Stock Prices and Social Dynamics - Assignment Example

Financial accounting

Chapter 6:

Q8

• Risk free-rates and risk premium

Risk-free rate: RF= r* + IP

Security r* + IP = RF

A 3% + 6% = 9%

B 3% + 9% = 12%

C 3% + 8% = 11%

D 3% + 5% = 8%

E 3% + 11% = 14%

• Following the fact that the expected inflation rates differ, it is most probable that the maturity of every security will also differ

c) Nominal rate: R=r* +IP +RP

Security r* + IP + RP = R

A 3% + 6% + 3% = 12%

B 3% + 9% + 2% = 14%

C 3% + 8% + 2% = 13%

D 3% + 5% + 4% = 12%

E 3% + 11% + 1% = 15%

Q11: bond prices and yield

• 0.97708*$1000=$977.08
• (0.05700*$1000)/$977.08

=$57.000/$977.08

=0.0583*100

=5.83%

• The bond is selling at a discount rate to its $1000 par value
• The yield to maturity tend to be greater than that of the current yield following the fact that the yield at maturity is composed of $22.92 in the price appreciation between today and May 15,2007 bond maturity.

Q 15: basic bond valuation

• I=10%, N=16, PMT=$120, FT=$1000

Solving for PV=$1,156.47

• Following the fact that the Complex systems’ bonds were issued out, this may have caused a shift in the relationship between supply and demand for money or caused a change in the risk of the firm.
• I=12%, N=16, PMT=$120, FV=$1000

Solving for PV =1000

In a situation when the required return is the same as the coupon rates, the value of the bond also tends to be equal to the par value: contrary to the above situation, if the required return appears to be less than the rates of the coupon, the bond will sell at premium value because its value becomes greater than the value at par

Q 17

• Bond value in situations when returns are changing

Bond

Calculator inputs

Calculator solutions

1

N=12, I=11%, PMT=$110, FV=$1000

$1000.00

2

N=12, I=15%, PMT=$110, FV=$1000

$783.18

3

N=12, I=8%, PMT=$110, FV=$100

$1226.08

b) Bond value against required returns

c) in a situation where the required return rates is less than the coupon rate, the market value tent to be greater than the value at par and as a result the bond tend to sell at premium. And when the return rates are greater than that of the coupon, the market value tend to be less than the par value and as a result, the bond tend to sell at a discount.

d) The required return on the bond is most likely to differ from the interest rates of the coupon either because economic conditions have changed resulting to a shift in the basic cost of the long-term funds or because the firm’s risks may have also changed over time.

Q 20: Yield to maturity

Bond A is selling at a discount to par

Bond B tend to sell at par value

Bond C is selling at a premium to par

Bond D is selling at a discount to par

Bond E is selling at a premium to par

Q 21

• Through the use of a financial calculator, the value of YTM is amounting to about 12.685%: accuracy of this value can be approved through inputting the YTM value in the bond valuation model which will prove the answer as follows:

N=15, I=12.685%, PMT=$120, FV=$1000

Solving for PV=$955.00

Following the fact that the value of PV is $955.00 and the market value of the bond is also $955, then it can be proved that the value of YMT is similar to the rate that is derived from the financial calculator.

• The market value of the bond appears to be approaching its par value as time towards maturity decreases and the yield to maturity tends to move towards the coupon interest rates as time to maturity decreases.

Q 25

Bond

Computer inputs

Calculated solution

A

N=24, I=4%,PMT=$50, FV=$1000

$1152.47

B

N=40, I=6%,PMT=60, FV=$1000

$1000.00

C

N=10, I=7%,PMT=$30, FV=$500

$464.88

D

N=20, I=5%,PMT=$70, FV=$1000

$1249.24

E

N=8, I=7%,PMT=$3, FV=$100

$76.11

• Contribution of Megan

10 years * $2000

=$20000

What Megan will have at the time of her retirement

FV=PV*FVIF10, 30=$31,874*17.449

=$556,169

Megan shall have contributed $20000 and have $556169 at retirement

• Contribution Melissa

65-35=30

30*$2000=$60000

What Melissa will have at the time of her retirement

FV=PV*FVIFA10, 30=$2000*164.494

=$328,988

Megan shall have contributed $60000 and have $328,988 at the time of his retirement

