FI 302, Business Finance Exam 2, Fall 2000 versions 1 & 8 KEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEY 1. (3 points) BS16 What is a 401k plan Most U.S. households single largest lifetime source of savings is a 401k plan. The 401k is a {ANSWER: C ; SET-UP: Backdrop!R451C1} a. defined benefit plan in which the employer promises the employee specific retirement annuity benefits b. a defined contribution plan in which the employee receives matching contributions from the employer, but the employee must pay taxes on the matching contributions c. defined contribution plan with significant tax deferral advantages d. defined benefit plan with significant tax deferral advantages e. defined contribution plan in which the employer promises the employee specific retirement annuity benefits 2. ROR3c What is AND(geometric,arithmetic) average ROR given 3 prices Two years ago you purchased a stock for $30. One year ago the price had moved to $19. Today it is at $40. Which one statement about the annual average rate of return is correct? {ANSWER: B ; SET-UP: PVFV!R80C1 ; QUESTION: ROR3c\\R89C2 ; CLUES: ror1= -36.67%, ror2=110.53%} a. The geometric average return is 14.1% and the arithmetic average return is 30.5%. b. The geometric average return is 15.5% and the arithmetic average return is 36.9%. c. The geometric average return is 15.5% and the arithmetic average return is 30.5%. d. The geometric average return is 14.1% and the arithmetic average return is 36.9%. e. The geometric average return is 14.1% and the arithmetic average return is 15.5%. 3. CY3b Find EAR given doubling period and intraperiod compounding A sum of money earns sufficient interest such that the balance doubles in 6 years. Given that it is compounded monthly, what is the effective annual rate? {ANSWER: D ; SET-UP: PVFV!R560C1 ; QUESTION: CY3b\\R569C6 } a. 11.89% b. 12.99% c. 11.54% d. 12.25% e. 12.61%
4. CY6a Find FV with intraperiod compounding A deposit exactly 11 years ago of $2,600 earns 10.1% annual interest compounded quarterly. There have been no other deposits or withdrawals. How much is in the account right now? {ANSWER: C ; SET-UP: PVFV!R626C1 ; QUESTION: CY6a\\R632C2 } a. $8,101 b. $8,425 c. $7,789 d. $7,489 e. $8,762 5. (3 points) TR1 Rule of 72 Which statement describes the rule of 72? {ANSWER: A ; SET-UP: PVFV!R32C1 ; QUESTION: TR1\\R40C2 } a. The approximate number of years required for a deposit to double equals 72 divided by the percentage interest rate. b. The number of months required for a deposit to double equals the decimal interest rate times 72. c. The simple sum of cash flows required for an investment to earn a positive rate of return equals the investment cost times 72. d. The simple sum of cash flows required for an investment to earn a positive rate of return equals the investment cost divided by 72. e. The number of months required for a deposit to double equals the decimal interest rate times 72. 6. CY15b Find PV given today s interest with intraperiod compounding An account was established 11 years ago with an initial deposit. Today the account is credited with its periodic interest of $490.58. The annual interest rate is 9.7% compounded quarterly. No other deposits or withdrawals have been made. How much was the initial deposit? {ANSWER: E ; SET-UP: PVFV!R802C1 ; QUESTION: CY15b\\R809C6 ; CLUES: last year s FV = $20,230 } a. $6,237 b. $6,876 c. $6,549 d. $7,581 e. $7,220 7. Multiple setup (MC5m) Here are two future expenses that you want to save for today: $4,200 payable in 4 years, and $7,300 payable in 9 years. You make an investment today that perfectly
finances the future expenses if the investment earns a target 9.0% average annual rate of return (compounded annually). MC5cm Find the shortfall given 2 irregular and different future expenses, target r and actual r The investment indeed grows sufficiently to finance your first expense. Unfortunately, for the entire investment horizon your actual annual rate of return falls short of the target by 90 basis points per year. When it is time to pay the second expense, how much money do you lack? {ANSWER: D ; SET-UP: Annuities!R208C1 ; QUESTION: MC5cm\\R217C6} a. $800 b. $601 c. $661 d. $727 e. $546 8. Multiple Setup (FV4m) You are considering two different strategies for a savings account that you intend to close exactly 25 years from today. For Strategy 1, deposit $230 per month for 4 years (first deposit today; last one exactly 4 years from today); no new deposits will be made after the end of the deposit period, but interest continues to accrue until the account is closed. For Strategy 2, you ll make your first monthly deposit exactly 4 years from today, each monthly deposit also equals $230, and you ll