Questions and Answers of Financial Modeling

1. Reconsider the leveraged-leasing example in this chapter. Show that if depreciation is straight line over 15 years, then the MPM rate of return is equal to the IRR. Explain.
4. Perform a sensitivity analysis (using Data|Table, see Chapter 26) on the certainty-equivalence factor in section 5.5, showing how the IRR of the differential cash flows varies with the CE factor.
3. Continuing with the same example: Find the maximum rental that ABC will pay and the minimum rental that XYZ will accept.
2. ABC Corporation is considering leasing an asset from XYZ Corporation. Here are the relevant facts:Show that it will be advantageous both for ABC to lease the asset and for XYZ to purchase the
1. 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
6. Suppose that the average EBITDA ratio for the bagel industry is 8. Use this EBITDA ratio to value Farmers Bagels' shares.
5. Do a sensitivity analysis of the section 4.6 valuation using the price/earnings (P/E) ratio, varying this ratio from 4 to 20.
4. Do a sensitivity analysis of the section 4.6 valuation using the market/book (M/B) ratio. Vary the M/B ratio from 0.8 to 2.
3. Extend the model in section 4.5 past 2001. Show that if Farmers will continue not to pay dividends, there will be a large buildup of cash and cash equivalents. "Fix" this problem by assuming that
2. The valuation model in section 4.5 assumes that increments to fixed assets at cost are a decreasing function of sales. Change the model and assume that net fixed assets are a constant function of
1. In the valuation model of section 4.5 for Farmers Bagels, build data tables that show the sensitivity ofa. The value of Farmers' equity to changes in the ratio of accounts receivable to sales.b.
10. This problem introduces the concept of "sustainable dividends": The firm whose financials are illustrated following wishes to maintain cash balances of 80 over the next 5 years. It also desires
9. In the project finance pro forma of section 3.9 it is assumed that the firm pays off its initial debt of 1,000 in equal installments of principal over five years. Change this assumption and assume
8. Repeat exercise 7, but this time replace the terminal value by an EBITDA ratio times year-5 anticipated EBITDA. Show a graph of the equity value of the firm as a function of the assumed year-5
7. In the valuation exercise of section 3.4, the terminal value is calculated using a Gordon dividend model on the cash flows. Replace this terminal value by the year-5 book value of debt plus
6. In the model of section 3.7, assume that the firm needs to have minimum cash balances of 25 at end of each year. Introduce this constraint into the model.
5. Consider the model in section 3.7 (where debt is the plug).a. Suppose that the firm has 1,000 shares and that it decides to pay, in year 1, a dividend per share of 15 cents. In addition, suppose
4. Referring again to the model of section 3.2, suppose that the fixed assets at cost follow the following step function:Incorporate this function into the model.
3. Suppose that in the model of section 3.2 the fixed assets at cost for years 1–5 are 100 percent of sales (in the current model, it is net fixed assets that are a function of sales). Change the
2. The model of section 3.2 includes cost of goods sold but not selling, general, and administrative (SG&A)expenses. Suppose that the firm has $200 of these expenses each year, irrespective of the
1. Here's a basic exercise that will help you understand what's going on in the modeling of financial statements.Replicate the models in sections 3.2, 3.7, and 3.8. That is, enter the correct
10. It is January 1, 1997. Normal America, Inc. (NA) has paid a year-end dividend in each of the last 10 years, as shown by the following table
9. You are considering buying the bonds of a very risky company. A bond with a $100 face value, a one-year maturity, and a coupon rate of 22% is selling for $95. You consider the probability that the
8. Consider a company that has βequity = 1.5 and βdebt = 0.4. Suppose that the risk-free rate of interest is 6 percent, the expected return on the market E(rm) is 15 percent and the corporate tax
7. Exercise on supernormal growth: ABC Corporation has just paid a dividend of $3 per share. You—an experienced analyst—feel quite sure that the growth rate of the company's dividends over the
6. A firm has a current stock price of $50 and has just paid a dividend of $5 per share.a. Assuming that investors in the firm anticipate a dividend growth rate of 10 percent, what is the firm's cost
5. On the spreadsheet associated with this chapter you will find the following monthly data for IBM's stock price and the S&P 500 index during 1998:a. Use these data to calculate IBM's β.b. Suppose
4. Consider the following dividend and price data for Chrysler Corporation:Use the Gordon model to calculate Chrysler's cost of equity in 1996.
