Questions and Answers of Financial Modeling

On the companion site of this book are some year-end numbers for Cisco’s equity. Restate the enterprise value in market terms.
Use the template for the ABC Corp. valuation in section 2.6 to value Amazon’s stock (AMZN).Assume that the weighted average cost of capital for AMZN is 10%, the growth rate for years 1–5 is 4%,
Unheardof, Inc., has just paid a dividend of $5 per share. This dividend is anticipated to increase at a rate of 15% per year. If the cost of equity for Unheardof is 25%, what is the market value of
Dismal.Com is a producer of depressing Internet products. The company is currently not paying dividends, but its chief financial officer thinks that starting in three years it can pay a dividend
The current stock price of TransContinental Airways is $65 per share. TCA currently pays an annual per-share dividend of $3. Over the past five years this dividend has grown annually at a rate of
Consider a company that has βequity = 1.5 and βdebt = 0.4. Suppose that the risk-free rate of interest is 6%, the expected return on the market E(rM) = 15%, and that the corporate tax rate is 40%.
On the companion website for this book, you will find the following monthly data for Cisco’s stock price and the SP500 index. Compute the equation rcsco, t = αcsco + βcsco * rSP500, t and include
It is January 1, 2020. Normal America, Inc. (NA), has paid a year-end dividend in each of the last 10 years, as shown by the table below:a. Calculate NA’s β with respect to the SP500.b. Suppose
Suppose that the SP500 price/earnings ratio is 17.5 and its dividend payout ratio is 55%, and that you estimate a future growth of dividends of 8%. What is E(rM)? 1 B C COMPUTING E(M) FROM MARKET P/E
At the end of December 2020, the price/earnings ratio of the SP500 was 19.24. Assume that the index is a proxy for the market and that it has a 60% dividend payout ratio. Also assume that dividends
The template for this exercise (see this book’s auxiliary website) gives the prices of the Vanguard Index 500 Fund (VFINX). This fund’s prices replicate the SP500 with dividends reinvested. Use
The template for this exercise (see this book’s auxiliary website) gives the 10-year history of Intel’s quarterly dividends. Compute Intel’s cost of equity rE using the Gordon dividend model.
You are considering buying the bonds of a very risky company. A bond with a $100 face value, a 1-year maturity, and a coupon rate of 22% is selling for $95. You consider the probability that the
On the website that accompanies this book, you’ll find information for Kellogg. Use this information and the template in section 4.1 to value Kellogg.
Choose a company with the following characteristics:It is listed in the United States.It has positive operating cash flows.It has positive net debts.Download the balance sheet, income statement, and
Your company is considering either purchasing or leasing an asset that costs $1,000,000. The asset, if purchased, will be depreciated on a straight-line basis over six years to a zero-residual value.
Continuing with the above example: Find the maximum rental that ABC will pay and the minimum rental that XYZ will accept.
Perform a sensitivity analysis (using Data|Table) on the certainty-equivalence (CE) factor in section 6.5, showing how the IRR of the differential cash flows varies with the CE factor.
Replicate the two graphs in section 7.4.
On January 23, 2020, the market price of a West Jefferson Development Bond was $1,122.32. The bond pays $59 in interest on March 1 and September 1 of each of the years 2020–2026. On September 1,
Rewrite the formula Dduration in section 7.5, so that if the timeToFirstPayment α is not inserted, then α automatically defaults to 1.
Using the example of section 7.7:a. Find a combination of bonds 1 and 3 with a duration of 8.b. Find a combination of bonds 1 and 2 with a duration of 8.c. Which portfolio (a orb) would you prefer to
Using the example of section 7.7:a. Find a combination of bonds 1 and 3 with a duration of 12.b. Find a combination of bonds 1 and 2 with a duration of 12.c. Which portfolio (a orb) would you prefer
A newly issued bond with one year to maturity has a price of 100, which equals its face value. The coupon rate on the bond is 15%; the probability of default in one year is 35%; and the bond’s
Using the transition matrix of the previous problem, assume a C-rated bond is selling at par on July 18, 2007.The bond’s maturity is July 17, 2017; it has a coupon (paid annually on July 17) of
The exercise file for this chapter (see auxiliary website) contains monthly data for stock prices of Kellogg and IBM. Compute the return statistics and graph a frontier of combinations of the two
The Excel file for these exercises (which can be found on the website accompanying this book) gives five years of monthly prices for two Vanguard funds—the Vanguard Index 500 Fund (VFINX) and the
Calculate the envelope set for the four assets below and show that the individual assets all lie within this envelope set.You should get a graph that looks something like the following: A B 1 2 A
Below you will find annual return data for six furniture companies for the years 2010–2020. Use these data to calculate the variance-covariance matrix of the returns.The remaining exercises refer
Compute the returns of the data and the statistics for the each of the assets (mean return, variance and standard deviation of return, beta).
Compute the GMVP using the sample variance-covariance matrix.
