Fight Finance

Question 64  inflation, real and nominal returns and cash flows, APR, effective rate

In Germany, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 0.04% pa.

The inflation rate is currently 1.4% 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) -1.3529627%

(b) -0.4977348%

(c) 0.4977348%

(d) 1.3529627%

(e) 1.3621776%

Question 82  portfolio return

Portfolio Details
Stock	Expected return	Standard deviation	Correlation	Dollars invested
A	0.1	0.4	0.5	60
B	0.2	0.6		140

What is the expected return of the above portfolio?

(a) 0.15

(b) 0.17

(c) 0.1908

(d) 0.2412

(e) 0.34

Question 131  APR, effective rate

Calculate the effective annual rates of the following three APR's:

• A credit card offering an interest rate of 18% pa, compounding monthly.
• A bond offering a yield of 6% pa, compounding semi-annually.
• An annual dividend-paying stock offering a return of 10% pa compounding annually.

All answers are given in the same order:

##r_\text{credit card, eff yrly}##, ##r_\text{bond, eff yrly}##, ##r_\text{stock, eff yrly}##

(a) 0.1956, 0.0609, 0.1.

(b) 0.015, 0.09, 0.1.

(c) 0.1881, 0.0609, 0.1025.

(d) 0.1956, 0.0617, 0.1047.

(e) 6.2876, 0.1236, 0.1.

Question 284  covariance, correlation

The following table shows a sample of historical total returns of shares in two different companies A and B.

Stock Returns
Total effective annual returns
Year	##r_A##	##r_B##
2007	0.2	0.4
2008	0.04	-0.2
2009	-0.1	-0.3
2010	0.18	0.5

What is the historical sample covariance (##\hat{\sigma}_{A,B}##) and correlation (##\rho_{A,B}##) of stock A and B's total effective annual returns?

(a) 0.05696, 0.702247

(b) 0.05696, 0.238663

(c) 0.053333, 0.936329

(d) 0.040889, 0.930519

(e) 0.04, 0.930519

Question 288  Annuity

There are many ways to write the ordinary annuity formula.

Which of the following is NOT equal to the ordinary annuity formula?

(a) ##V_0 = \dfrac{C_1}{r} \left(1-\dfrac{1}{(1+r)^T} \right) ##

(b) ##V_0 = \dfrac{C_1 \left(1-\dfrac{1}{(1+r)^T} \right)}{r}##

(c) ##V_0 = C_1\dfrac{\left(1-(1+r)^{-T} \right)}{r}##

(d) ##V_0 = C_1 \left(1-(1+r)^{-T} \right) r^{-1}##

(e) ##V_0 = C_1 \left(r^{-1}-(1+r)^{-T-1} \right)##

Question 375  interest tax shield, CFFA

One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use net operating profit after tax (NOPAT).

###\begin{aligned} FFCF &= NOPAT + Depr - CapEx -\Delta NWC \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC \\ \end{aligned} \\###

Does this annual FFCF or the annual interest tax shield?

Question 397  financial distress, leverage, capital structure, NPV

A levered firm has a market value of assets of $10m. Its debt is all comprised of zero-coupon bonds which mature in one year and have a combined face value of $9.9m.

Investors are risk-neutral and therefore all debt and equity holders demand the same required return of 10% pa.

Therefore the current market capitalisation of debt ##(D_0)## is $9m and equity ##(E_0)## is $1m.

A new project presents itself which requires an investment of $2m and will provide a:

• $6.6m cash flow with probability 0.5 in the good state of the world, and a
• -$4.4m (notice the negative sign) cash flow with probability 0.5 in the bad state of the world.

The project can be funded using the company's excess cash, no debt or equity raisings are required.

What would be the new market capitalisation of equity ##(E_\text{0, with project})## if shareholders vote to proceed with the project, and therefore should shareholders proceed with the project?

(a) $2.5m, so they should vote yes.

(b) $2.045455m, so they should vote yes.

(c) $0.9m, so they should vote no.

(d) $0, so they should vote no.

(e) -$0.9m, so they should vote no.

Question 773  CFFA, WACC, interest tax shield, DDM

Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the operating and firm free cash flows are constant (but not equal to each other).

Data on a Levered Firm with Perpetual Cash Flows
Item abbreviation	Value	Item full name
##\text{OFCF}##	$48.5m	Operating free cash flow
##\text{FFCF or CFFA}##	$50m	Firm free cash flow or cash flow from assets
##g##	0% pa	Growth rate of OFCF and FFCF
##\text{WACC}_\text{BeforeTax}##	10% pa	Weighted average cost of capital before tax
##\text{WACC}_\text{AfterTax}##	9.7% pa	Weighted average cost of capital after tax
##r_\text{D}##	5% pa	Cost of debt
##r_\text{EL}##	11.25% pa	Cost of levered equity
##D/V_L##	20% pa	Debt to assets ratio, where the asset value includes tax shields
##t_c##	30%	Corporate tax rate

 

What is the value of the levered firm including interest tax shields?

(a) $515.464m

(b) $500m

(c) $485m

(d) $444.444m

(e) $431.111m

Question 949  future, contango

If futures prices are in contango, then futures prices (##F_{0,T}##) are than, than or to spot prices (##S_0##)?

Question 998  yield curve, term structure of interest rates

Which of the following statements is NOT correct? An inverted US government bond yield curve indicates that:

(a) Bond market participants believe that the US Federal Reserve will lower short term interest rates in the future.

(b) Fiscal policy will be more contractionary, with lower government spending.

(c) Bond market participants expect that the national economy is expected to have lower economic growth in the future.

(d) Inflation is likely to be lower in the future.

(e) Long term bond yields to maturity (YTM's) are lower than short term bond YTM's.