Questions and Answers of Financial Modeling

Calculate the holding period yield on a 90-day Certificate of Deposit (CD)bought at a yield of 5.0% p.a. and sold five days later at 4.8% p.a.
Suppose that on April 16, 2001, the following yields prevail in the market for US Treasury notes:Using linear interpolation, find the approximate four-year and five-year points on the above yield
If you are familiar with Excel you might like to try the following problem;otherwise you may prefer to attempt answering the question after you have read Chapter 5.In Question 1 you were asked to
An estate pays an annuity certain (cash payable whether or not the annuitant survives) of $50,000 per annum for five years. Assume the payments are made at the end of the period. From the sixth year
Find the present value of $500 payable monthly for six months. The first of the six payments occurs five months from now. The compound interest rate is 1.1% per month.
Find the effective rate p.a. if the nominal rate per annum compounded quarterly is 12%.
12% p.a. nominal compounded monthly is equivalent to what nominal rate p.a. compounded quarterly?
8% p.a. nominal compounded half-yearly is equivalent to what nominal rate p.a. compounded monthly?
Consider a bond with maturity date March 1, 2009, coupon 7% p.a. (paid semi-annually). The market yield increases from 7% to 8% on March 1, 2001.On a face value of $1m., what is the percentage change
Price the coupon bond of Question 6 on the March 2, 2001 at 8% market yield.Why is there a price difference? (This problem is more difficult as there is a partial coupon period).
Price a seven-year zero coupon bond with face value $1m at a market yield of 8% p.a. Assume semi-annual compounding. Price the same bond at a market yield of 7% p.a. and compare its sensitivity with
Calculate Macaulay duration for the bonds in Question 8, first at a yield of 7%, then at 8%.
Price a 180 day T-bill with face value $1m when the bank discount rate is 7%.
Price a 180-day CD at a market yield of 7%. Why is the price different from that of the T-Bill in problem 10?
Suppose that the table below lists prices of two Eurodollar time deposit contracts quoted on the Chicago Mercantile Exchange on June 12, 2001.The date is June 12, 2001. A corporate treasurer wishes
On June 12, 2001 a corporate treasurer managing a liability portfolio consisting of 22 million of ten-year fixed rate debt is considering interest rate forecasts in the ten-year area of the yield
Use the swap zero coupon rates to value two coupon bonds, each with face value $1,000,000 with maturity five years but with differing six-month coupon rates as follows:(i) A coupon rate of 10%(ii) A
Given your prices from Q1, calculate the yields to maturity for each bond. Are they the same?
In Chapter 2, we determined the duration of a set of cash flows by using the yield as the valuation tool. You can also find the duration by using the zero coupon rates; the result is called
Let’s do a bit of swap valuation. Well known lunchtime bon viveur Sherry van Plonk puts a five-year swap on her books at the set of zeros implied by the data in Table 3.6. She is receiving the
During their very enjoyable lunch, well known tax consultant Darth Evader has suggested to Ms. van Plonk that she do him a swap whereby he will make a single payment up front, in return for a set of
Find the Fisher-Weil duration of the swap in Question 4 above (valued using the post-lunch rates).
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 percent; the probability of default in one year is 35 percent; and the
Consider a case of five possible rating states, A, B, C, D, and E. States A, B, and C are initial bond ratings, D symbolizes first-time default, and E indicates default in the previous period. Assume
Consider the following two calls:• Both calls are written on shares of ABC Corporation, whose current share price is $100. ABC does not pay any dividends.• Both calls have one year to
A share of ABC Corporation sells for $95. A call on the share with exercise price$90 sells for $8.a. Graph the profit pattern from buying one share and one call on the share.b. Graph the profit
A European call with a maturity of six months and exercise price X = 80, written on a stock whose current price is 85, is selling for $$12.00;$ a European put written on the same stock with the
A stock selling for $$25$ today will, in one year, be worth either $$35$ or $$20.$ If the interest rate is 8 percent, what is the value today of a one-year call option on the stock with
All reliable analysts agree that a share of ABC Corporation, selling today for $$50,$ will be priced at either $$65$ or $$45$ one year from now. They further agree that the probabilities of
A stock is currently selling for $$60.$ The price of the stock at the end of the year is expected either to increase by 25 percent or to decrease by 20 percent. The riskless interest rate is 5
Produce a graph similar to Figure 20.2 for puts.
Figure 20.3 shows the call theta as a function of time to maturity. Produce a similar graph for puts.
