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Frequently Asked Questions

Site: moodle@NovaSBE
Course: 2581-Advanced Financial Management-2425_S2
Book: Frequently Asked Questions
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Date: Saturday, 7 June 2025, 2:14 PM

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There are questions since the beginning till the last moment of any course. Answering to course questions is an important part of the learning process and this can be done, not only by instructors but also by students.



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Exercise Set 1 (Q5)

Question 5 of this exercise requires students to calculate the break-even point of sales (Total fixed costs/ (Gross profit/Sales)). Students ask why the net sales value is considered as Revenue here instead of the Total Revenue. The reasoning is that we consider net sales (i.e. sales - loyalty program costs) as this is the actual value the firm has received. Loyalty programs work as discounts and therefore should be subtracted.



Exercise set 2 (Q12a)

Doubts arise in this question as to which rate to use, and why the Rm has been used instead of the EAR.

Students should always take into consideration the periodicity of the cash flow stream to understand which rate should be used to discount the cash flows. In this question, the cash flows are expected to be monthly, and the APR is compounded monthly and so this is the correct rate to use. It should be divided by 12 to arrive at the monthly rate (5%/12 = 4.167%) which is the Rm.

Alternatively, even if students first convert the APR to an EAR as follows: EAR = (1+(5%/12))^12-1) = 5.116%
And then calculate the monthly Rm
Rm = (1+5.116%)^1/12 - 1 = 4.17%

They will arrive at the same Rm.

The key takeway is that whenever we have an annuity/perpetuity we must al- ways match the discount rate with the periodicity of the cash stream.
a. If you receive every year, you use the EAR
b. If you receive every month, you use the APR monthly compounding divided by 12.


Exercise set 2 (Q12b)

Students have been asking why some Future values are discounted to the power of a few months instead of the whole year and vice versa to arrive at Present values.
For instance, in Exercise Set 2, question 12b, the future value has been calculated taking into consideration only 11 months and not 12. This is done because the question explicitly requires us to calculate the money Mr. Paulino will have on his 40th birthday if he only starts saving two months from now.

The Present value is always calculated for period N-1 (which is the last day of the previous month), hence if savings start in the end of February of Year N, we will discount it to the end of January of year N to find the present value. Following this reasoning, 12 months - 1 month of discounting gives us an 11 month period.



Midterm exam 2019 (Q2a)

For project 1, the question states that the first positive cash flow occurs 3 years from now and grows at 0.5% forever. When a cash flow is expected to occur forever, the Present Value is calculated using the perpetuity formula.

Here, some students ask why the discounting period in the perpetuity formula is 2 years instead of the 3 years stated in the question. The answer is that the perpetuity formula provides the PV of a stream of CFs, where the first CF occurs at the end of the first year.

Thus, when applying the formula to the CF of 10,000 in 3 years, the perpetuity formula gives the value in the year before, that is, in year 2. Therefore we then discount 2 periods to get the PV at t=0.

For project 2, it is stated in the question that cash flows will start in year 3 and will grow at 2.5% for three years (i.e. from year 3-4, 4-5, and 5-6). Students have asked why the annuity has been powered to 4, despite the cash flows only growing during the next 3 years.

The logic behind powering the annuity to 4 years is that there is a cash flow in year 3 itself as well, and so in total there are 4 periods in which the CFs are expected to be received. Hence, we are going to consider the year 3, year 4, year 5 and year 6 CFs to arrive at the annuity value.

Students may be confusing the period here, as in some other exercises we have only taken into consideration the CFs in the years when there is growth and the initial CF is discounted separately when it does not have growth.



