Financial Math
Which response is correct?
a) When valuing an asset, cash flows that are expected to occur at different points in time can simply be added together without adjustment.
b) $50 that is expected to be received in 5 years’ time is less valuable today than $50 that is expected to be received tomorrow.
c) The present value of a cash flow expected to occur 1 year from now will increase as the expected risk associated with that cash flow increases.
d) More than one of the above options are correct.
b) $50 that is expected to be received in 5 years’ time is less valuable today than $50 that is expected to be received tomorrow.
Exactly nine years ago you invested in a non-dividend paying share at a price of $5.40. Today you sold the share for $7.24. What is your geometric average annual rate of return from the investment?
𝑅𝑔 = 3.31% 𝑝.𝑎
You start with a portfolio of $10,000 invested in Asset A. You sell $4,000 of your portfolio and invest the proceeds into Asset B. You also collect the following information relating to Asset A and Asset B.
- Standard deviation of returns for Asset A 30% per annum
- Standard deviation of returns for Asset B 20% per annum
- Standard deviation of returns for the Market 25% per annum
- Correlation between the returns of Asset A and Asset B 0.8
- Correlation between the returns of Asset A and the Market 0.4
- Correlation between the returns of Asset B and the Market 0.3
- Risk-free rate of return 5% per annum
- Market risk premium 6% per annum
Calculate the standard deviation of returns for your portfolio.
Very long formula....
You are employed in your first graduate role and are asked to provide an
investment decision relating to two mutually exclusive projects. Project X has
a NPV of negative $100m (i.e. -$100m) while Project Y has a NPV of negative
$80m (i.e. -$80m). Which of the following statements correctly describes the
decision you should make?
(a) We should invest in Project X
(b) We should invest in Project Y
(c) We should reject both projects
(d) We are unable to say, we need additional information
(c) We should reject both projects
Decision Rule: Accept if positive NPV
The library in the FBE building
Giblin Eunson Library
You are evaluating the present value of an annuity with the following characteristics. It is
promising annual cash flows of 10% of the $100 face value of the asset. The first cash flow will
occur in 5 years’ time and there will be 7 cash flows that will occur in total. The required rate of
return for the annuity is 8% per annum.
Which of the following options is closest to the present value of the annuity described above?
a) $32.81
b) $38.27
c) $52.07
d) Unable to answer, need more information
b) $38.27
Company Limited is a listed company that has just today announced a current earnings per share amount of $2.50 per share and have just paid a dividend of $2 per share. Company Limited has a dividend payout ratio of 80% and analysts have forecast a long-term dividend growth rate of 6% p.a. and have estimated that the required rate of return on Company Limited shares is 12% p.a.
Estimate the value of Company Limited’s growth opportunities (expressed on a per share basis).
The difference is the PV of growth opportunities = $14.50
You start with a portfolio of $10,000 invested in Asset A. You sell $4,000 of your portfolio and invest the proceeds into Asset B. You also collect the following information relating to Asset A and Asset B.
- Standard deviation of returns for Asset A 30% per annum
- Standard deviation of returns for Asset B 20% per annum
- Standard deviation of returns for the Market 25% per annum
- Correlation between the returns of Asset A and Asset B 0.8
- Correlation between the returns of Asset A and the Market 0.4
- Correlation between the returns of Asset B and the Market 0.3
- Risk-free rate of return 5% per annum
- Market risk premium 6% per annum
Calculate the expected return of your portfolio
Very long formula...
It is possible for a profitable project to be negative NPV.
True or False
True – for two reasons. Firstly, profit just implies that revenues exceed expenses, that is you get more out of a project than what you put in.
For a project to be positive NPV, the rate of return that the project is expected to produce must exceed the required rate of return (which compensates for risk, inflation and opportunity cost). If it does not, then the project may be profitable but have negative NPV
Meals at campus canteen cost?
$5.20
A bank quotes you a borrowing rate of 12% per annum compounding monthly. Which of the
following rates are equivalent to the rate quoted (within two decimal points when expressed as a
percentage e.g. 15.67%)?
a) 1.00% per month compounding monthly
b) 3.00% per quarter compounding quarterly
c) 4.06% per quarter compounding quarterly
d) More than one of the above options are correct
a) 1.00% per month compounding monthly
During its life a fixed coupon paying bond will only ever increase in value because as time passes you get closer and closer to the repayment of the face value of the bond
False – for at least two reasons. Firstly, an increase in yield at any time can result in a decrease in the value of the bond. Secondly, the bond’s value declines on the day that a coupon is paid
When adding an asset to a portfolio, the only time that you have achieved a diversification benefit by adding that asset is when the standard deviation of returns for the portfolio is lower than it was before adding the asset. If it increases, there is no diversification benefit.
Diversification benefits are measured by comparing the risk of the portfolio with the weighted average standard deviation of returns of the assets in the portfolio.
The standard deviation might actually increase, even when you’ve achieved a diversification benefit.
What is the name of the subject with code FNCE20005
Corporate Financial Decision Making
Consider the following information obtained today:
• Relevant rate of return observed in the market = 6% per annum compounding monthly
• Expected cash flow in 1 years’ time: $1000
Which of the following is closest to the PV of the cash flow given the information above?
a) $941.91
b) $942.18
c) $943.40
d) $970.52
a) $941.91
The British government partially funded its war with Napoleon-led France by issuing perpetual bonds promising 3% annual coupons on a face value of £100 at an average market yield of 5% p.a.. By doing so they were able to initially raise an average of £100 per bond.
True or False
False - coupon rate < market yield so would not have made Face value on bond
Which of the following statements correctly describe the Capital Market Line
(a) The CML can be used to find the discount rate applicable to portfolios that have no diversifiable risk.
(b) The CML can be used to price individual assets – such as the shares of ANZ Banking Group.
(c) The CML describes the relationship between systematic risk – measured using beta – and the expected return for an asset.
(d) More than one of the above statements is correct
(a) The CML can be used to find the discount rate applicable to portfolios that have no diversifiable risk.
Your firm is considering investing in one of two mutually exclusive projects – Project A and Project B.
You are provided with the following information:
• The incremental IRR(A-B) = 7% per annum
• IRR(A) = 20% per annum and NPVA > $0 for all discount rates less than 20% per annum and NPV(A) < $0 for all discount rates greater than 20% per annum
• IRR(B) = 25% per annum and NPV(B) > $0 for all discount rates less than 25% per annum and NPV(B) < $0 for all discount rates greater than 25% per annum
Provide a written explanation, supported by a NPV graph, of the investment decisions you would make assuming different discount rates ranging from 0% p.a. to 30% p.a
We would invest in project A when discount rate is less than 7% p.a.
We would be indifferent between project A and B when discount rate is equal to 7% p.a.
We would invest in project B when discount rate is greater than 7% p.a. and less than 25% p.a.
We would be indifferent between investing in project B and another project with zero NPV if the discount rate is 25%
We would reject both projects if the discount rate was greater than 25% p.a.
Which professor won Nobel prize in 2025
Professor Richard Robson