Although θ is generally negative, there are cases (typically of high interest rates)where it can be positive:• An in-the-money put with a high interest rate• An in-the-money call on a currency
You are a portfolio manager, and you want to invest in an asset having σ = 40 percent. You want to create a put on the investment so that at the end of the year you have losses no greater than 5
Your company is considering purchasing 10 machines, each of which has the following expected cash flows (the entry in B4 of −$550 is the cost of the machine):You estimate the appropriate discount
Your company is considering the purchase of a new piece of equipment. The equipment costs $$50,000,$ and your analysis indicates that the PV of the future cash fl ows from the equipment is
Consider the project whose cash flows are as follows:a. Using the state prices, value the project.b. Suppose that at date 2 the project can be abandoned at no cost. What does this fact do to its
Suppose that the market portfolio has mean µ = 15 percent and standard deviationσ = 20 percent.a. If the risk-free rate of interest is 8 percent, calculate the one-period state prices for an up and
Consider the following cash flows:a. If the cost of capital is 30 percent and the risk-free rate is 5 percent, fi nd the state prices that match the project’s NPV.b. If there exists an abandonment
The attached spreadsheet fm3_chapter08.xls includes price data for the Dow-Jones 30 Industrials from July 1997 through July 2007. Isolating the data for Alcoa (AA)and Johnson & Johnson (JNJ),
Using the data from the previous exercise, compute the statistics for each of the preceding two subperiods, July 1997–July 2002 and July 2002–July 2007.
Suppose that in July 1997 you bought and held through July 2007 a portfolio composed of 50% Alcoa (AA) and 50% Johnson & Johnson (JNJ) stock.a. Compute the average monthly return and standard
Following are annual return statistics for two mutual funds from the Vanguard family:Use Excel to graph the combinations of standard deviation of return (x-axis) and expected return (y-axis) from
Using the database of the DJ Industrials (for 1997–2007), compute for General Electric (GE), Home Depot (HD), and Procter & Gamble (PG)a. Average monthly returnsb. Covariances of the monthly
Consider the following data for six furniture companies:a. Given this matrix, and assuming that the risk-free rate is 0 percent, calculate the effi cient portfolio of these six fi rms.b. Repeat,
Calculate the envelope set for the following four assets and show that the individual assets all lie within this envelope set.You should get a graph which looks something like the following: A B C DE
In the following table you will fi nd annual return data for six furniture companies between the years 1982 and 1992. Use these data to calculate the variancecovariance matrix of the returns. A B 1 E
For the fi rms from the previous example, calculate the variance-covariance matrix using the single-index model. Assume that the variance of the market portfolio is 18%.
In the Excel notebook fm3_problems10.xls on the disk accompanying this book, you will fi nd monthly price data for the 30 stocks in the Dow-Jones Index of 30 Industrials for July 1997–July 2007.
The following chart shows the variance-covariance matrix and the mean returns for six stocks. All the data are for monthly data (raw data are on the disk with the book).a. Compute the global minimum
This exercise asks you to repeat the computations of section 11.1 for a somewhat different percent. In the fi le fm3_problems11.xls you will fi nd monthly returns for the Dow-Jones 30 Industrials and
In a well-known paper, Roll (1978), discusses tests of the SML in a four-asset context:a. Derive two effi cient portfolios in this four-asset model and draw a graph of the effi cient frontier.b. Show
You have decided to create your own index of high-beta components of the DowJones 30 Industrials. Using Yahoo’s stock screener, you come up with the following data.a. Compute the
Distinguish between the four lenses of the balanced scorecard and provide an example of a business measure for each category for a family-owned grocery store.5. What are some problems that companies
ABC Corporation has a stock price P0 = 50. The firm has just paid a dividend of $3 per share, and intelligent shareholders think that this dividend will grow by a rate of 5 percent per year. Use the
Unheardof, Inc., has just paid a dividend of $5 per share. This dividend is anticipated to increase at a rate of 15 percent per year. If the cost of equity for Unheardof is 25 percent, what should be
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 of
Consider the following dividend and price data for Chrysler:Use the Gordon model to calculate Chrysler’s cost of equity at the end of 1996. A 1 B C CHRYSLER CORPORATION (C) E Year-end Dividend
The current stock price of TransContinental Airways is $$65$ per share. TCA currently pays an annual per-share dividend of $$3.$ Over the past five years this dividend has grown annually at a
ABC Corporation has just paid a dividend of $3 per share. You—an experienced analyst—feel quite sure that the growth rate of the company’s dividends over the next ten years will be 15 percent
You are considering buying the bonds of a very risky company. A bond with a $$100$ face value, a one-year maturity, and a coupon rate of 22 percent is selling for $$95.You$ consider the
Suppose that in the model of section 3.1 the fixed assets at cost for years 1–5 are 100 percent of sales (in the current model, it is net fixed assets which are a function of sales). Change the
Referring again to the model of section 3.2, suppose that the fixed assets at cost follow the following step function:Incorporate this function into the model. [100% Sales if Sales 1,200 1,200 <
Consider the model in section 3.6 (where debt is the plug).a. Suppose that the firm has 1,000 shares and that it decides to pay, in year 1, a dividend per share of 15 cents. In addition, suppose that
In the valuation exercise of section 3.4, the terminal value is calculated using a Gordon dividend model on the cash flows. Replace this terminal value by the year-5 book value of debt plus equity.