Using the efficient portfolio instead of the SP500:a. Compute the monthly returns on the efficient portfolio.b. Regress the average monthly returns of the stocks on their betas with respect to the
You have decided to create your own index of higher-beta components of the Dow-Jones 30 Industrials. Using Yahoo’s stock screener, you come up with the following data:a. Compute the
You are an analyst investing in the high-beta portfolio from the previous problem. You believe that the monthly return of Schlumberger (SLB) will be 0.5% higher than the market expected return.What
Another analyst believes that SLB return will be 0.5% higher than the market expected return per month over the next year and that the NVIDIA Corporation (NVDA) return will be lower by 0.2%than the
A European call with a maturity of six months and exercise price X = 80 is selling for $12. The option is written on a stock whose current price is $85; a European put, written on the same stock with
Prove Proposition 6.Then solve the following problem: Three puts on shares of XYZ with the same expiration date are selling at the following prices:Exercise price 40: 6 Exercise price 50: 4 Exercise
The current stock price of ABC Corp. is 50.Prices for six-month calls on ABC are given in the table below. Draw a profit diagram of the following strategy: Buy one 40 call, write two 50 calls, buy
A stock selling for $25 today will, in a year, be worth either $35 or $20. If the interest rate is 8%, what is the value today of a 1-year call option on the stock with exercise price $30? Use the
All reliable analysts agree that a share of ABC Corp., selling today for $50, will be priced at either$65 or $45 one year from now. They further agree that the probabilities of these events are 0.6
A prominent securities firm introduced a new financial product. This product, called “The Best of Both Worlds” (BOBOW for short), costs $10. It matures in five years, at which point it repays the
This problem is a continuation of the discussion of section 17.6. Show that as n → ∞, the binomial European put price converges to the Black-Scholes put price. (Note that, as part of the
Here’s a simplified version of exercise 10.Consider an alternative parameterization of the binomial:Construct binomial European call and put option pricing functions in VBA for this
An investment bank is offering a security linked to the price, two years from today, for Bisco stock, which is currently at $3 per share. Denote Bisco’s stock price in two periods by S2. The
Use the Black-Scholes model to price the following:A call option on a stock whose current price is 50, with exercise price X = 50, T = 0.5, r = 2%, σ= 25%.A put option with the same parameters.
Use the data from exercise 1 and Data|Table to produce a graph comparing a call’s intrinsic value[defined as Max(S − X, 0)] and its Black-Scholes price. From this graph you should be able to
Use the data from exercise 1 and Data|Table to produce a graph comparing a put’s intrinsic value[defined as Max(X − S, 0)] and its Black-Scholes price. From this graph you should be able to
The table below gives prices for Apple (AAPL) options on April 10, 2020. The option with exercise price X = $270 is assumed to be the at-the-money option.a. Compute the implied volatility of each
Reexamine the X = 240 call for AAPL in the previous exercise. What price would be necessary for this call in order for the implied volatility to be 60%?
As shown in this chapter, Merton (1973) shows that for the case of an asset with price S paying a continuously compounded dividend yield k, this leads to the following call option pricing formula:a.
On April 10, 2020, call and put options to purchase and sell 10,000 euros at $1.0975 per euro are traded on the Chicago Mercantile Exchange. The options’ expiration date is April 30, 2020. If the
Note that you can use the Black-Scholes formula to calculate the call option premium as a percentage of the exercise price in terms of S/X:Implement this in a spreadsheet or R. C=SN(d)- Xe "N(d)
Note that you can also calculate the Black-Scholes put option premium as a percentage of the exercise price in terms of S/X:a. Implement this in a spreadsheet or R.b. Find the ratio of S/X for which
Produce a graph similar the second panel of figure 19.1 for puts. Delta 1 08 0.6 0.4 0.2 D -0.2 -0.4 -0.6 -0.8 Figure 19.1 20 -Call delta -Put delta 40 8 Stock price 80 100 120 140
Figure 19.2 shows the call theta as a function of time to maturity. Produce a similar graph for puts. Theta 6543NHO12 5 -6 -8 -9 -10 -11 -12 Stock price 20 40 80 100 120 140 -Call theta -Put theta
Although θ is generally negative, there are cases (typically of high interest rates) where it can be positive, including:An in-the-money put with a high interest rate An in-the-money call on a
Your company is considering purchasing 10 machines, each of which has the following expected cash flows (the entry in B3 of −$550 is the cost of the machine):You estimate the appropriate discount
Consider the project whose cash flows are given below:a. Using the state prices, value the project.b. Suppose that at date 2 the project can be abandoned at no cost. How is this affecting the value
Consider the cash flows below:a. If the cost of capital is 30% and the risk-free rate is 5%, find the state prices that match the project’s NPV.b. If there exists an abandonment option so that we
Here is a random-number generator you can make yourself:Start with some number, Seed.Let X1 = Seed + π. LetThe first random number is Random = X2 − Integer(X2), where Integer(X2) is the integer
Many states have daily lotteries, which are played as follows: Sometime during the day, you buy a lottery ticket, on which the seller inscribes a number you choose, between 000 and 999.That night
Marcus decides that he needs at least $2 million by the time he hits 60.Run 100 simulations in order to determine the approximate probability of achieving this goal.Compute the average and standard
Martha is playing a coin-toss game in which she tosses two coins. The probability of heads on the second coin is correlated with correlation ρ = 0.6 with the probability of heads on the first coin.
