Exam Midterm Finance 340 February 13, 2008 Name:
Exam Instructions: This exam should have 8 pages (including this one) and 15 questions: 8 multiple choice, and 7 problem-solving or short answer. Multiple choice questions are worth 3 points each; the point value is given for the other problems. The entire exam is worth 100 points. You may use a calculator and the provided formula sheet on this exam. You must show your work in order to receive credit for your answers. Partial credit will be given for partially correct answers. If a question asks "Why/Explain", you should give an explanation that would convince a skeptic. You may use the back of a page if you need additional space to write an answer.
Solutions
Suggestions: Use your time wisely. Move on to another problem if you feel like you're stuck. You may ask me questions if you are unclear about a problem. I might be able to clarify the problem for you.
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Business Finance Midterm Exam
d
1. The current real rate is 2.25% and the inflation rate is 2.40%. What precise rate would you expect to see on a Treasury bill? Circle the most accurate answer, to the nearest 0.01%. a. 1.00% b. 2.65% c. 4.65% d. 4.70% e. 5.19% f. None of these.
b
2. You need to borrow $20,000 to buy a new car. You have 2 choices: borrow from bank A which charges 10% compounded annually, or from bank B which charges 9.80% compounded monthly. Which would you choose and why? a. b. c. d. e. A because the future value in one year is higher. A because it has a lower effective annual rate. B because it has a lower effective annual rate. B because it has a lower APR. A because it has the higher quoted rate.
d
3. A bond with an annual coupon of $70 originally sold at par for $1,000. The current market interest rate on this bond is 8%. This bond will currently sell at a . Additionally, any person (who does not currently own the bond) that buys the bond today, and holds the bond until maturity, will realize a capital . a. b. c. d. e. f. discount; premium; premium; discount; par; par; loss gain loss gain loss neither loss nor gain
d
4. The future value of a single lump sum will increase more rapidly when: I. II. The interest rate increases. The interest rate decreases. b. III only. III. IV. The frequency of compounding increases. The frequency of compounding decreases.
a. I only.
c. II & III only. d. I & III only. e. I & IV only. f. None of these.
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Business Finance Midterm Exam
d
5. In the evaluation of cash flow in a capital budgeting decision, which of the following is/are NOT relevant? Circle the best LETTER below. I. The size of the cash flow. II. The timing of the cash flow. III. The risk of the cash flow. IV. The accounting earnings from the cash flow. a. b. c. I only I and II only II only d. IV only e. II and IV only f. They are all relevant.
d
6. A friend who owns a perpetuity that promises to pay $8,000 at the end of each year, forever, comes to you and offers to sell you all of the payments to be received after the 10th year. At an interest rate of 8%, what is the maximum amount you be willing to pay today to receive payment numbers 11 and onwards? (Answer within $1.00.) a. $3,705.55 b. $8,000.00 $42,888.29 d. $46,319.35 e. $100,000 f. none of these.
(This question is similar to Short Answer problem #15 on page 6 of Quiz 1 practice problems.) The value of the perpetuity at year 10 is $8,000/.08 = $100,000, and the present value today is 100,000 / 1.0810 = answer shown in (d.).
b
7. Obama Products, Inc. just issued 10-year, 8% coupon bonds at par value. Outstanding Clinton Corp. bonds, which currently have a maturity of 10 years, sell at a premium to par and are viewed by investors as having the same risk as the Obama bonds. Therefore, it must be true that: a. b. c. d. e. f. The coupon rate on the Obama bonds is equal to that on the Clinton bonds. The coupon rate on the Obama bonds is lower than that on the Clinton bonds. The coupon payment on the Obama bonds is higher than that on the Clinton bonds. The yield to maturity on Obama bonds is higher than the yield to maturity on Clinton bonds. The Obama bonds are priced at a premium. None of these are true.
Since Obama bonds were issued at par, then the YTM on these bonds equals the coupon rate of 8%. Clinton bonds have the same risk and maturity as Obama bonds; therefore Clinton bonds must have the same YTM. If Clinton bonds are selling at a premium, then the coupon rate is more than the YTM, and therefore more than the coupon rate on Obama bonds. c 8. You plan to borrow at an offered rate of 10.20 percent APR, compounded weekly. What is the effective annual rate you pay on this loan? a. 10.20%
EAR 1
b. 10.60%
.102 52
52
c. 10.73%
d. 19.62%
e. 53.04%
f.
none of these.
1 ; EAR = 10.73 percent
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Business Finance Midterm Exam
Problem Solving and Short Answer:
1. TRUE/FALSE & EXPLAIN: The goal of a financial manager is to maximize earnings. [8 pts] FALSE. The goal of the financial manager is to increase the value of the company (increase shareholder wealth), by maximizing the PV of cash flows. Maximizing earnings is not the same thing. First of all, earnings are not cash flows, but are accounting constructs instead. You can't buy anything with earnings, but you can buy things with cash flows. Second, which earnings should I maximize? I could maximize this year's earnings by not spending anything on future production, thus killing next year's earnings. How should I weight earnings in various years? Luckily NPV evaluates all future cash flows for us!
2.