2) Amount at retirement

=$1000000

Number of years that Fan has saved

65-25=40 years

PV= CF/ (1+r) n

PV=1000000/ (100%+5%) 40

PV=8278; contribution of Fan per year

Number of years that Minghao saved

65-40=25years

Contribution of Minghao per year

PV=1000000/ (100%+5%) 25

PV=$20952

The amount that Minghao must contribute per year than Fan to reach their goals of $1000000 at age 65

=$12674-$8278=$12674

Minghao must contribute $12674 per year more than Fan

3) A line showing all the cash flows associated with the Patriots plan for Bill’s retirement annuity

Amount per year

$150000/20

$7500

Scale: 5 years: $3750

Amount $37500 $75000 $112500 $150000

0 5 10 15 20

Years

The amount that Patriots needs to accumulate so as to fund Bill’s annuity

Total amount for 20 years

$150000*20

=$3000000

100%=$3000000

107%=?

107/100*$3000000

=$321000

Patriots’ equal annual end-of-year deposits

$321000/20

=$160500

The amount Patriots would have to deposit annually if the rates shifts from 7% to 8%

100%=$3000000

108%=?

108/100*$3000000

=$3240000

Amount per year

=$3240000/20

=$162000

Chapter 7

Q 5: preferred stock valuation

• Annual dividend on TXS preferred stock

10% of $65

=10/100*65

=$6.5

• The price of TXS preferred stock at the rate of 8%

If 100%=$65

108%=?

108/100*65

=$70.2

• The value of preferred stock if it is cumulative

Where

Vo (per value) =value of the asset at time zero

CF1 is the expected cash flow at year t

r is the appropriate required returns (discount rates)

n is the relevant time period

PV=65/ (108/100)2

PV=65/1.1664

PV=$54.167

Q 6: common stock value; zero growth

PV= CF/ (1+r) n

Where PV=value of the asset at time zero

CF1 is the expected cash flow at year t

r is the appropriate required returns (discount rates)

n is the relevant time period

PV= 100/ (100/100+16/100)10

PV=100/ (1.16)10

PV=100/4.411

PV=$22.67

PV=100/ (1.12)10

PV=100/3.11

PV=$32.20

$32.2-22.67

$9.53

Sally will have a capital gain on her share of about $9.53 (32.20-22.67)

Q 9 constant stock value: constant growth

If 5%= $1.2 per share

?=28 per share

28*5/1.2

=116.67%-100%

=16.67%

Q12 common stock value: variable growth

PV= CF1/ (1+r) 1+ CF2/ 1+r) 2+CF3/ 1+r) 3

2.5% =$2.55 per share

15%=?

= (15*2.55)/2.5

=38.25/2.5

=$15.3 per share

Q 17

• Cool Tech’s common stock value per share

Number of shares of common stock outstanding=1100000

Market value of preferred stock= $1000000

Value of stock per share=1100000/1000000

=$1.1

• Buying the stock at the market rates would results into capital loss therefore it is not advisable to buy the stock
• When the rates changes from 2% to 3%, it would result into capital gain and therefore purchasing the stock is advisable

Q 19 valuation with price/ earnings multiple

Firm

Expected EPS

Price/ earnings multiple

Common stock value employing price

A

$3.00

6.2

18.6

B

$4.50

10.0

45

C

$1.80

12.6

22.68

D

2.40

8.9

E

5.10

15.0

76.5

Work cited

Kemp, Malcolm. "Stock Prices and Social Dynamics." Brooking Papers on Economic Activity 1.2 (2004): 457-511.

Tobin, M. Market Consistency: Model Calibration in Imperfect Markets. Washington DC: New Yok Press, 2011.