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FINC19011 Business Finance Term 3

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  • Course Code: FINC19011
  • University: Central Queensland University
  • Country: Australia

Question:

You wish to buy a house after 4 years. The purchase price of the house, 4 years from now, is expected to be $250,000. You currently have $50,000 as deposit in a bank account. The bank account pays 4% p.a. interest compounded monthly. You have the plan to save $1000 monthly in this bank account over the next 4 years. You expect that you will use the money to which your account will grow for paying parts of the purchase price. Additionally, at the time of your purchase, you have the plan to borrow from the bank to fund the rest of the purchase price of the house. The bank provides home loan at 6.5% p.a. compounded monthly over a span of 20 years and expectantly this rate will remain the same at the time of the purchase. Considering the information, please answer the following:

(a)To what amount your bank deposit will grow at the time of your purchase (4 years from now)?

(b)How much money will you need to borrow from the bank at the time of purchase?

(c)What will be your annual repayment for the loan after you have taken it? 

Questions:

(a)A bank account provides 2.5% p.a. interest compounded annually. How much money will an investor need to invest so that the investment grows to $3,500 after 4 years?             

(b)How many years will it take an investment of $1,000 to grow to $2,500 if the investment pays 4% p.a. compounded quarterly?

(c)For an investment, the market risk premium is 7% and the beta is 1.8. If the risk-free rate is 5%, what is the investment's expected rate of return?

(d)A bond matures in 10 years. The bond has a coupon rate of 5% paid semi-annually and its face value is $1000. The market interest rate for similar bonds is 7%.

i.What is the value of this bond?

ii.Does the bond sell at par, premium or discount?

(e)For a rapidly growing German company, the growth rate is projected to be 25% for the next three years. At the end of 3 years, the growth rate is expected to settle to 5% and remain so for foreseeable future. The company has recently paid a dividend of €3.5. Assume that the investors' required rate of return for the company's shares is 17%. Given the information, please answer the following:

i.What is the value of this company's share?

If the current market price of the share is €35, is the share a desirable purchase?

 

Answer:

Solution 1:

In order to start a business in Australia a person first needs to select the most suitable business structure. The major forms of business structure from which the investor has to choose are sole proprietorship, partnership and company.

Sole proprietorship is the form of business in which all the risks and rewards belong to one person. This single person is wholly responsible for all the aspects of the business. This is the simplest form of business structure and relatively the most inexpensive one. (Fabozzi & ‎ Mann, 2012)

The partnership form of business is very similar to that of sole proprietorship. The risks and rewards of the business are distributed amongst all the partners in the agreed partnership ratio. Each partner is liable for the actions of any other partner. This is also a simple business form. The benefit of this type of structure over proprietorship is that the risks are divided amongst all the partners.

The company form of business structure is the most complex form of business structure. Under this business structure the corporate veil divides the ownership and management. The company stands as a separate legal entity and can sue and be sued in its name. The owners hold a stake in the company in the form of shares and are responsible for the management. The liability of the shareholders under this business structure is limited to the value of shares held by them. (Berk, Demarzo & Harford, 2012)

Therefore, based on the availability of the capital, scale of operations and risks involved, the best suitable form of business structure is to be opted for.

 

Solution 2:

An investor can invest in bond or equity market or in both. Based on his requirements and ability to deal with risk they can take a decision (Graham & Dodd, 2009). Few factors which can help an investor take a decision are listed below:

  • Liquidity:the equity market is more liquid than the bond market. Equity is traded over the counter and can be any time easily converted into cash, as and when required. The bonds usually have a lock in period and cannot be converted into cash. Therefore, a person who is need of high liquid investments should invest in the equity market. 
  • Fixed Income:an investor who looks for a stable income should not opt for equity market. In the bond market the investor gets to earn fixed coupon interest at particular intervals. But there is no such fixed income in equity investment. The equity investor may or may not earn dividend. The amount of dividend is based on the profits earned by the company. The management then decides if any dividend is required to be paid or the profits are to be retained for further expansion. Therefore, an investor who wants to earn a stable income should not invest in the equity market. (Graham, Buffett & Zweig, 2013)
  • Risk:the equity market involves more risk than the bond market. The prices of the stock are governed by the market forces and the investor may or may not earn any profits. When the investor expects that the market price of a share is expected to rise he would invest in that share. Similarly other investors would also buy that share. In order to fill in the demand supply gap, the share price increases. As soon as the price increases the investors start selling that stock and the price tends to fall. Therefore it is difficult to predict the movement in stock prices. Due to this volatile nature, the equity market involves high risk. An investor not willing to take risks should invest in bond market. (Robert Parrino, 2013)
  • Rate of returns:the bonds are also referred to as risk free investments. The coupon in the bond market in very low since it has low risks. Due to high risks involved in the equity market, the return in the equity market includes the risk premium. The coupon provided in the bond market is risk free and hence lower that the returns of the equity market. Therefore a person seeking to earn stable but low returns should invest in the bond market, but the investor who has the ability to take risks and wants to earn high profits should invest in equity market. (Penman, 2013)

Solution 3:

Part a:

Share

02 March 2017

03 November 2017

Difference in Price

 Dividend per share

Total Return per share

Total number of shares

BHP.AX

25.7

27.69

1.99

1.52

3.5061

500

CBA.AX

83.86

77.79

-6.07

3.29

-2.7843

500

TLS.AX

4.57

3.5

-1.07

0.22

-0.8486

500

Share

Total Return

Total Investment

Number of Days of Investment

 Holding Period Yield

BHP.AX

1753.05

12850

246

                               20.24

CBA.AX

-1392.15

41930

246

                                -4.93

TLS.AX

-424.3

2285

246

                              -27.55

Part b.