Assume the following term structure of interest rates:
1 year 2 years 4.0% 4.2% All rates are quoted as APR's.
3 years 4.4%
4 years 5.0%
a. What is the price of a 3% coupon bond, with face value of $1,000, that matures in exactly 3 years? [5]
PV
30 1 .04
1
30 1 .042
2
1030 1 .044
3
28.85 27.63 905.18 961.66
b. Assume you don't have your calculator. If you had to estimate the yield-to-maturity on the bond in the question above within 10 basis points (0.10%), what would your best guess be? Explain your reasoning. [5]
I would guess around 4.38% (answers greater than 4.3% and less than 4.4% are acceptable estimates--the exact answer is 4.392%). Since YTM is a weighted-average of the discount rates for the cash flows in the bond, it must lie between 4% and 4.4%. Since the weights are approximately proportional to the size of the cash flows, the weighted average will be pulled much more toward 4.4% than toward 4%.
c. Consider the price of the bond above, compared with the price of a 3-year $1000 zero-coupon bond (STRIP). Show the price of the STRIP. Why do the prices of these bonds differ? Explain the difference in the prices. [4]
The STRIP has only one cash flow, $1000 at maturity. Since the coupon bond pays $30 every year in addition to the $1000 at maturity, it must have a higher price. (For the curious, the price of the STRIP = PV
1000 1 .044
3
878.82 )
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Business Finance Midterm Exam
3. List and explain the three components of an interest rate (required rate of return). [6] (This was covered in class twice, and on Quiz 1.) The determinants of an interest rate or required return are: Real risk-free rate of interest--the underlying compensation that you demand, even if you know you will get your money back. Expected inflation--additional compensation to account for the expectation that prices will rise before you get your money back Risk--additional compensation that varies depending on how risky the investment or borrower is. The more risk, the higher the required return
4. Last week, President Bush issued a $3.1-trillion fiscal 2009 budget proposal, with wide expectations that the US will incur record levels of deficits (borrowings) for 2008 and 2009 to support this government's level of spending. The proposed budget represents a $1.2 trillion increase since Bush took office after President Clinton, beginning in 2001. Assume the inflation rate averages 3.0% annually from 2001 through 2009. Show (to 0.01%) the nominal annual growth rate and real annual growth rate in spending during this period. Has spending increased in real terms? [10] (Rates of growth are similar to rates of interest--in basic terms, a rate of interest can be thought of as the growth of rate an investment.) Nominal growth rate: r = (FV / PV )^(1/t) 1 = (3.1 / 1.9)^(1/8) 1 = .0631 = 6.31%
Real growth: (1+r) = (1+nom) / (1+infl) r = (1.0631)/ (1.03) 1 = .0321 = 3.21% Thus, spending has increased in real terms. That is, given these figures, government spending has increased by 3.21% annually in real terms--and, at an annual nominal rate of over twice that as the annual inflation rate. You could also calculate $1.9 * (1.03)^8 = $2.41 trillion, which would equal the inflation-adjusted 2001 spending in 2009's dollars. Then compare this to the $3.1 T budget proposal, and see that indeed, real spending will have increased.
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Business Finance Midterm Exam
5. Last year, Cingular announced plans to launch a music service on its cell-phone network in partnership with Napster, Yahoo and other online music providers. Hinterland Wireless, operating in North and South Dakota, plans to jump on this bandwagon and deliver "True Country" songs over its network. For planning purposes, Hinterland management believes that cash flows can be realized for 3 years, but that competition and technological change will necessitate termination of the venture at the end of year three. Over the last month, Hinterland spent $150,000 on focus groups to see if its customers would use the service (the response was enthusiastic!). To serve this small niche, Hinterland will need to both invest in new equipment worth $900,000, and use existing equipment. The new equipment will be depreciated under the straight-line method to a zero book value over the 3-year life of the project. They will be able to sell this equipment for $200,000 at the end of three years. The existing equipment is currently fully-depreciated to its salvage (book value) of $10,000, and currently has no other use at the company. Hinterland could sell this existing equipment for $40,000 today; it will be worth nothing after 3 years. The company expects increases in revenue of $1,040,000 each year for 3 years, with additional costs of $680,000 each year. Net working capital will immediately increase from $20,000 to $60,000 today if the project is taken, stay at that level, then return to the $20,000 level at the end of year 3. The tax rate is 34%. Their opportunity cost of capital is 11%. Should Hinterland embark on this venture? [18]
Note the focus groups are money already spent, and therefore sunk costs, and irrelevant. For this problem, you could use the following setup, with the following calculations: Proceeds in year 3 = 200,000 (200,000 0)*(0.34) = 132,000 Opportunity cost of existing equip. = 40,000 (40,000 10,000)*(0.34) = 29,800 Change in NWC is 40,000 immediately, therefore a 40,000 outflow now.
