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56

41. 42. 43. 44.

50m Chapter 9

1. 1.00

2. .82

3. 12.9%

4. 116.8%

5. ) \$25,633

6. ) Option

7. 8.07%

8. \$767.55

9. fl) 720

10. 13.89% . .00685

12. b) ) 1- -

13. ) 1,161,400

14. ) \$141,500

15. 7.91%

16. ) \$946.93

17. ) \$857.33

18. 6.4646

19. ) 9.64%

20. 26.45%

21. Minimum = \$128,614 Maximum = \$129,470

b) \$23,736 ) \$16,658 b) Option

b) 240

<f) 1 - -"" b) 16,600 ) 1.11% b) \$128,300

b) \$1036.53 b) \$1000.00

b) 10.51%

c) 7.975% rf) 7.953% /) Yes

(v + 2 2)

24. 25.

a(0 =

28. a) \$3616

30. \$1591 32.

33. a) (1) -1.8012 b) (1) 1.8854

34. a) 0 Z>) 94.307 35.

1250

b) 2.2035 c) 1.7628 d) .6046

*(0 = V (V + V)

(2) 0 (3) 1.8343 (2) 0 (3) -1.7531 c) 312.5

i(n + l)(n + 2)

36. 38.

\$13,223 in 1-year zero coupon bonds \$15,061 in 3-year zero coupon bonds \$9624 in 5-year zero coupons bonds

39. \$9091 in 1-year zero coupon bonds \$8265 in 2-year zero coupon bonds \$7513 in 3-year zero coupon bonds \$6830 in 4-year zero coupon bonds \$6209 in 5-year zero coupon bonds

40. a) \$179.37 b) 12.01%

41. a) 0 < P] < .6980 b) No solution exists

42. a) .2186 < Pi< .5931 b) No solution exists

Chapter 10

3. a) 8% in all years b) 0 in year 1; .01 in year 2; .Olyin year 3

c) \$1294.92 rf)\$1224.94 e) \$1259,71 f) \$1259.82 g) 26.08

4. a) .07997 b) .79390 c) .16630 d) .( 735

5. mean = 2.5772

s.d. = .0169

6. a) mean = 1.823 b) mean = 14.121 c) = .549 d) mean = 7.298

s.d. = .058 s.d. = .297 s.d. = .017 s.d. = .134

40. \$4.6!

\$365.63

\$116,500

31.33% 7 + 4

 Svmbol Section Description Symbol Section Description accumulated value of a decreasing annuity retrospective loan balance 10.4 a measure of equity required to support liabiUties {+ flat price of a bond e{t) 10.3 error term in AR(1) and AR(2) processes „m ,+ market price of a bond 10.5 exercise (striking) price of an option 10.5 value of a callable bond 10.2 expectation of random variable X 10.5 value of a noncallable bond expected present value convexity project financing rate redemption value of a bond forward rate 10.5 value of a call 10.6 value of call if stock goes down App. IV probabihty density ftinction fiinction being solved using iteration contribution, deposit face amount, par value of a bond contribution, deposit at time /j. present value of single payment at time n redemption value of a serial bond bond coupon 10.6 value of call if stock goes up accrued bond coupon summation of redemption values of serial bonds Fix) App. IV cumulative distribution fiinction cov[X, Y] 10.3 covariance of random variables X and modified coupon rate on a bond effective rate of discount gix) iteration formula rate of simple discount rate of compound discount «1. 82 10.3 roots of die characteristic equation for die AR(2) process factor in the declining balance method of depreciation base amount of a bond App. Ill common difference in an arithmetic progression factor in a variation of die declining balance mediod of present value of level perpetuity starting at time n depreciation 10.6 length of time interval in binomial lattice duration, Macaulay duration periodic charge of an asset effective rate of discount from time n - 1 to present value of increasing perpetuity starting at time nominal rate of discount convertible mthly effective rate of interest rate of simple interest 10.5 constants in the Black-Scholes formula rate of compound interest sinking ftind deposit yiekl rate, internal rate of relim 7.10 dividend on stock investment rate when j is the reinvestment rate D> depreciation charge interest rate on loan in sinkinj fiind method annual percentage rate (APR) Di,D2 day of date nominal rate of interest present value of a decreasing annuity

436 The Symbol

E, m,

«2

Pv Pi

10.2 10.2 10.2

2.3 various 10.5

7.4 9.5 10.6

9.10

 10.5 P{i)

cumulative distribution fiinction for the standard normal distribution

premium or discount on a \$1 bond

probabiUty bond does not default

probability of price increases in binomial lattice

probability bond does not default at time /

proportion of fiinds in different investments in asset/liability matching

price of a bond price of a put

price of a serial bond

summation of prices of serial bonds

amount of principal repaid on loan amount of principal adjustment on bond

instantaneous rate at which principal is being repaid

net present value

net present value based on spot rates probability bond defaults

expenses at setdement on real estate mortgage that must be reflected in APR

Symbol Section Description

..(m)

Sjt\

j„(mi) S

5.9 project return rate

7.3 coupon rate on a bond

9.4 rate of inflation 10.4 yield rate in CAPM

App. ni common ratio in a geometric progression

10.4 return on equity

10.4 risk-free rate of interest

10.4 yield rate on a specific security

10.4 appropriate rate to discount liabilities

10.4 yield rate on die market portfolio

4.3 equivalent payment per interest conversion period

6.3 level installment payment to repay a loan

8.5 level periodic return

5.2 return, wididrawal

6.6 varying installment payments to repay a loan

9.9 net receipt in immunization

App. Ill sum of a progression

App. Vin sum of an annuity

1U.2 variance of rate of interest

9.10 wididrawal amounts at different times in asset/liability matching

accumulated value of an n-period

3.2 annuity-immediate

3.3 annuity-due

4.4 annuity-immediate payable mdily

4.4 annuity-due payable mdily

4.5 continuous annuity

App. Vin expected value of die sum of an annuity

8.5 salvage value of asset after depreciation

10.5 current stock price

8.4 sum of die first r positive integers

App. IX random variable for die value of an asset

Section Description

9.9 cash outflow generated by UabiUties

App. VIII first moment about the origin App. VIII second moment about the origin 10.2 first moment of 1 + j, about the origin

second moment of 1 + J, about the origin first moment of (1 + i,)" about the origin second moment of (1 + about the origin periodic maintenance expense month of date the term of a transaction

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