continue making monthly deposits for 21 years, so that you make the final deposit exactly 25 years from today when you close the account. The savings rate always is 7.00% compounded monthly. {SET-UP: Annuities!R162C1 ; CLUES: FV(Strategy 1)= $56,309 ; FV(Strategy 2)= $132,321 } FV4bm Find FV from first of two different retirement strategies How much does Strategy 1 accumulate at the time of retirement? {ANSWER: C ; SET-UP: Annuities!R162C1 ; QUESTION: FV4bm\\R173C6 } a. $48,641 b. $51,074 c. $56,309 d. $59,124 e. $53,627 9. Multiple setup (PV3m) You might invest in an asset that will return after-tax cash flow to you of $2,500 per month for 9 months (first payment one month from now), followed by $3,100 per month
for 5 months. You make an offer to buy the asset so that you ll get your target annual rate of return of 15.4% (compounded monthly ). {SET-UP: Annuities!R185C1 ; CLUES: pv(inflows)=$34,425 } PV3am Quantitatively and qualitatively compare the target and actual ROR given the return stream and various cost scenarios Describe how the actual cost determines whether the actual rate of return is smaller or larger than the target rate of return. {ANSWER: C ; SET-UP: Annuities!R185C1 ; QUESTION: PV3am\\R197C3 } a. For every cost less than $41,309 the actual rate of return is more than the target. b. For every cost more than $41,309 the actual rate of return is more than the target. c. For a cost of $34,425 the actual rate of return equals the target. d. For every cost more than $26,480 the actual rate of return is more than the target. e. For every cost less than $26,480 the actual rate of return is less than the target. 10. Multiple setup (AM4m) The Bank issued a home mortgage of $143,000 at 10.10% repayable monthly over 30 years. Today the bank received payment number 155 and, as a result, the Bank properly records the loan s book value equal to the outstanding balance. {SET-UP: Annuities!R313C1 ; CLUES: PMT = $1,266 ; # REMAINING = 205} AM4cm Find loan s AND(book value, market value) given new rate to sell loan In order to raise cash, however, the Bank intends to sell the loan for the highest price it can get. The selling price of the loan, its market value, is set so that the loan offers the buyer a rate of return equal to 8.80% ; this is slightly greater than the prevailing interest rate on new and similar loans. How does the loan s book value compare to its market value? {ANSWER: B ; SET-UP: Annuities!R313C1 ; QUESTION: AM4cm\\R323C2} a. The loan s market value is $133,981 and its book value is $127,086. b. The loan s market value is $133,981 and its book value is $123,385. c. The loan s market value is $121,801 and its book value is $123,385. d. The loan s market value is $110,728 and its book value is $123,385. e. The loan s market value is $121,801 and its book value is $127,086. 11. (3 points)
TR5 For which stream is the present value the OR(smallest, biggest) Suppose two alternative investments promise cash flow streams that possess equal lives. Further, suppose the simple sum of the cash flows for each investment is the same amount. Given a positive interest rate, which investment has the smallest present value? {ANSWER: C ; SET-UP: Annuities!R121C1 ; QUESTION: TR5\\R132C18 } a. an investment which generates equal cash flows each period. b. an investment which generates most cash flows at the beginning of its life. c. an investment which generates most cash flows at the end of its life. d. there is no reliable relationship between the distribution of cash flows and present value. e. an investment that is being discounted by a small discount rate. 12. TS1a Find each deposit for a perpetual endowment You wish to establish an endowment fund that will provide students with a $2,200 scholarship every semiannum, perpetually. You will make deposits semiannually, with the first one today and the final one in 7 years. The first scholarship is to be awarded one semiannum after the last deposit, and the savings rate is 6.30% compounded semiannually. How much is each deposit? {ANSWER: E ; SET-UP: Annuities!R358C1 ; QUESTION: TS1a\\R369C2 ; CLUES: fv target=$41,370, nsavings=15, } a. $3,399 b. $3,300 c. $3,606 d. $3,501 e. $3,714 13. CB1 Find the monthly payback period The Company pays $23,000 for an asset that is expected to generate after-tax cash flows at a rate of $900 per month for the first year, $1,400 per month for the second year, and $1,000 per month for the third year. How long, in months, is the investment s payback period? {ANSWER: A ; SET-UP: CapB!R12C1 ; QUESTION: CB1\\R20C2 } a. 20.7 b. 16.5 c. 13.2 d. 18.5 e. 14.7 14. CB2b Given alternative investment s cash flows, at what rate are the NPV s equal Consider the following cash flows for two mutually exclusive investments: t=0 t=1 t=2 t=3 A ($630) $473 $296 $124 B ($830) $98 $286 $875
