Indicate whether the sentence or statement is true (enter “A” on your clicker) or false (enter “B” on your clicker).
Project F has a higher IRR however Project F has a lower NPV than Project G at low discount rates.
If the yield spread between U.S. Treasuries and the rate on your loans has remained constant, then your firm will likely benefit from refinancing its fixed-rate loans.
decrease in A/P (accounts payable)
It is therefore likely that Firm A has a higher CAPM equity beta than Firm B.
Multiple Choice (10 questions, 4 points for each question, 40 points total)
Identify the letter of the choice that best completes the statement or answers the question. For numerical problems, choose the response closest to (i.e. has the minimum absolute value from) the number you calculate.
Which of the following formulas, at a discount rate of 15% will properly calculate the Present Value of this sequence?
a. | PV = (1/1.15^1)*(100/(0.15 – 0.10)) | d. | PV = 100/1.15^3 + (1/1.15^4)*(110/(0.15 – 0.10)) |
b. | PV = (1/1.15^2)*(100/(0.15 – 0.10)) | e. | None of the other choices properly calculates the PV of this sequence. |
c. | PV = (1/1.15^3)*(100/(0.15 – 0.10)) |
a. | r_{A}> r_{E }> r_{D} | d. | r_{E}> r_{A}> r_{D} |
b. | r_{D}> r_{A}> r_{E} | e. | None of the other choices are true. |
c. | r_{A}> r_{D}> r_{E} |
a. | a high beta, and a high expected return | d. | a low/negative beta, and low/negative expected return |
b. | a high beta, but a low/negative expected return | e. | a high beta, and a zero expected return |
c. | a low/negative beta, but a high expected return |
a. | $600,000 | d. | $525,000 |
b. | $575,000 | e. | $500,000 |
c. | $550,000 |
a. | Non-diversifiable risk | c. | unique risk |
b. | Idiosyncratic risk | d. | Specific risk |
a. | The y-axis intercept | d. | The spread of the points about the line of best fit |
b. | The x-axis intercept | e. | The spread of the points above and below the average excess return |
c. | The slope of the line |
a. | The excess return on the market. | d. | The returns on high book-to-market firms versus low book-to-market firms. |
b. | The momentum of stock prices over time. | e. | All of the other factors were included in the Fama-French model. |
c. | The returns on small-firm stocks versus large-firm stocks. |
a. | The EAR, for a loan having 10% APR, is greater if it is compounded daily instead of monthly. | c. | The market value of a publicly-traded firm’s equity equals its stock price times the number of shares outstanding. |
b. | An annuity due is worth less than a regular annuity having the same discount rate and number of payments. | d. | For a given amount financed, assuming the same interest rate, the monthly payment for an interest-only mortgage is typically less than that for a traditional mortgage. |
a. | Varies the cut-off point with the interest rate | c. | Requires an arbitrary choice of a cut-off point |
b. | Determines a cut-off point so that all projects accepted by the NPV rule will be accepted by the payback period rule | d. | Both A and C |
a. | 500 | d. | 1 |
b. | 249,500 | e. | Impossible to determine |
c. | 250,000 |
Short Answer (8 questions, 10 points each, 80 points total)
You will need to show your work to get any partial credit in this section.
Factor Sensitivities | |||||
Factor | Coca-Cola | Ford | Pfizer | Microsoft | |
Market | 0.36 | 2 | 0.58 | 0.89 | |
Size | -0.23 | -0.03 | -0.47 | -0.07 | |
Book-to-Market | 0.38 | 1.1 | -0.15 | -1.17 |
Answer: _______________
Stock X: Expected return, 8%; Std. Deviation of return, 16.0%
Stock Y: Expected return, 7%; Std. Deviation of return, 12.0%
Correlation between returns on X and Y is 0.30.
What is the expected standard deviation of a portfolio that has 35% invested in Stock X and 65% invested in Stock Y?
Answer: _______________
Who cares more about diversifiable risk, the CEO of a publicly-traded firm or the firm’s shareholders? If there is a difference, explain why such a difference exists.
.
Given a 7-year straight-line depreciation schedule, a 35% tax rate, and an 8% discount rate, find the NPV of the cost of purchasing the machine. Note that the maintenance will cost $20K/year and the capital expenditure amount is $150K.
NPV = _____________
CAGR = __________ % per year
A/R = __________
You estimate the total operating expense for your division at $3.9M. You also estimate 31 Days Payable Outstanding. What is the estimate for A/P?
A/P = __________
CMH: -30%, -45%, 15%;
S: -20%, -30%, 5%.
Consider a portfolio that consists of 40% of CMH and 60% of S. Calculate the standard deviation of this portfolio. Answer as a percentage with two decimal places, as in 1.23%.
Answer: _______________
If the market capitalization rate is 8%, what is the price of Stock C?
Answer: __________
Problems (4 questions, points in parentheses, 110 points total). You must show your work for these problems! For interest rate questions, please answer with two numbers after the decimals, e.g. 1.23%.