Review Quiz 2 (Q10)

In Q10 of the review quiz, some students have asked about how to solve the question. Going by steps, the solution would be as follows:
1. First calculate the Future value of the college fee 18 years from now, taking

into consideration the stated growth rate of 4%. FV=PV x (1+g)^n
FV=12.500 x (1.04)^18
=>25.322

2. Next, using the PV of a growing annuity formula, calculate the present value she will need to have available at the age of 18 to pay for all 4 years of her undergraduate education:
PV of a growing annuity= CF1/r-g x (1- (1+g)^n/(1+r)^n)

= 25.322/7%-4% x (1-(1+4%)^4/(1+7%)^4) = 90.754

This $90.654 is not the final answer, as the PV we have arrived at is the PV at the age of 17 (remember PV is always the present value in period N-1) and so it should be forwarded one year to arrive at the PV at age 18:
= 90.754 x (1.07)

=> $97.107 ~$97.110



Exercise Set 3 Stocks and Bonds (Q6)

This question asks what would happen to the share price if instead of a 100% payout ratio, it were to have a policy of distributing only 40% of its earnings as dividends and the remaining would be invested to generate an ROE of 8%.

Here, the following formula will enable us to calculate the share price: S0 = Dividend x (1+g)/(R-g)
Where dividend = €5 x 40% = 2
And growth rate = 60% x 8% = 4.8%

S0 = 2 x (1+4.8%) / (10%-4.8%) S0 = €40.3

In this way, students may prove mathematically that the price will go down. Alternatively, using intuition, students could understand that the price will decrease as the ROE (8%) < Return required by shareholders (10%), which means if the company is retaining part of its earnings, it will generate less than the discount rate, justifying a lower share price.





General question

Students ask about how a positive retention rate could lead to a negative PVGO.
The answer is that when shareholders are able to get a return higher than the project’s ROE elsewhere, a positive retention rate would lead to a negative PVGO as the company is not as efficient in generating returns as is the share- holder by investing elsewhere. Hence in this situation (ROE < Required return of shareholders) the shareholders would prefer the firm not to invest in its own projects, but to invest themselves in external projects.



General question

Students have often questioned the interpretation of a negative Return on Equity (Net income/BV of equity) which usually happens in the following two situations:
1. When the net income is negative, which may imply that the company is currently incurring some losses and should be interpreted based on the company’s financial situation.

2. When the Book value of equity is negative, and hence despite having a positive net income, the ROE is going to be negative due to a negative denominator. In this instance, a higher ROE (even though it is negative) may imply that the company is performing well in terms of profit generation.

In both instances, students should look for the details behind this ratio and justify their interpretation.



Assignment

When asked to estimate betas based on monthly data from past years, students ask if for the sake of consistency, they should use monthly average returns of both the market portfolio and risk-free assets.

The beta measures how much returns of a stock move when the return of the market moves. More specifically, it measures how much the return of a stock increases when the market return increases by 1 percentage point. It is a sensitivity metric and therefore does not necessarily depend on whether returns are monthly or annual. Therefore, we don't annualise the beta as it already captures the correct measure. By using monthly returns, the CAPM result will be a monthly return and so has to be annualised in the end.


Exercise set 5 (Q8)

The question asks to select the correct answer assuming a world where the CAPM conditions are verified. The correct answer is d) One stock with higher volatility might have lower expected return than another stock with lower volatility.

Investors can eliminate company-specific risk (Idiosyncratic risk) simply by properly diversifying portfolios, they are not compensated for bearing unsystematic risk. And because well-diversified investors are exposed only to systematic risk, with CAPM the relevant risk in the financial market’s risk/expected return tradeoff is systematic risk rather than total risk. Thus, an investor is rewarded with higher expected returns for bearing only market-related risk. Therefore, in d) stock A with higher volatility might have lower expected return than another stock B with lower volatility, if its systematic risk is lower than B's systematic risk (which implies that A has a higher idiosyncratic risk than B).


General question

Some students have had doubts regarding the calculation of the salvage value of an asset. The salvage value formula is as follows:
Salvage value = Sale price of asset - (t x Gain on Sale)
Which gives the value net of taxes that the firm will receive by disposing the asset. When there is a loss on the sale of an asset, the company has the right to pay a lower tax (it works as a subsidy), and so the tax amount should be added to the sales value.

