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Exam 1
FIN360, Spring 2008
Extra credit
- [2 points each] The bill under consideration in Virginia regarding payday loans would cap the APR on a payday loan to 36 percent. However, lenders may also add a 10% fee and a $5 verfication fee.
a. What is the EAR on a payday loan of $100 over two weeks under this new law? 5,067.55% Interest on payment in two weeks = 100(0.36/26) + 10 + 5 = 15. (1+0.163846)^26 – 1 = 5,067.55%
b. What is the EAR on a payday loan of $500 over two weeks under this new law? 1,981.509% Interest on payment in two weeks = 500(0.36/26) + 50 + 5 = 61. (1+(61.92307692/500)) 26 – 1 = 1,981.509%
- [2 points] The ABC Company has a bond issue outstanding that matures in three years, has a coupon of 6 percent (paid semi-annually), and is priced considering the following yield curve:
Maturity Yield 1-year 4% 2-year 5% 3-year 6%
What is the value of the bond today (in bond quote terms), based on this yield curve? _$100.177
Period
Cash flow
Discount
rate
Present
value
Total 100.
Instruction: Select the best answer for each question. Record your answer on the scantron sheet.
Capital markets
- Which of the following statements is not correct?
A. A stock listed on the NYSE cannot trade in another market, such as the Nasdaq. B. A good market is characterized by available information, price continuity, liquidity, low transactions costs, and information efficiency. C. Investment bankers are prohibited from working with other investment bankers to bring a company’s security offering to the market. D. The New York Stock Exchange uses a specialists system, the Nasdaq market uses market makers, but both markets also use computerized matching of trading.
- Buying a stock on margin: A. is illegal. B. is similar to selling a stock short. C. will hedge an investment in the underlying security. D. will leverage the holdings, exaggerating any gain or loss on the security investment.
- The “normal” yield curve is described as one in which the yields on longer-maturity securities are higher than those on shorter-maturity securities. A. True B. False
- Which of the following is not considered a money-market security? A. Common stock B. Eurodollar deposits C. Repurchase agreement D. Negotiated certificate of deposit
- Another name for a mutual fund is a(n): A. ETF B. open-end fund C. closed-end fund D. unit investment trust
Valuation principles
- Suppose you finance your car with a loan of $12,000 at an APR of 6 percent for four years, and make equal payments monthly. The elements of the calculation are for the monthly payment is [with PV = present value; FV = future value; n = number of payments; i = rate per period]: A. PV = $12,000; i = 6 percent; n = 4 B. PV = $12,000; i = 0.5 percent; n = 48 C. FV = $12,000; i = 6 percent; n = 4 D. FV = $12,000; i = 0.5 percent; n = 48
- Suppose your credit card charges 18 percent interest per year, but you have to pay the interest monthly. The effective annual percentage rate (EAR) falls into which of the following ranges? A. EAR < 19.00% B. 19.00% < EAR < 19.25% C. 19.25% < EAR < 19.50%
C. €3319.
€ 1000 (e1.2) = € 3320.
- Suppose you invest $10,000 in an investment that produces a return of 10 percent for each of the first five years, 5 percent for the next year, 0 percent in the seventh year, and –5 percent for each of the last three years. At the end of ten years, your investment has a value closest to: A. $14,498. B. $15,523. C. $15,529. D. $15,915. E. $16,911.
FV = $10,000 (1.10) 5 (1.05) (1) (0.95) 3 = $14,498.
- The amount that you would you have to deposit today in an account that pays 5 percent interest, compounded annually, to meet three annual withdrawals of $100,000 each (with no balance remaining after the third withdrawal), with the first payment 10 years from today is closest to: A. $159, B. $167, C. $175, D. $184,
PV 9 = $272,324. PV 0 = $175,543.
