# BFIN 620 IN-CLASS Practice Exam 1 Problems WI2010.pdf

## Business Finance 620 with Rives/weinstock at The Ohio State University *

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- BFIN 620 IN-CLASS Practice Exam 1 Problems WI2010.pdf

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ANS: C from Chapters 1-2 7 ANS: A from Chapters 1-2 (A) is not a true statement because commercial paper is traded in the money market. The other three statements are all correct. 8 ANS: A from Chapter 3 A payable is created when a firm purchases something on credit. Until the firm pays the bill, it has both the goods or services it purchased and the cash that will ultimately be used to pay the bill. Thus, increasing payables (creating a payable) represents a source of cash to the firm. All the other transactions listed represent uses of cash. 9 ANS: D from Chapter 3 The firm will pay 15% on the first $50,000 of taxable income, 25% on the next $25,000, and finally, 34% on the remaining $18,000. This yields a total tax bill of $19,870 ( = 0.15 x 50000 + 0.25 x 25000 + 0.34 x 18000). 10 ANS: C from Chapter 4 ROE is the ratio of Net Income to Equity. What the questions asks is, if Net Income remains constant and ROE falls from 24% to 18%, then how much must Equity have to changed. For ROE to decline in the face of a constant Net Income, Equity must have increased over the year. Long-term debt has nothing to do with ROE in this formulation (it’s not about the DuPont System ROE because you don’t have information on all the component pieces from DuPont), so you can eliminated answers (B) and (D). Between (A) and (C), (C) is the only answer choice that has Equity increasing, so (C) is correct. 11 ANS: D from Chapter 4 The question asks you to find ROA, which according to the formula sheet, equals the ratio of (Net Income + Interest) to Average Annual Assets. You already have one of these values (Average Annual Assets), so you need to find the other (Net Income + Interest). Of the other ratios shown, only the operating profit margin contains (Net Income + Interest). You know the value of this ratio (13%). If you can find the Revenue denominator, then you can compute (Net Income + Interest). Revenue then can (Net Income If $110,000 is 25 days of sales, then annual revenue is 1,606,000, which equals 110000 (365/25); all we’re doing her is “annualizing” the revenue associated with receivables >> if we earn $110,000 over 25 days (which amounts to $4,400 a day), then how much will we earn over 365 days. Multiplying $4,400 by 365 equals $1,606,000, which is the answer above. Multiplying the $1,606,000 revenue by operating profit margin yields the numerator of ROA . Thus, net income plus interest = 0.13 x 1,606,000, or $208,780 Finally, divide $208,780 by average annual assets to obtain ROA = 15%. You DO NOT need the times interest earned ratio. 12 ANS: C from Chapter 5 First, draw a timeline for the stream of cash flows to visualize the problem. In effect, you’re compounding each cash flow from the point that it’s paid in the stream to the end of Year 5. Thus: > $200 is compounded over 5 years (today through end of Year 5) > $500 is compounded over 3 years (end of Year 2 to end of Year 5)py > $800 is compounded over 1 year (end of Year 4 to end of Year 5) Before you do these calculations, note that the APR is paid in bi-monthly installments. To use the interest rate with a unit of time measured in years, you need the EAR. Convert the APR to the EAR with the expression on the formula sheet. The result is 6.152%. Now, find the FV of each of the three cash flows and add the results. You should get just over $1,700. 13 ANS: A from Chapter 5 This mortgage loan requires monthly payments. First, find the monthly mortgage payment ($316.288) to finance $33,500 over 180 months at 0.65% per month (=7.8% / 12). Because you’re working with months, you need the monthly rate of interest. Mortgage loans are amortizing loans, which means they’re governed by the formula for the PV of an ordinary annuity (see the formula sheet; also review the lecture slides at the end of the Chapter 5 slide deck).;p To find the monthly mortgage payment: > the PV = 33,500 > the number of time periods (months) = 180 (12 x 15 years) > the monthly interest rate is 0.65% (or 0.0065 for calculations). Plug these values into the PV-of-constant-annuity formula to obtain $316.29. Next, find the PV of this mortgage payment stream at the same interest rate over the final 120 months of the loan (the part of the loan you won’t be around for). By the end of the 60 th month, you owe the lender that part of the $33,500 you borrowed that you haven’t yet repaid. You do not owe the interest for the final 120 months, because the bank won’t earn it. Use the formula for the PV of a constant annuity to 14 find the PV of the 120-month stream of $316 monthly payments at 0.65%. This result ($26,297) is the outstanding principal (yet to be repaid) in the remaining 120 monthly payments). ANS: B from Chapter 5 This is a more challenging problem. Here’s some guidance: > Start by drawing a timeline to orient yourself with respect to the stream of cash flows in question. > Once you see the timeline, you need to classify the cash flows. (a) Is this a perpetuity or an annuity? (b) Are the cash flows level or growing? (c) Are you looking for the PV or the FV? Answer these three questions to select the right formula from the formula sheet. > What you’re looking for is the FV of a growing annuity. The initial cash flow is $5,000. The rate of growth of cash flows is 10%. The discount rate is 6.65% (it’s an annual rate so you don’t have to shift to an EAR; it’s already an EAR!).y; > When you plug the appropriate values into the formula for the FV of a growing annuity, you get $3,886,598. If you don’t get this (or something reasonably close, allowing for rounding error), check your math!! 15 ANS: B from Chapter 5 You can figure this one out. Here’s some guidance: > Start with a timeline to orient yourself with respect to the cash flow stream. > Note the frequency of compounding on the APR. What is the EAR? V l th it t b fi di th PV f th i $8 000 t t th> a ue e annu y s ream y n ng e o the n ne , paymen s a e EAR. What value do you get? > What