking PE ratio will equal the inverse of the firm's expected capital return.

(e) This firm's forward looking PE ratio is equal to the expected payback period, which is the time it will take for the sum of the cash flows to equal the share price.

Question 519  DDM

A stock is just about to pay a dividend of $1 tonight. Future annual dividends are expected to grow by 2% pa. The next dividend of $1 will be paid tonight, and the year after that the dividend will be $1.02 (=1*(1+0.02)^1), and a year later 1.0404 (=1*(1+0.04)^2) and so on forever.

Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.

Calculate the current stock price.

(a) $10

(b) $12.254902

(c) $12.5

(d) $12.75

(e) $13.75

Question 611  debt terminology

You owe money. Are you a or a ?

Question 759  time calculation, fully amortising loan, no explanation

Five years ago you entered into a fully amortising home loan with a principal of $500,000, an interest rate of 4.5% pa compounding monthly with a term of 25 years.

Then interest rates suddenly fall to 3% pa (t=0), but you continue to pay the same monthly home loan payments as you did before. How long will it now take to pay off your home loan? Measure the time taken to pay off the home loan from the current time which is 5 years after the home loan was first entered into.

Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 5, which was the 60th payment since the loan was granted. Also assume that rates were and are expected to remain constant.

(a) 240 months, which is 20 years.

(b) 202 months, which is 16 years and 10 months.

(c) 168 months, which is 14 years.

(d) 152 months, which is 12 years and 8 months.

(e) 117 months, which is 9 years and 9 months.

Question 779  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Fred owns some BHP shares. He has calculated BHP’s monthly returns for each month in the past 30 years using this formula:

###r_\text{t monthly}=\ln⁡ \left( \dfrac{P_t}{P_{t-1}} \right)###

He then took the arithmetic average and found it to be 0.8% per month using this formula:

###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.008=0.8\% \text{ per month}###

He also found the standard deviation of these monthly returns which was 15% per month:

###\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly} - \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.15=15\%\text{ per month}###

Assume that the past historical average return is the true population average of future expected returns and the stock's returns calculated above ##(r_\text{t monthly})## are normally distributed. Which of the below statements about Fred’s BHP shares is NOT correct?

(a) The returns ##r_\text{t monthly}## are continuously compounded monthly returns.

(b) The mean, median and mode of the continuously compounded annual return is expected to equal 0.8% per month.

(c) The annualised average continuously compounded return is ##\bar{r}_\text{cc annual}=12×0.008=0.096=9.6\%\text{ pa}##. The annualised standard deviation is ##\sigma_\text{annual} = \sqrt{12}×0.15=0.519615242 = 52\%\text{ pa}##.

(d) If the current price of the BHP shares is $20, they're expected to have a median value of $52.2339 ##(= 20×e^{0.008×12×10})## in 10 years.

(e) If the current price of the BHP shares is $20, they're expected to have a mean value of $13.5411 ##(= 20×e^{(0.008 - 0.15^2/2)×12×10})## in 10 years.

Question 925  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate, no explanation

The arithmetic average and standard deviation of returns on the ASX200 accumulation index over the 24 years from 31 Dec 1992 to 31 Dec 2016 were calculated as follows:

###\bar{r}_\text{yearly} = \dfrac{ \displaystyle\sum\limits_{t=1992}^{24}{\left( \ln⁡ \left( \dfrac{P_{t+1}}{P_t} \right) \right)} }{T} = \text{AALGDR} =0.0949=9.49\% \text{ pa}###

###\sigma_\text{yearly} = \dfrac{ \displaystyle\sum\limits_{t=1992}^{24}{\left( \left( \ln⁡ \left( \dfrac{P_{t+1}}{P_t} \right) - \bar{r}_\text{yearly} \right)^2 \right)} }{T} = \text{SDLGDR} = 0.1692=16.92\text{ pp pa}###

Assume that the log gross discrete returns are normally distributed and that the above estimates are true population statistics, not sample statistics, so there is no standard error in the sample mean or standard deviation estimates. Also assume that the standardised normal Z-statistic corresponding to a one-tail probability of 2.5% is exactly -1.96.

Which of the following statements is NOT correct? If you invested $1m today in the ASX200, then over the next 4 years:

(a) Continuously compounded mean and median returns are both 37.96% over the 4 year period.

(b) 95% confidence interval of the continuously compounded returns is between -28.3664% and 104.2864% over the 4 year period.

(c) Mean dollar value is $1.547835m while its median dollar value is $1.4617m in 4 years.

(d) 95% confidence interval of the dollar value is between $0.75302m and $2.17038m in 4 years.

(e) 95% confidence interval of the effective annual return is between -24.698% and 183.7332% over the 4 year period.