3. Dismal.com is a producer of depressing Internet products. The company is not currently paying dividends, but its chief financial officer thinks that starting in 3 years it can pay a dividend of
2. 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 should be the market
1. ABC Corp. has a stock price P0 = 50. The firm has just paid a dividend of $3 per share, and knowledgable shareholders think that this dividend will grow by a rate of 5% per year. Use the Gordon
14. You have $25,000 in the bank, in a savings account that draws 5 percent interest. Your business needs$25,000, and you are considering two options: (a) Use the money in your savings account or (b)
13. You have just turned 35, and you intend to start saving for your retirement. Once you retire in 30 years (when you turn 65), you would like to have an income of $100,000 per year for the next 20
12. A mutual fund has been advertising that, had you deposited $250 per month in the fund for the last 10 years, you would now have accumulated $85,000. Assuming that these deposits were made at the
11. Redo the calculation of exercise 10, this time assuming that you make five deposits at the beginning of this year and the following four years. How much will you accumulate by the end of year 5?
10. You are considering a savings plan that calls for a deposit of $15,000 at the end of each of the next five years.If the plan offers an interest rate of 10 percent, how much will you accumulate at
9. You are considering buying a car from a local auto dealer. The dealer offers you one of two payment options:n You can pay $30,000 cash.n The "deferred payment plan": You can pay the dealer $5,000
8. You have just taken a car loan of $15,000. The loan is for 48 months at an annual interest rate of 15 percent(which the bank translates to a monthly rate of 15 percent/12 = 1.25 percent). The 48
7. Calculate the flat annual payment required to pay off a five-year loan of $100,000 bearing an interest rate of 13 percent.
6. An alternative definition of the IRR is the rate that makes the principal at the beginning of year 6 equal to zero.[5] This is shown in the preceding printout, in which cell E14 gives the
5. In this exercise we solve iteratively for the internal rate of return. Consider an investment that costs 800 and has cash flows of 300, 200, 150, 122, 133 in years 1–5 (see cells A8:B13 in the
4. The following cash-flow pattern has two IRRs. Use Excel to draw a graph of the NPV of these cash flows as a function of the discount rate. Then use the IRR function to identify the two IRRs. Would
3. You are offered an investment with the following conditions:n The cost of the investment is 1,000.n The investment pays out a sum X at the end of the first year; this payout grows at the rate of
2. You just took a $10,000, five-year loan. Payments at the end of each year are flat (equal in every year) at an interest rate of 15 percent. Calculate the appropriate loan table, showing the
1. You are offered an asset costing $600 that has cash flows of $100 at the end of each of the next 10 years.a. If the appropriate discount rate for the asset is 8 percent, should you purchase it?b.