(#s in 1000s) revenues - costs - depr = EBIT - taxes (34%) = NI + depr - cap exp + proceeds - opp cost + CF from NWC = FCF 0 1 1,040.0 680.0 300.0 60.0 20.4 39.6 300.0 2 1,040.0 680.0 300.0 60.0 20.4 39.6 300.0 3 1,040.0 680.0 300.0 60.0 20.4 39.6 300.0 132.0 29.8 -40.0 -969.8 339.6 339.6 40.0 511.6
900.0
Calculating the NPV:
1 1 172.0 14.15 thousand 3 3 .11 .11 1.11 1.11 The NPV is negative, so Hinterland should not undertake the project. ( If you assume that the old equipment will be written off as worthless at the end of three years (which would be technically more accurate), then add a tax benefit of 0 .34*(0-10,000) = 3400 in year 3. Including this tax benefit increases the NPV by $2.49 thousand to -11.66 thousand. This was easy to miss on exam day, so I graded leniently on this point. ) NPV 969.8 339.6
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Business Finance Midterm Exam
6. You currently have a 30-year fixed rate mortgage with an annual interest rate of 8% and monthly payments. The initial principal was $300,000, and you have made 18 monthly payments so far. You are considering refinancing your mortgage, and your friendly mortgage broker has offered this mortgage: a new 30 year fixed-rate loan at a 7% APR, compounded monthly, with three points. To arrange the new loan, you will also pay fixed transactions costs (in addition to the points) of approximately $1,500. Assume that by the time your refinancing closes (60 days from now), you will have made 2 more payments on your current mortgage. Also assume that the new principal amount you refinance will equal the remaining principal balance outstanding on your original mortgage as of the closing date. Assume you plan to be in your house for 4 years after the closing date of the refinancing, at which point you sell your house and repay any remaining principal outstanding on your mortgage. You may ignore taxes for your analysis. Assume that your annual opportunity cost of capital is 6% (compounded monthly), and that monthly mortgage payments are made at the end of each month. Answer the following questions to analyze the attractiveness of this refinancing: a.) What are your monthly mortgage payments with your current mortgage? [5]
(This entire question (#6) follows the mortgage refinancing case, simplified to one alternative.) Your monthly payments are:
PMT
principal PV (annuity)
1 .08 12
300,000 1 .08 .08 360 (1 ) 12 12
$2,201.29
b.) Assume that you may NOT finance the points or closing costs--these costs must be paid upon closing. What will be the amount of your new loan? [5]
By the time the refinancing closes, you will have made 20 monthly payments, so there will be 360 - 20 = 340 payments left, and your remaining principal will be
PV= 2201.29
1 .08 12
1 .08 (1 12 .08 340 ) 12
$295,708.66
c.) What would be your monthly mortgage payments under the new loan? [4]
If you refinance, your beginning principal on the new mortgage will be $295,708.66. To compute your payments:
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Business Finance Midterm Exam
.07 12 295,708.66 .07 1 (1 ) 12
$1,967.36 ; equivalent , ly
360
1 .07 12
295,708.66 1 .07 .07 360 (1 ) 12 12
$1,967.36
d.) For now, ignore any differences in principal outstanding with either loan in 4 years. Using the figures you calculated above, analyze the value of refinancing. Based on your calculations, should you refinance your mortgage, and why? (If you are unsure of your answer for part c., you may assume the new loan payments are $2,000--this is incorrect, but you may proceed using this figure.) [6] Calculate the monthly savings of the new mortgage (relative to your current mortgage). Compare these savings to the associated transactions costs by using the NPV tool.
New loan SAVINGS (monthly): Old pmt. 2,201.29 New pmt. 1,967.36 Savings 233.93 COSTS (at closing): Points 8,871.26 Fixed 1,500.00 Total 10,371.26 In order to decide about refinancing, you need to compare the initial cost (points plus fees) with the benefits. To compute the NPV of the new loan, use the 6% opportunity cost of capital (.005 per month), and calculate the PV of the payment savings for 48 months (assumed time you will keep the house):
1 (1 .005) 48 .005 NPV = -10,371.26 + 9,960.94 = -410.32 (rounding may result in slightly different numbers. If you used $2000 for new pmt, your monthly savings will be 201.29, the NPV = -1,800.27 and same decision results.) NPV 10371.26 233.93
The NPV is negative; therefore, you should not refinance.
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Business Finance Midterm Exam
e.) (Extra credit--all or nothing--do this last, if at all!) What will be your remaining principal balance 4 years from the closing date with your current mortgage, and under the new mortgage? Does this additional calculation change your answer in part d.)? That is, will you choose to refinance given this additional information? [+4]
In four years, 48 more payments will be made on either mortgage. The remaining payments on the current loan will number 360-20-48 = 292, and on the new loan 360-48 = 312. Remaining principal amounts: .08 292 1 (1 ) 12 $282,753.19 Current: 2201.29 .08 12 .07 312 1 (1 ) 12 $282,326.92 New: 1,967.36 .07 12 (Note: expressions in brackets are equal to the PV(annuity) formulas, inverted and simplified--see part c. above) In 4 years, the remaining principal is 426.27 lower (less) with the new loan, and thus 426.27 more equity will be realized upon sale. In PV terms, 426.27 / (1.005)^48 = 335.52, which is insufficient to make the NPV positive. Thus, this additional calculation does not change the answer in part d)--the new loan remains an unattractive alternative.
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