The Gain on Sale is the taxable amount from the sale.
Gain on Sale = Sale price - Book Value of the asset (at the time of the sale).

Note: Refer to slide 6 of the in-classroom lectures for further details.



General question

In this unit, a frequent question is regarding the number of shares to consider while calculating the price of each share in the merged company. Students can obtain information regarding the merger/acquisition from the question itself and obtain an understanding as to what will happen to the acquired company’s shares. For e.g. where the acquirer buys the target and the target ceases to exist, its shares disappear. In this case, the total number of shares of the acquirer firm stays constant.

On the other hand, if the target is paid in shares instead of cash, the target company would receive new shares in the new merged firm and so the quantity of shares to consider for the merged company would be the number of shares the merged company now has in total (hence, include any shares issued as payment to the target company, and exclude any shares that disappear after the acquisition).



Exercise Set Calculating synergies value (Q2)

The last question of this exercise asks to calculate the total value of synergies after the acquisition. Students ask why we multiply the increase in sales (€1.2 x 10%) by the gross margin (40%) instead of simply taking the increase in sales (€1.2 x 10%) amount.

The reason is that the synergies should measure the incremental FCF the firms will receive. Hence, the increase in sales that should be included should not be the full 10% x 1.2M because the firm does not receive that full value at the end of the day. The increase in sales is accompanied by an increase in variable costs, and that should be taken into account. This is why we multiply by the gross margin.




Exercise set 8 (Q1 & Q2)

Students have asked why in certain situations, the following formula is used to calculate the Cost of Equity (Re) = Ra + D/E (Ra - Rd), while ignoring the tax implications on the cost of equity (1-T). The answer is that when the D/E ratio is constant, we should assume that the Beta of the ITS is equal to the beta of A and therefore the following proposition holds: Re = Ra + D/E (Ra - Rd).

On the other hand, when we assume beta of ITS is equal to beta of D, then proposition II is Re = Ra + D/E (Ra - Rd) (1-t).

However, the calculation of the WACC should always take into account the tax rate, and hence be the after tax WACC.

Further details can be found in slides 44-47 of the video lectures.



Exercise set 8 (Q3)

In exercise 3, the firm is considering the issuance of €25 million of debt and buy back shares. Here, students ask why the share price remains the same before and after the issuance of debt. The reason is that the NPV of the debt issue is zero as all the MM assumptions hold and so capital structure has no impact on the value of the firm.

On the other hand, in exercise 4 the share price goes from €100 to €96.75 after the debt issuance. This happens because there are two imperfections here: taxes and bankruptcy and so the NPV of the debt issue should take into consideration the PV of the Interest tax shield as well as the PV of costs of financial distress.

Students should aim to understand what the NPV of the project is in each situation. The project in this case is the debt issue. On announcement of the debt issue, the stock price immediately reflects the new information that the firm is doing a negative NPV project. On announcement, the firm has not undertaken the project yet and so the number of shares outstanding are unchanged at this point. And so the value of the firm (and of equity) becomes V = Vu + NPV = 100 - 3.25 = 96.75. Dividing this by 1 million shares outstanding, we can obtain the share price. After this, the firm issues debt and repurchases shares, but no new information becomes available and therefore the share price does not change further.

Note: For more details, consult the video lecture on Capital Structure between slides 5 and 11 (NPV and the value of the firm).



General question

Students ask about the discount rate at which the PV of the Costs of financial distress should be calculated. The answer depends on what the risk of the Interest tax shield is:

  • If D is permanent or low, Beta {ITS} = Beta (D) and that means you should discount ITS with rD

  • If D/E is constant or high, Beta {ITS} = Beta (A) and that means you should discount ITS with rA.

Note: For more details, consult slide 18 of the video lectures on the Limits of Debt.