Your boss claims that projects A and B represent exactly the same net present value for your company. You politely point out that, because of differences in cash flow timing, the only way these projects have the same net present value is if your company s actual financing rate equals what rate? {ANSWER: A ; SET-UP: CapB!R32C1 ; QUESTION: CB2b\\R42C6 ; CLUES: IRR for A and B are 25.18% and 17.50%; NPVs at 0% financing rate for A and B: $263 and $429. The cross-over point is 11.27%. } a. 11.3% b. 9.7% c. 10.4% d. 13.1% e. 12.2% 15. Multiple setup (CB3m) You took out a 30-year mortgage (monthly payments) for $80,000 at 9.90% and payment number 36 is due today. You are deciding whether you should refinance the outstanding principal by borrowing at today s lower rate of 7.60% an amount that just pays off the old loan. The new loan is for 30 years as of today. The total fees for getting the new loan equal 3.6% of the original loan s outstanding principal. The first payment for the new loan would be due one month from today. {SET-UP: CapB!R54C1 ; CLUES: outstanding balance on original loan: $78,492 } CB3am Refinancing example, AMORTIZE fees, find NPV Suppose you amortize the fees over the life of the new loan. What is the net present value of the refinancing venture if your personal discount rate is 13%? {ANSWER: E ; SET-UP: CapB!R54C1 ; QUESTION: CB3am\\R70C2 ; CLUES: outstanding balance on original loan: $78,492 } a. $11,438 b. $9,453 c. $12,582 d. $8,594 e. $10,398 16. (3 points) MB10 Normal yield curve Which of the following best describes a graph of the normal yield curve? {ANSWER: B ; SET-UP: Verbal!R60C1; QUESTION: MB10\\R67C2 } a. yield-to-maturity on vertical axis, term on horizontal axis, and a negative slope b. yield-to-maturity on vertical axis, term on horizontal axis, and a positive slope c. price on vertical axis, time to maturity on horizontal axis, and a line that curves toward $1000
d. price on vertical axis, coupon rate on horizontal axis, and slope equal to yield-tomaturity e. yield-to-maturity on horizontal axis, price on vertical axis, and a line that curves toward $1000 17. BD2 Treasury bond issued at par, what is change in ytm given change in price A 30-year Treasury bond was issued yesterday at par (i.e., at its $1,000 face value). Its coupon rate is 7.40%. Today, its price decreased $20.70. By how many basis points did the yield-to-maturity change? {ANSWER: D ; SET-UP: BondV!R31C1 ; QUESTION: BD2\\R42C2 } a. 20 b. -12 c. -13 d. 18 e. 15 18. Multiple setup (BD3m) A bond with a coupon rate of 5.80% has a yield-to-maturity that today equals 6.20%. The $1,000 bond pays coupons every 6 months, 25 coupons remain, and a coupon was paid yesterday. Suppose you buy this bond and hold it so that you receive 6 coupons. You sell the bond upon receiving that last coupon. {SET-UP: BondV!R54C1 ; CLUES: original price = $966 } BD3cm Find this seasoned bond s price when you later sell it (changing ytm) Suppose that when you sell the bond its yield-to-maturity has decreased by 210 basis points. What will be the bond s price when you sell it? {ANSWER: B ; SET-UP: BondV!R54C1 ; QUESTION: BD3cm\\R67C12 } a. $1,068 b. $1,133 c. $1,100 d. $1,006 e. $1,037 19. (3 points) MB7 Bond price to coupon rate relation Which statement about bond prices is most accurate? {ANSWER: E ; SET-UP: Backdrop!R567C1 } a. For a premium bond the yield-to-maturity exeeds the coupon rate b. For a discount bond the coupon rate exceeds the yield to maturity c. With an interest rate decline the price rises more for short-term bonds than for longterm bonds d. When a bond is sold at an interest rate less than the initial yield to maturity then the actual rate of return is less than the promised yield
e. With an interest rate increase the price falls more for long-term bonds than for shortterm bonds 20. BD5a Riding the yield curve problem; 2-year horizon The yield-to-maturity for a zero coupon bond is 7.40% for a 1-year bond, 8.49% for a 2- year bond, and 8.92% for a 3-year bond. You wish to make a 2-year investment and obviously can buy the 2-year bond and hold it to maturity. Suppose, however, that you think the yield curve will remain the same throughout the future. You can pursue an alternative strategy of buying a 3-year bond, holding it for 2 years, and selling it when it has one year remaining to maturity. Relative to the 2-year yield-to-maturity, by how many basis points does this alternative strategy enhance your average annual rate of return? (Assume, if necessary, that you can buy fractions of bonds.) {ANSWER: A ; SET-UP: BondV!R100C1 ; QUESTION: BD5a\\R116C2 } a. 119 b. 134 c. 188 d. 168 e. 150