- You are given the following cash flows:
End of period Cash flow 2008 -$20, 2009 $ 50, 2010 -$ 50, 2011 $ 0 2012 $20,
The value of these cash flow at the end of 2007 , if the discount rate is 10 percent, is closest to: A. − $2, B. − $2, C. − $ D. $
Cash flow
Number of
discount
periods
Present
value
Total ($2,006.82)
- If $100 is placed in an account that earns a nominal, annual rate of 10 percent, compounded semi-annually, the value of this investment will be closest to which value in five years? A. $110. B. $161. C. $162. D. $164.
FV = $100 (1+0.05) 10 = $162.
Valuation applications
- According to the dividend discount model, A. the value of a stock is equal to the present value of all future earnings. B. the value of a stock is equal to the present value of all future dividends. C. the value of a stock is equal to the present value of all future cash flows from operations.
- The Ozark Mountain Company is pays a dividend of $2 per share each year and dividends are not expected to change. The valuation of a share of Ozark Mountain stock can be determined using which of the following methods? A. The perpetuity model, D/re. B. The dividend valuation model with a growth rate of zero. C. The two-stage dividend valuation model, with the first stage growth of D/P D. The perpetuity model, or the dividend value model with zero growth.
- Suppose investors require a 10 percent rate of return on a stock with the same level of risk as the Valley Company stock. Using the dividend valuation model, the value of a share of Valley Company stock if next period's dividend is $1.34 per share and these dividends are expected to grow at a rate of 6 percent per year, is closest to: A. $13. B. $33. C. $35. D. $36.
P 0 = $1.34 / (0.10-0.06) = $33.
- The Taylor Company is expected to pay a dividend of $1 per share next year. The required rate of return on Taylor common stock is 10 percent. The value of a share of Taylor stock using the dividend valuation model, if dividends are not expected to grow, is closest to: A. a) $ B. b) $ C. c) $ D. d) $
P 0 = $1 / 0.
PV = $1,
FV = $1,
PMT = $
N = 10
Solve for i: I = 1.79704% YTM = 3.
- The Strong Company bonds have a face value of $1,000 each, a 5 percent coupon (paid semiannually), 10 years to maturity, and are priced to yield 7.375 percent. The value of a Strong bond is: A. 48. B. 66. C. 83. D. 83.
FV = $1, PMT = $ N = 20 I = 7.375% / 2 = 3.6875% Solve for PV: $834. Quote = 83.
- Which of the following bonds has the largest current quote?
A. A bond with five years remaining to maturity, an 9 percent coupon (paid semi-annually), priced to yield 10 percent. B. A zero-coupon bond with three years remaining to maturity that is priced to yield 4 percent. C. A bond with ten years remaining to maturity, a 6 percent coupon (paid semi-annually) that is priced to yield 7 percent.
A: 96. B: 88. C: 92.
Returns and yields
- Which of the following statements is an incorrect statement? A. The current yield is another name for a bond’s yield to maturity. B. A bond selling at a discount has a yield-to-maturity that is greater than its coupon rate. C. The yield to maturity is the annualized six-month yield for a bond that pays interest semi-annually. D. The yield to call is the yield on a bond assuming that the bond is called at a specified price and at a specified call date.
- Suppose the discount yield on a U.S. Treasury bill is 3.25 percent. If this bill has a maturity of 45 days, its investment yield is closest to: A. 3.25000 percent B. 3.26326 percent C. 3.29514 percent D. 3.39858 percent
0.0325 = [(Face-Price)/Face] [360/45] 0.0325 = [(Face-Price)/Face] 8
0.0040625 = 1- Price/Face P/F = 0. P = 99.
Investment yield = [(100-99.59375)/99.59375] [365/45] = 0.0330858 or 3.30858%
- An investment of $1,000 increases in value to $1,250 in three years. The annual compound growth rate is closest to: A. 7.72% B. 8.83% C. 16.67% D. 25%
$1,250 = $1,000 (1 + i)^3
- Consider a bond with a 6 percent coupon (paid semiannually) and five years remaining to maturity. Suppose you invest in this bond today, with a current quote of 90, and expect to hold this bond to for three years, at which time you expect the yield on this bond to be 8 percent. If you can reinvest interest payments to yield 7 percent per year, the yield on this investment will be closest to: A. 2.31% B. 4.25% C. 7.00% D. 8.83%
FV of interest: [PMT=3; i=3.5; N=6 Solve for FV of ordinary annuity] = 19. FV of bond: [PMT=3; i=4; N=4; FV=100 Solve for PV of bond] = 96. Total value from investment 116.