For example, suppose your firm sells a sophisticated instrument. This instrument–which relies on Microsoft Windows for your customer to operate–creates random errors. (Everyone in your firm now realizes that NO ONE should EVER rely on WINDOWS for any operational software. Always use real software, not WINDOWS, for your business operational needs.) You may lose an occasional customer due to these errors. Should you fix all such errors? Certainly, there are many quality control zealots who would claim that you should fix every quality problem that ever arises. (Assume in the below that all cash flows occur at the end of the month. Assume 0% inflation and no taxes.)
NPV_0 = _______________
NPV_0 = _______________
Equivalent Annual Cost = _______________
Equivalent Annual Cost = _______________
.
PV = _______________
Using a 12% APR, and your renegotiated schedule, what is the present value of these lease payments?
PV = _______________
Change in PV = _______________
Payback period = _________ years
NPV = $ _____ K
iii) Now assume the impact of this development spending will not be felt in perpetuity but over 10 years only (i.e. in Years 7-16). Recalculate the NPV of the $300K spending in Development.
NPV’ = $ _____ K
Finance 325, Fall 2020, Midterm
Answer Section
TRUE/FALSE
An undiversified investor will prefer the lower standard deviation of Stock B.
A well-diversified investor is more concerned with market risk than with unique risk and would prefer Stock A.
PTS: 1
The key item, of course, is all else equal.
PTS: 1
The IRR rule would say to choose Project F as it has a higher IRR. However, at low discount rates, anyone choosing Project F would be making a mistake as Project G has higher NPV at lower discount rates.
PTS: 1
If g = r, then all the terms of the perpetuity have the same present value and then you are adding up the present values of an infinite number of such terms and that would give you an infinite present value.
If g>r, then you have the same situation only it’s worse as the present values of each of the terms are getting larger. Also makes no economic sense.
If g<r, then the present value of each successive term is getting smaller. This enables the infinite sum of these decreasingly-small present values to add up to a single number. (In math terms that is called “convergence.”)
PTS: 1
If T-Note yields have fallend, and if the yield spread is the same, then the firm can “call” its existing loans and refinance at much lower rates, potentially saving large amounts of interest expense.
However, if T-Note yields have increased, then your firm should remain happy that it has already contractually guaranteed a low rate of interest on its loans. It should definitely not refinance those loans at a higher rate of interest.
PTS: 1
TSLA is more exposed to macroeconomic risk and thus has a CAPM beta greater than 1.0.
PTS: 1
Firm A will do much better than Firm B when the economy does well but will do much worse when the economy does poorly. Thus Firm A will likely have a higher CAPM asset beta. And since the firms are financed with the same debt ratio, Firm A will also have a higher CAPM equity beta.
PTS: 1
MULTIPLE CHOICE
r_{E}> r_{A}> r_{D}
PTS: 1
The contract itself likely has a negative expected return and is negatively correlated to this student’s portfolio of assets. (They typical student has very little cash, no financial assets, limited possessions, the value of the car itself, and the value of his/her human capital.) Thus the contract has low/negative beta.
PTS: 1
Depreciate $600K over 10 years, or $60K/year. 6 years depreciation is $360K, thus book value is 800K – 360K = 440K.
PTS: 1
Firm-specific risk is diversifiable.
PTS: 1
Beta is given as the slope of the line of best fit in this model.
PTS: 1
There will be 500^2 terms total, or 250,000 terms. 500 will be firm-specific. The other 249,500 terms will be interaction terms related to the various covariances.
PTS: 1
SHORT ANSWER
r_PFE = 5 + 0.58*7.6 – 0.47*3.7 -0.15*5.2 = 6.89%
PTS: 1
Portfolio Variance = (0.35*0.16)^2 + (0.65*0.12)^2 + 2*(0.35*0.16)*(0.65*0.12)0.30
= 0.00314 + 0.00608 + 0.00262 = 0.0118
Portfolio std. deviation = 0.0118^0.5 = 10.9%
Note that the portfolio std. deviation is less than that for either stock.
PTS: 1
The CEO will care more about firm-specific risk than shareholders. Shareholders are generally diversified. The CEO, however, is typically not diversified or is typically far less diversified than shareholders. The CEO’s personal wealth will be very much overweighted depending on the firm’s results. The CEO may have stock options and incentives to reward performance. But even the CEO’s current and future salary depend more on the success of the firm.
Since the shareholders don’t care so much about firm-specific risk, you can see that they will likely tolerate more such risk than the CEO or the management team.
PTS: 1
There are a few ways to figure this out.
One way is to consider separately the maintenance (a 10-year annuity) versus the impact of depreciation (7-year annuity). Remember that the tax effect of depreciation is favorable and will offset, to some extent, the other costs.
