Fight Finance

Question 16  credit card, APR, effective rate

A credit card offers an interest rate of 18% pa, compounding monthly.

Find the effective monthly rate, effective annual rate and the effective daily rate. Assume that there are 365 days in a year.

All answers are given in the same order:

### r_\text{eff monthly} , r_\text{eff yearly} , r_\text{eff daily} ###

(a) 0.0072, 0.09, 0.0002.

(b) 0.0139, 0.18, 0.0005.

(c) 0.0139, 6.2876, 0.0055.

(d) 0.015, 0.1956, 0.0005.

(e) 0.015, 0.1956, 0.006.

Question 40  DDM, perpetuity with growth

A stock is expected to pay the following dividends:

Cash Flows of a Stock
Time (yrs)	0	1	2	3	4	...
Dividend ($)	0.00	1.00	1.05	1.10	1.15	...

After year 4, the annual dividend will grow in perpetuity at 5% pa, so;

• the dividend at t=5 will be $1.15(1+0.05),
• the dividend at t=6 will be $1.15(1+0.05)^2, and so on.

The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What will be the price of the stock in three and a half years (t = 3.5)?

(a) $27.7567

(b) $24.1226

(c) $23.5680

(d) $22.4457

(e) $3.6341

Question 129  debt terminology

An 'interest rate' is the same thing as a 'coupon rate'. or ?

Question 359  CFFA

Which one of the following will have no effect on net income (NI) but decrease cash flow from assets (CFFA or FFCF) 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 increase in rent expense (a type of recurring fixed cost, FC).

(c) An increase in depreciation expense (Depr).

(d) An increase in inventories (a current asset).

(e) An decrease in interest expense (IntExp).

Question 450  CAPM, risk, portfolio risk, no explanation

The accounting identity states that the book value of a company's assets (A) equals its liabilities (L) plus owners equity (OE), so A = L + OE.

The finance version states that the market value of a company's assets (V) equals the market value of its debt (D) plus equity (E), so V = D + E.

Therefore a business's assets can be seen as a portfolio of the debt and equity that fund the assets.

Let ##\sigma_\text{V total}^2## be the total variance of returns on assets, ##\sigma_\text{V syst}^2## be the systematic variance of returns on assets, and ##\sigma_\text{V idio}^2## be the idiosyncratic variance of returns on assets, and ##\rho_\text{D idio, E idio}## be the correlation between the idiosyncratic returns on debt and equity.

Which of the following equations is NOT correct?

(a) ##r_V = \dfrac{D}{V}.r_D + \dfrac{E}{V}.r_E##

(b) ##\beta_V = \dfrac{D}{V}.\beta_D + \dfrac{E}{V}.\beta_E##

(c) ##\sigma_\text{V syst}^2 = \left(\dfrac{D}{V}\right)^2.\sigma_\text{D syst}^2 + \left(\dfrac{E}{V}\right)^2.\sigma_\text{E syst}^2##

(d) ##\sigma_\text{V idio}^2 = \left(\dfrac{D}{V}\right)^2.\sigma_\text{D idio}^2 + \left(\dfrac{E}{V}\right)^2.\sigma_\text{E idio}^2 + 2.\dfrac{D}{V}.\dfrac{E}{V}.\rho_\text{D idio, E idio}.\sigma_\text{D idio}.\sigma_\text{E idio}##

(e) ##\sigma_\text{V total}^2 = \left(\dfrac{D}{V}\right)^2.\sigma_\text{D total}^2 + \left(\dfrac{E}{V}\right)^2.\sigma_\text{E total}^2##

Question 469  franking credit, personal tax on dividends, imputation tax system, no explanation

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?

(a) $13.50

(b) $15.00

(c) $30.00

(d) $31.50

(e) $45.00

Question 489  NPV, IRR, pay back period, DDM

A firm is considering a business project which costs $11m now and is expected to pay a constant $1m at the end of every year forever.

Assume that the initial $11m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.

Which of the following statements about net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?

(a) The NPV is negative $1m.

(b) The IRR is 9.09% pa, less than the 10% cost of capital.

(c) The payback period is infinite, the project will never pay itself off.

(d) The project should be rejected.

(e) If the project is accepted then the market value of the firm's assets will fall by $1m.

Question 625  dividend re-investment plan, capital raising

Which of the following statements about dividend re-investment plans (DRP's) is NOT correct?

(a) DRP's are voluntary, shareholders only participate if they choose.

(b) DRP's increase the number of shares.

(c) The number of shares issued to a shareholder participating in a DRP is usually calculated as their total dividends owed, divided by the allocation share price which is usually close to the current market share price.

(d) DRP's do not incur brokerage costs for the shareholder. This is unlike the case where the shareholder uses the cash dividend to buy more shares herself.

(e) If all shareholders participated in a company's DRP, the company would not pay any dividends and the firm's share price would not fall due to the cash dividend or the DRP.

Question 739  real and nominal returns and cash flows, inflation

There are a number of different formulas involving real and nominal returns and cash flows. Which one of the following formulas is NOT correct? All returns are effective annual rates. Note that the symbol ##\approx## means 'approximately equal to'.

(a) ##r_\text{real} \approx r_\text{nominal} - r_\text{inflation}##

(b) ##(1+r_\text{real})^t = \left( \dfrac{1+r_\text{nominal}}{1+r_\text{inflation}} \right)^t ##

(c) ##V_\text{t,real} = V_\text{t,nominal}.(1+r_\text{inflation})^t##

(d) ##V_\text{0} = \dfrac{V_\text{t,nominal}}{(1+r_\text{nominal})^t}##

(e) ##V_\text{0} = \dfrac{V_\text{t,real}}{(1+r_\text{real})^t}##

Question 897  comparative advantage in trade, production possibilities curve, no explanation

Adam and Bella are the only people on a remote island. Their production possibility curves are shown in the graph.

Which of the following statements is NOT correct?

(a) The equation of Adam’s production possibilities line is coconuts = -7/6*dates + 7.

(b) The equation of Bella’s production possibilities line is coconuts = -3/5*dates + 5

(c) Adam could pick 2 dates and 4.667 coconuts in one hour.

(d) Bella could pick 2 dates and 1.8 coconuts in one hour.