PV = 90 N= FV=116. Solve for i: I = 8.8339%
Other
- If the market is expecting a cut in the Federal Funds target rate to 2.5 percent, and if the Federal Reserve does not change their target to 2.5 percent, we should expect the market: A. to react negatively. B. not to change. C. to react positively.
- Consider the following month-end closing prices of a stock:
Month end
Closing stock price January $ February $ March $ April $ May $ June $ The stock paid dividends of $1.5 in March. The value at the end of June of $1 invested at the end of January is closest to:
Exam 1 Formula
Valuation basics
s
FV = PV (1 + i) n^ PV ൌ FV ሺଵା୧ሻ^ i= FV 1 PV
ln FV - ln PV n = ln (1+i)
where FV is the future value, PV is the present value i is the rate of interest, and n is the number of compounding periods
FV = PV e APR x^ PV = (^) APR x
FV
e where x is the number of years APR is the annual percentage rate e Euler’s e
FV =
N N CF(1+i)N-t =CF (1+i)N-t ∑ ∑ t=1 t=
( ) N N (^) 1+i)N CF 1
t t t 1 t 1
PV = CF CF 1-
= (1+i)^ = (1^ i) i
+ ⎜⎜^ ⎟⎟
∑ ∑
where
N (^1) ∑
N-t
t t = 1 (1^ +i) N ∑ +i)
is the annuity discount factor; and
(1 (^) is the annuity compound factor. t=
PV =
CF
i N (^) CFt
Pres value of the investment = ∑
t=1 (1+i)t
ent
where CF (^) t is the cash flow at the end of period t; i is the discount rate; and N is the number of periods;
Stock valuation
t (^0) t t (^1) e
D
P
(1 r )
∞
=
where P 0 is price of a share of stock today; D (^) t is the dividend at the end of period t; r (^) e is the required rate of return; and t indicates the period.
0 1 0 e e
D (1 g) D P (r g) (r g)
1 1 1 1 1 1
N 1 N 2 N N t t t e 2 0 1 (^0) t t N t t (^1) e t (^1) e e t (^1) e e
st
D D
e 2 N
(1 g ) D D (r g ) D (1 g ) (r g ) P (1 r ) (1 r ) (^) (1 r ) (1 r ) (1 r )
PV of all dividends = PV of 1 stage divi
∞
= = =
= = ⎢^ ⎥^ + = ⎢^ ⎥+
+ ⎢⎣^ + ⎥⎦^ + ⎢⎣^ + ⎥⎦ +
PV of 2^ nd
dends stage dividends
where N 1 is the length of first stage g 1 is the g 2 is the
Bond valuation
growth of dividends in the first stage growth of dividends in the second stage
N (^) Ct (^) M
1+r (1+r )
= ⎢^ ⎥+
∑ t N
t=1 (^) d d
V
where V is the value of the bond; Ct is the coupon payment at the end of period t; M is the maturity value; and r
Yields
d is the yield [Note: for semi-annual coupons, rd is the six-month yield].
APR = i x n EAR = eAPR^ - 1
Yield to maturity = YTM = rd x 2
where rd is the six-month yield. rd solves the following:
Face (^) - Purchase Discount value^ price^360 = x yield (^) Face value Maturity of bill in days
Face (^) - Purchase Investment value^ price^365 yield =^ x Purchase price Maturity of bill in days
⎡ ⎤ ⎢ ⎥ ⎣ ⎦
Tax-exempt municipal yiel Taxable equivalent yield = (1 - marginal tax rate)
d