In section 22.2 we designed a macro that calculates the value of π using Monte Carlo and updates the screen every iteration. Modify the macro so that it updates the screen only every 1,000
Use Monte Carlo to calculate the integral of the function Exp(x) for 0 Here’s the graph of this function: 21 18 15 12 9 Exp(x) 3 0 0 9 13 0.5 Graph of Exp(x), 0 < x
One of the messages of this chapter is that while Monte Carlo is a clever method of calculation, it shouldn’t be used when some better method exists. The MC valuation of π in section 22.2, for
Here in exercise 5, we show you two alternative ways to compute the value of π. All are substantially better than Monte Carlo!a. The first method for computing π is:Use this formula to approximate
Assume that a stock is traded at $12. The stock has an expected annual return of 12% and standard deviation of 35% per year.a. Use Norm.S.Inv(Rand()) to produce a simulation of monthly stock prices,
Expand the previous exercise to produce a simulation of daily stock prices for 250 days(approximately one year of trading days).
Repeat question 3 but in R and not Excel.
Write a program (either in VBA or R) that reproduces the lognormal frequency distribution for an arbitrary number of runs. That is, this program should:Produce N normal random deviates.For each
The exercise file for this chapter contains daily price data for the SP500 and for Abbott Laboratories for the three months from April to June 2020. Use this data to compute the annual average,
The exercise file for this chapter gives daily returns from 1987 to 2020 for the Vanguard Index 500 Fund (VFINX). This is a fund that tracks the SP500, where the returns include dividends.Compute the
The previous example assumes that the risk-free rate is constant. An alternative, perhaps more plausible model might be to assume that the risk-free rate is mean reverting, with a long-run mean.Under
The website that accompanies this book gives five years of monthly price data for five U.S. stocks.Compute the monthly returns for the stocks.Compute the stocks’ average monthly returns and
Go back to the numerical example of section 26.5. Write a VBA function that solves for the implied asset value Va. (Hint: Use the bisection method.) Then use this function to create a graph showing
Create a VBA subroutine (call it Exercise1()) that generates a random number and prints it on the screen in a message box, which looks like this:Note: Use the VBA keyword Rnd. Microsoft Excel You
Create a VBA subroutine (call it Exercise2()) that generates five random numbers and prints them out on the screen in a message box like the following:Note: Use
Create a VBA subroutine (call it Exercise3()) that generates five random digits of either 1 or 0 and prints them out on the screen in a message box like the following: Microsoft Excel The random
Suppose a stock price follows a binomial distribution. We want to create a random price path for the stock in a VBA macro. Here is the input with some sample output:Write a VBA an appropriate
The Excel function PV(rate, number_periods, payment) calculates the present value of a constant payment. In the spreadsheet example below, for example:(Note that we have put the payment as a negative
Use Excel to perform the following matrix operations: 2 12 a. 48 2 780-23 10 -9 17 3 904 b. 50 256 206 C. 4 8 7 10-9 2 80-2 173
Find the inverses of the following matrices: C. b. a. 367 2227 214 2 2544 3220 COLL 9106
Transpose the following matrices using the Excel array function Transpose. 3 a. A=-15 2 3 b. B=-2 7-900 3-3 11 12 1
Describe the process of going public by a private company.
Describe the process of going private by a public company.
Identify the true statement(s) about corporation types from among the following:A. Nonprofit corporations by definition cannot generate profits.B. Transferring ownership from seller to buyer is more
From the corporate issuer’s perspective, the risk level of bonds compared to stocks is ___________.A. lower B. higher C. the same
True or false: Bondholders can become shareholders through non-market-based means.Justify your answer.A. True.B. False.
Explain potential conflicts of interest between debtholders and equityholders.
State a reason for the declining number of public companies in developed markets.
Which group of company stakeholders would be least affected if the firm’s financial position weakens?A. Suppliers B. Customers C. Managers and employees
Which of the following represents a principal-agent conflict between shareholders and management?A. Risk tolerance B. Multiple share classes C. Accounting and reporting practices
Which of the following statements regarding stakeholder management is most accurate?A. Company management ensures compliance with all applicable laws and regulations.B. Directors are excluded from
Which of the following issues discussed at a shareholders’ general meeting would most likely require only a simple majority vote for approval?A. Voting on a merger B. Election of directors C.
Which of the following statements about environmental, social, and governance (ESG)in investment analysis is correct?A. ESG factors are strictly intangible in nature.B. ESG terminology is easily
The existence of “stranded assets” is a specific concern among investors of:A. energy companies.B. health care companies.C. property companies.
An investor concerned about clean-up costs resulting from breaches in a publicly traded company’s safety standards would most likely consider which factors in her investment analysis?A. Social
_______ investing is the umbrella term used to describe investment strategies that incorporate environmental, social, and governance (ESG) factors into their approaches.A. ESG B. Sustainable C.
An investor concerned about a publicly traded company’s data privacy and security practices would most likely incorporate which type of ESG factors in an investment analysis?A. Social B. Governance

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