1. Show that, if Xn is a martingale, then it has uncorrelated increments, i.e. E[(Xm - Xn)(Xk - X,)] = 0, where 0
Exercise 3.1.3 Verify that E(YFs) Y is true for t;
Exercise 3.1.8 Suppose that the simple integrand process Z is deterministic, i.e. that Z1,Z2, . . . , Zn are constants. Verify that, in this case, the stochastic integral Ytn is a random variable
Exercises 10.1 SVI parametrization Gatheral [89] presents the following \Stochastic Volatility Inspired" (SVI)parametrization of the implied volatilityBS(; k)2 = a + b(k ???? m) +p(k ???? m)2 +
Exercises 4.1 Conformal metrics on a Riemann surface Let us consider the metric on a Riemann surface ds2 = F(y)(dx2 + dy2)1. Compute the Christoel symbols ????k ij .2. Prove that the geodesic
Exercises 4.2 Christoel symbols Prove that under a change of coordinates from fxig to fxi0 g, the Christoel symbols do not transform in a covariant way but into????k0 i0j0 = @xk0@xp@2xp@xi0@xj0| {z
Exercises 4.3 Lie algebra A vector space G is called a Lie algebra if there exists a product (called Lie bracket) [; ] : G G ! G with the following properties Antisymmetry: [x; y] = ????[y; x] ;
Exercises 5.1 Generalized skew averaging Let us consider the LV model df = f +Xn i=1i(t)ln f f0i!dWt By using the proposition 5.3, prove that this model produces an equivalent implied at the
Exercises 6.1 Mixing solution and Hull-White decomposition For general SVMs, there is no closed-form formula for European call options.To circumvent this diculty, we can use asymptotic methods as
Exercises 6.2 Variance swap Compute the variance swap for the Heston and SABR model:VST =1 TZ T 0EP[a2s
Exercises 8.1 Markov LMM As seen in this chapter, the MC simulation of a LMM is time-consuming.The main problem comes from the drifts which are reminiscent of the non-Markovian nature of the HJM
Exercises 9.1 Symmetry 1. For a LVM dened by dft = C(ft)dWt, prove that the intrinsic fair value of a European call option dened as G(; f0;K) C(;K) ???? max(f0 ???? K; 0)is G(; f0;K) =p
Exercises 3.1 Volatility swap A Volatility swap is a contract that pays at a maturity date T the realized volatility realized (which is the square root of the realized variance) of a stock or index
Exercises 3.2 Ho-Lee equity hybrid model The purpose of this exercise is to price exotic options depending on a single stock and characterized by a large maturity date. As a consequence, the
Exercises 2.3 Wick's identity Let Wt be a Brownian motion.1. Prove that EP[eiuWt ] = e????u2t 22. Deduce the following formula, called the Wick identity, 8n 2 N EP[(Wt)2n] =(2n ???? 1)!2n????1(n ????
Exercises 2.1 Central limit theorem We have N independent r.v. xi = f+1;????1g such that p(+1) = p(????1) = 1 2 .We dene the sum X =PN i=1 xi 1. Compute the mean-value E[X].2. Compute the variance
Exercises 2.2 Prove that (2.1) satises the denition of a measure.
Exercises 2.4 Exponential martingale Let us dene Mt = exp(Wt ???? t 2 ) with Wt a Brownian motion. Prove that Mt is a martingale using the denition 2.9. Then prove that Mt is a (local)martingale
Exercises 2.5 It^o's isometry Let us consider a deterministic function f : R ! R.1. Prove that EP[Z t 0f(s)dWs] = 0 EP[Z t 0f(s)dWs2] =Z t 0f(s)2ds Hint: Assume that f(s) can be approximated by
Exercises 2.6 Ornstein-Uhlenbeck SDE The Ornstein-Uhlenbeck process is dened by the following SDE dXt = ????Xtdt + dWt with the initial condition X0 = x0 2 R.1. Is there a unique solution?Hint:
Exercises 2.9 P&L Theta-Gamma We study the variation of a trader's self-nancing portfolio composed of an asset with price St at time t and a European option with payo (ST ) at the maturity date T.
Exercise 1.3.12 If ν and θ are stopping times, then so are min(ν, θ) and max(ν, θ).Let ν be any nonnegative integer random variable that is finite with probability one. Let Xn, n ≥ 0 be a
Exercise 1.3.11 If θ is a stopping time, then θj = min(θ, j ), where j is a fixed integer, is also a stopping time. Clearly θj ≤ j .
a) Suppose that as a trader from Bank A, you call a trader at Bank B and ask for a quote on the Mexican peso. She quotes USD/MXN = 8.9767 - 86.Under this scenario, what are your three options, and at
Find the two-way GBP/DEM (British pound vis-à-vis the German mark) cross rate given the following market quotes: Foreign Exchange Rate BID OFFER GBP/USD 1.4402 1.4408 USD/DEM 2.2291 2.2296
Compute the bid and offer for the NZD against the CAD from the following rates of exchange. In other words, construct a NZD/CAD two-way cross rate. Here, both the NZD and the CAD are reported as
Fill in the missing legs (marked Ø and Ù) for the no-arbitrage spot FX quote table below. Be sure to show all your calculations. Foreign Exchange Rate BID OFFER AUD/EUR 1 0.6001 AUD/USD .5254
(a) Suppose that you are a US exporter of goods to New Zealand and have a NZD receivable due in 120 days. The forward dealers are all off at a market luncheon, and their prices are not available.