is the date of this PV? It’s not today! REMEMBER >> the date of a PV is one time period (year, month, quarter, etc) in front of the first cash flow in a stream. > Once you determine the date of the PV, discount this measure to today at the EAR, using the simple FV-PV formula. The PV today is the total amount you would need to fund all nine payments down the road if you had to put up the entire amount today. But you don’t! Further, you already have $4,500 of today’s PV. If you want to fund the rest over the years between today and the start of the annuity stream, then you’re looking for the (level) annual payment amount that would be supported by the PV today (net of the $4,500) at the EAR. Which formula should you use to find this payment? This is the annual payment the problem asks you to find. 16 This is the problem to find. Question 1 We are looking for the amount of money required to support a future payment stream of $90,000 a year over 25 years. The discount rate is 6% (compounded annually – we’re working with annual cash flows). We use the PV of a constant annuity formula because the cash flows are level, equally spaced and run over a fixed period of time. Substituting these values into the PV annuity formula gives $1,150,502. This is the minimum amount of money you would need to have on hdtth ttf25 ti t if t d t d $90 000 dhand a the s ar o a 25-year re remen if you wan e o raw , a year an not run out of money for 25 years. Question 2 Now, the $1,150,502 from Question 1 becomes your investing target. Starting at age 25 and running to age 75, how much do you need to deposit in your account gg each year to reach $1,150,502 at age 75. Here, $1,150,502 is the FV of a 5-year payment stream earning 6% annual interest. The cash flows are level, equally spaced, and have a starting point and an ending point. Because you know the FV of the stream, you can use the FV of a constant annuity formula to find the annual payment. The result is $3,963. If you deposit this much in your account at the end of each of the next 50 years, and the account earns 6% annual interest, you’ll wind up with $1 150 502 $1, , . 56 Question 3(a) The first part of Question 3 asks you to find the capital stock needed at retirement (age 75) to support a stream of annual payments over the next 25 years (to age 100) which start at $90,000 a year and grow at 3% a year. Here, you have equally spaced payments that running over a fixed time period (25 years), but the payments are growing at 3% a year. This represent a growing annuity. Because you want to know the value of this stream at the beginning, you want the annuity’s PV. Plugging the values into the formula yields $4,463,542. This is the minimum amount you would need to have on hand at age 75 to support a 25-year annual payment stream that begins at $90,000 and grows at 3% a year. Note that this figure is much larger than the $1,150,502 capital stock you would need to support a level payment of $90,000 a year. You need roughly another $3.3 million at age 75 to support what may seem like a modest annual rate of increase in payment amount; this should give you an idea of how important inflation can be in retirement income planning. Question 3(b) This question is identical to Question 2, except we’re now saving to reach a larger dollar amount at age 75. Rather than setting aside $3,963 a year to fund a 25-year stream of level $90,000 payments, we need to save more than $15,000 a year to reach the $4,463,542 target. While $3,963 a year might be manageable for many savers (it amounts to roughly $330 a month), $15,281 a year is a significant pile of cash to defer from current household expenditures. expenditures. 57 Question 4 This question is identical to Question 1, except that we’ve changed the frequency from once a year to once a month (which is more realistic for most savers). Here, we still have a constant annuity, and we’re still looking for the PV of the 25-year payment stream (the amount we need to have on hand at age 75), but the unit of time is now the month, so all the measures need to be converted to a monthly basis. The payment stream now consists of 300 months (=25 years) of $7,500 a month (monthly equivalent of $90,000 a year). The appropriate rate of interest (to match the other monthly values) is 0.5%. This is the monthly rate of interest, which we find by dividing the APR by 12. Spending on a monthly basis (rather than once a year) means we’ll be withdrawing funds faster from the account. Thus, we’ll need more capital at the start to support the payment stream. This explains ,pp why the capital stock at age 75 here ($1,164,051) is larger than the result from Question 1. We use the PV of a constant annuity formula for the same reason mentioned in Question 1 (level, equally spaced cash flows, running over a fixed time period, where we want to find the value of the stream at the outset – at the start of retirement). Question 5 This question is identical to Question 2, except that we’re setting aside money once a month rather than once a year Because money enters the account at a faster pace on a monthly basis (11/12’sof . Because money the faster on s of our total annual deposit enters the account before the end of the year), we wind up earning more interest over 50 years (from month-to-month interest compounding) than would be the case with annual deposits (where our entire annual deposit doesn’t enter the account until the end of the year). With more interest income, we don’t need to deposit as much each month, which helps explain why the monthly deposit is only $307 (well below the $330 a month figure implied by Question 2, where we’re making annual deposits). We use the FV of a constant annuity formula for the same reason mentioned in Question 2 (level, equally spaced cash flows, running over a fixed time period, where we have the FV of the stream and want to find the payment that leads to this FV; the PV of the stream is zero there’s nothing in our account when we start making deposits at age 25)stream – there’s nothing our when we start making at age 25). 58 Bill Microsoft PowerPoint - BFIN 620 Practice Exam Questions WI2010 NEW JAN20 [Compatibility Mode]

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