Repeat exercise 7, but this time replace the terminal value by an EBITDA ratio times year-5 anticipated EBITDA. Show a graph of the equity value of the firm as a function of the assumed year-5 EBITDA
In the project finance pro forma of section 3.9 it is assumed that the fi rm pays off its initial debt of $1,000 in equal installments of principal over five years. Change this assumption and assume
This problem introduces the concept of “sustainable dividends”: The firm whose financials are illustrated in the following spreadsheet wishes to maintain cash balances of 80 over the next five
Your company is considering either purchasing or leasing an asset that costs $$1,000,000.$ The asset, if purchased, will be depreciated on a straight-line basis over six years to a zero residual
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 asset
Continuing with the same example: Find the maximum rental that ABC will pay and the minimum rental that XYZ will accept.
Perform a sensitivity analysis on the certaintyequivalence factor in section 6.5, showing how the IRR of the differential cash fl ows varies with the CE factor
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.
In the leveraged-lease example of section 7.6, fi nd the lowest lease rental so that the MPM is equal to the IRR (assume the original depreciation schedule)
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.
You just took a $10,000, five-year loan. Payments at the end of each year are fl at(equal in every year) at an interest rate of 15 percent. Calculate the appropriate loan table, showing the breakdown
You are offered an investment with the following conditions:• The cost of the investment is $1,000.• The investment pays out a sum X at the end of the fi rst year; this payout grows at the rate
The following cash-fl ow pattern has two IRRs. Use Excel to draw a graph of the NPV of these cash fl ows as a function of the discount rate. Then use the IRR function to identify the two IRRs. Would
In this exercise we solve iteratively for the internal rate of return. Consider an investment that costs 800 and has cash fl ows of 300, 200, 150, 122, 133 in years 1–5(see cells A8:B13 in the
An alternative definition of the IRR is the rate that makes the principal at the beginning of year 6 equal to zero.In the preceding printout cell E9 gives the principal at the beginning of year 6.
Calculate the fl at annual payment required to pay off a fi ve-year loan of $100,000 bearing an interest rate of 13 percent.
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%/12= 1.25%). The 48 payments (to be
You are considering buying a car from a local auto dealer. The dealer offers you one of two payment options:• You can pay $30,000 cash.• The “deferred payment plan”: You can pay the dealer
You are considering a savings plan that calls for a deposit of $15,000 at the end of each of the next fi ve years. If the plan offers an interest rate of 10 percent, how much will you accumulate at
You currently 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
Use XIRR to compute the internal rate of return for the following investment: A B 1 Date Cash flow 2 30-Jun-07 -899 3 14-Feb-08| 70 4 14-Feb-09 70 5 14-Feb-10| 70 6 14-Feb-11 70 7 14-Feb-12 70 8
Use XNPV to value the following investment. Assume that the annual discount rate is 15 percent. 4567 A Date 30-Jun-07 B Cash flow -500 14-Feb-08 100 14-Feb-09 300 8 14-Feb-10 400 9 14-Feb-11 600 10
In the companion website to this book you’ll find the exercise Excel file for this chapter. This file gives data for three mutual funds. Compute the discrete annual returns for each fund and then
You just took a $10,000, 5-year mortgage loan. Payments at the end of each year are flat (equal in every year) at an interest rate of 15%. Calculate the appropriate loan amortization table, showing
You are offered an investment with the following conditions:The cost of the investment is $1,000.The investment pays out a sum X at the end of the first year; this payout grows at the rate of 10% per
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, and 133 in years 1 to 5.Setting up the loan
An alternative definition of the IRR is the rate that makes the principal at the beginning of year 6 equal to zero.9 This is shown in the printout above, in which cell E9 gives the principal at the
Calculate the flat annual payment required to pay off a 13%, 5-year mortgage loan of $100,000.
You are considering buying a car from a local auto dealer. The dealer offers you one of two payment options:You can pay $30,000 cash.You can choose a “deferred payment plan,” paying the dealer
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%, how much will you accumulate at the end
Redo the previous calculation, 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?
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
You currently have $25,000 in the bank, in a savings account that draws 5% interest. Your business needs $25,000, and you are considering two options: (a) Use the money in your savings account or(b)
Three years of balance sheets for Apple are given on the companion site of this book. Required:a. Restate these balance sheets so that the accounting enterprise value is on the left side.b. Use the
On the companion site of this book you’ll find Cisco’s consolidated statement of cash flows.Examine and transform it into a free cash flow.

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