Share

Expected Return

Weights

Portfolio Return

BHP.AX

20.24

0.6

 12.14

CBA.AX

4.93

0.2

 0.99

TLS.AX

27.55

0.2

 5.51

 

 

 

 18.64

Share

Expected Return

Weights

Portfolio Return

BHP.AX

20.24

0.4

 8.10

CBA.AX

4.93

0.4

 1.97

TLS.AX

27.55

0.2

 5.51

 

 

 

 15.58

Part c.

Share

Beta

Weights

Portfolio Beta

BHP.AX

1.39

0.6

0.834

CBA.AX

1.33

0.2

0.266

TLS.AX

0.79

0.2

0.158

 

 

 

1.258

Share

Beta

Weights

Portfolio Beta

BHP.AX

1.39

0.4

0.556

CBA.AX

1.33

0.4

0.532

TLS.AX

0.79

0.2

0.158

 

 

 

1.246

Part d:

The first portfolio with the ratio of 0.6, 0.2 and 0.2 is much riskier than the other portfolio since the beta of first portfolio is higher than that of the other portfolio.

Solution 4:

Part a:

 

Value of Invested $50000 at the end of year four

FV=PV*(1+i/m)^(m*n)

Here

 

 

PV

25000

 

I

4%

 

M

12

 

N

4

 

FV

=

25000*(1+4/12)^(12*4)

 

=

29,329.97

Value of $1000 Invested monthly at the end of year four

FV

=

c*{(1+i)^n-1}

Here

 

 

C

1000

 

I

0.0033333

 

N

48

 

FV

=

1000*{(1+.003)^48-1}

 

 

0.003

 

=

51,545.06

Total Funds available at the end of year 4

80,875.00

Part b:

Amount of Loan To be taken

Total Funds required

 2,50,000

Total Funds available

 80,875

Loan to be taken

 1,69,125

Part c:

Assuming Equal annual payments for 20 years are required to be made

PV of Annuity

=

FV

 

PVIAF(i,n)

Here

 

 

FV

169125

 

i (0.065/12)

0.01

 

N

20

 

PVIAF(I,n)

 18.05

 

PV of Annuity

=

1,69,125.00

 

18.05

 

=

9,372.12

Therefore, $9372 will have to be paid annually for 20 years including the interest due amount.

Working: Calculation of PVIAF

1

0.990099

2

0.980296

3

0.97059

4

0.96098

5

0.951466

6

0.942045

7

0.932718

8

0.923483

9

0.91434

10

0.905287

11

0.896324

12

0.887449

13

0.878663

14

0.869963

15

0.861349

16

0.852821

17

0.844377

18

0.836017

19

0.82774

20

0.819544

 

18.04555

Solution 5:

Part a:

In order to calculate the future value the formula is:

 

 

FV

=

 PV*(1+i)^n

Here,

 

 

FV

3500

 

I

2.50%

 

N

4

 

Therefore,

 

 

3500

=

 PV*(1+.025)^4

PV

=

 3,500

 

 

 (1+.025)^4

 

=

 3,171

Therefore, the investor needs to invest $3171 today in order to receive $3500 after 4 years with interest 2.5% compounded annually.

Part b:

In order to calculate the future value the formula is:

 

 

FV

=

 PV*(1+i/4)^(n*4)

Here

 

 

FV

2500

 

PV

1000

 

I

4%

 

Therefore,

 

 

2500

=

 1000*(1+0.01)^(4n)

2.5

=

 1.01^4n

N

=

 22.75 years

Therefore, an investor needs to invest $1000 today for a period of 22.75 years to get $ 2500 with interest 44% compounded quarterly.

Part c:

As per CAPM

 

 

Re

=

 Rf+(Rm-Rf)*Beta

Here

 

 

Rf

5%

 

Rm-Rf

7%

 

Beta

1.8

 

Therefore

 

 

Rf

=

 5+(7*1.8)

 

=

17.60%

Part d (i):

In order to calculate the bond value

 

 

P0

=

 PV of Future cash Flows

 

=

 Face Value + Coupon Value *PVIAF(i,n)

Here

 

 

Face Value

1,000

 

Coupon Value

25

 

I

3.50%

 

N

20

 

Therefore

 

 

P0

=

 1000+25*PVIAF(3.5%,20)

 

=

 1000+(25*14.21)

 

=

 1,355

Part d (ii):

The Bond is trading at premium.

Part e (i):

Calculation of Share Price using Dividend Discount Model

Year

Dividend

 PV Factor @ 17%

PV of Dividend

1

4.38

0.8547009

3.74

2

5.47

0.7305136

3.99

3

6.84

0.6243706

4.27

Dividend for year 4

7.182

 

 

Price of the share at the end of year 3

=

7.182

 

17.5-.5

 

 

=

 42.25

 

PV of this Price

=

 42.25/(1.175^4)

 

 

=

 22.17

 

Therefore Price of the share today

=

 12+22.17

 

 

=

 34.17

 

Part e (ii):

Since the share is currently trading at $35 and the theoretical price of the share is $34.17 we can say that the share is trading rich and the investor should go short.

 

References

Berk, J., Demarzo, P., & Harford, J. (2012). Fundamentals of corporate finance. Boston, MA: Prentice Hall.

Fabozzi, F. J., & ‎ Mann, S. V. (2012). The Handbook of Fixed Income Securities. New York: McGraw-Hill Education.

Graham, B., & Dodd, D. (2009). Security analysis. New York: McGraw-Hill.

Graham, B., Buffett, W., & Zweig, J. (2013). The intelligent investor. New York: Harper Collins.

Penman, S. (2013). Financial statement analysis and security valuation. New York: McGraw-Hill Irwin.

Robert Parrino, D. S.-K. (2013). Fundamentals of Corporate Finance, 2nd Edition. Milton: John Wiley & Sons

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