The PV of after-tax maintenance costs is: PV_m = (20*0.65/0.08)(1-1/1.08^10) = $87.23K
The PV of the depreciation tax shield is: PV_dep = ((150/7)*0.35/0.08)(1-1/1.08^7) = $39.05K
The NPV of the cost of the machine = -$150K – 87.23K + $39.0K = -$198.18K
PTS: 1
(2382.12/1387.17)^(1/10) – 1 = 5.56% per year.
PTS: 1
A/R = $4.5M*(60/365) = $740K.
A/P = $3.9M*(31/365) = $331K
These figures closely resemble 2011 estimates for the MMDC division in the NHDC case.
PTS: 1
The returns of the portfolio are:
-24%, -36%, 9%.
Average portfolio return is -17%
The deviations from their means are (in percentage terms):
-7, -19, 26
Portfolio Variance = (1/(3-1))*(49 + 361 +676 ) = 1086/2 = 543 (Really 0.0543, if you were keeping score in decimal form)
Standard deviation = 543^0.5 = 23.3%
(Note that this problem follows closely your Bb homework assignment.)
Here is a snapshot that lays it out efficiently and correctly. (The square root sign was omitted, but was used.)
PTS: 1
Cash flows are:
t=1, $10
t=2, $11
t=3, $11.55
3% per year thereafter.
PV = 10/1.08 + 11/1.08^2 + (1/1.08^2)*(11.55 / (0.08 – 0.03) ) = $216.74
Alternatively, and longer way to do it…
PV = 10/1.08 + 11/1.08^2 + 11.55/1.08^3 + (1/1.08^3)*(11.55*1.03 / (0.08 – 0.03) ) = $216.74
PTS: 1
PROBLEM
PV of Benefits of the Fix = (1/1.01^5)*($1,000/0.01) = $100K/1.01^5=$95.15K.
The costs of the fix are an annuity. PV of Costs = (12/0.01)(1-1/1.01^5) = $58.24K.
The NPV to fix the problem is: 95.15 – 58.24 = +36.9.
The firm should fix the problem and generally firms will fix problems if they’re viewed as significant and perpetual.
PV of Fix = (1/1.01^5)*{(1/0.01)(1-1/1.01^31)} = $28.65K.
The costs of the fix are an annuity, same as in part (a). PV of Costs = (12/0.01)(1-1/1.01^5) = $58.24K.
The NPV to fix the problem is: 28.65 – 58.24 = -29.59. The firm should NOT fix the problem.
Generally firms will NOT fix problems if they’re viewed as insignificant and temporary.
PTS: 1
Calculate EAC_a, given a 14-year timeline:
$45.35K = (EAC_a/0.05)(1-1/1.05^14)
EAC_a = $4.58K
Calculate EAC_b, given a 19-year timeline:
$53.09K = (EAC_b/0.05)(1-1/1.05^19)
EAC_b = $4.39K
However, and this is a stretch, it could be that the quality of equipment available at time t=14 is much better than we currently expect and therefore the EAC will drop once it becomes apparent that such equipment is available. But forecasting prices 14 years in the future is a crapshoot, so to speak, and can’t really be done with any precision.
Also, you may think there are additional innovations that may arise over the next 5 years that are not now on the drawing board. So there is some “option value” in delaying your purchase until the next generation of technology arrives. The U.S. military, by the way, faces this problem all the time. Do we order equipment today, using the technology that is on the drawing board now, or do we wait a number of years until the next generation of innovations will deliver more powerful products?
For a down-home version of this question, you can ask me why I didn’t paint my fence by my house, now 19-years old. Or put money/effort into maintaining my 15-year old water heater. Or why I do very little maintenance on my 17-year-old car, or…you get the idea.
PTS: 1
It is critical to understand that 12% APR corresponds to a discount rate of 1% per month.
PV = 3 + (3/0.01)(1-1/1.01^23) = $64.37K
Alternatively, you can calculate
PV = (3/0.01)(1-1/1.01^24)*1.01 = $64.37K
You get the same answer either way.
The first annuity has PV as of time 0 of
PV = (3/0.01)(1-1/1.01^12) = $33.77K
The second annuity has payments that start at month 14 and go to month 25. The PV of these payments as of time 0 is
PV = (3/0.01)(1-1/1.01^12) / 1.01^13 = $33.77K / 1.01^13 = $29.67K
The PV of these two delayed annuities is
33.77 + 29.67 = $63.44K
Change in PV = $64.37K – $63.44K = $0.93K, which is approximately 1.5% of the PV of the original lease.
PTS: 1
iii) The unit cost savings form a 10-year annuity. NPV’ = -300 + 198.25/0.12*(1-1/1.12^10) = 820K
PTS: 1
NAME: ___________________________
(Your midterm is graded anonymously, only put your name in the above space.)
Reminders:
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Thank you for your cooperation!
T/F (20 pts) + M/C (40 pts) = _________
Short Answer (80 pts) _________
Long Answer (110 pts) _________
Total (250 pts) _________
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