Not too long ago, we saw an MBA questionnaire circulated to corporate treasurers asking them whether they practiced formal risk management techniques. Would the following categories of recipients
Although we have followed convention in using the arithmetic mean of returns, for returns data, the geometric mean is often – and more correctly – used.The geometric mean g is defined implicitly
Here are some random variables of different kinds. What sort of density shape do you think each would have? (Look in particular at the symmetry, kurtosis angles, and whether the shape might be
We know from the Normal tables that for a standard Normal density, prob (z >1.96) = 0.025. Because the Normal density is symmetric, we can also say that prob (z Assume that the distribution of a
Do scatter diagrams for the following (the first variable named should be on the vertical axis):(i) Bond returns versus CD returns.(ii) Bond returns versus stock market returns (the S&P500).(iii)
(a) How might regression techniques be used for purposes of prediction?(b) If you use regression models for this purpose, what are the likely sources of error in your forecast? Assume that you have
Aptitude test: Can you be a stock analyst?(a) Look at the company names associated with the data in the date file. Bearing in mind what you know about the way that stock returns vary according to the
As a CAPM exercise, you can take a different tack and look at the beta for the government bond index against the share market. Theory suggests that at least for a pure discount bond, there should be
The ordered mean difference (OMD) was developed* as a technique in performance measurement that measures how well a given fund’s return does against a benchmark return. Essentially, it captures the
Can you think of some more examples - and perhaps better ones! – where you might want to hedge some price or return, but the available derivative instrument is not perfectly correlated with your
It has been said that the CAPM model and related portfolio models represent a form of hedge relationship. Suppose that you are a portfolio manager, and you find a stock that has a negative beta on
(You may need a bit of help with this one.) Take a random walk process as specified in the form (2) of Section 8.4 in the text. You are now at time 0, and you know B0.(i) What is the predicted value
Repeat Question 3 but this time with the process:Analyze the way in which the variance of your forecast increases or decreases with the horizon T, and relate this to the size of the absolute value of
Use your data in Example 8.4 to explore the time value of the option. Graph the price of the SPI call option against maturity. Notice how the time value diminishes more rapidly, the closer you get to
(i) Determine which of the following matrix products can be found, and find them.(a) AB (b) AC (c) CA (d) CB (e) BC (ii) Suppose that you have an N x 1 vector 1, whose every element consists of the
In Section 9.2 you will find an answer to the inverse of the matrix below.Check that answer is correct using Excel A = 2 1 1 105 3 42
Consider the following set of equations:(i) From first principles, try to solve it. Does this set have a unique solution?(ii) Write the set of equations in matrix-vector form.(iii) Relate the
Here are some useful manipulations with statistical applications.(i) Suppose that you have a N × k matrix of N observations on each of k random variables. This is often called a data matrix. What
Following the practicum of Section 9.5, you could try the following:(i) Pick a set of five stocks that you think will show nicely complementary properties for purposes of diversification. Then repeat
Compute P (possibly using mathematical Appendix A.1), where = P = (1.06) [1-((1.06))] 1-(1.06)
Find the annual compound rate at which $800 will double after eight years.
It is known that $4000 will accumulate to $4500 after five quarters. Find the quarterly rate of compound interest.
With interest at 6% per annum compound, how long will it take $1000 to accumulate to $1500?
A target retirement benefit of $200,000 is to be provided after seven years.This benefit will be funded by an initial contribution of $70,000 and a lump sum payment after five years. If the fund
A certain vintage car is expected to double in value in 12 years. Find the annual rate of appreciation for this vehicle.
How long does it take to triple your money at 10% per annum compound interest? (Hint: Use logs. See mathematical Appendix A.4.)
A special “bond” pays $60,000 in three years and a further $80,000 in five years from now. Determine the price of the bond assuming that the interest rate for the first three years is 3.5% per

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