# The Australian treasury is issuing 10 years bond that have face value of \$100 paying half yearly coupons at 4 % p.a. . The bond mature at par. Spencer purchase the bond that are priced at a yield to a maturity of 5.2%p.a. If Lisa buys the bond from the Sp

Question The Australian treasury is issuing 10 years bond that have face value of \$100 paying half yearly coupons at 4 % p.a. . The bond mature at par. Spencer purchase the bond that are priced at a yield to a maturity of 5.2%p.a. If Lisa buys the bond from the Spencer in 2 years time for \$95.115, has the yield to maturity risen or fallen?

Answer - Yield for Lisa: FV = 100; PV = 95.115; PMT (semi-annual coupon) = coupon rate*FV/2 = 4%*100/2 = 2; N (number of coupons pending) = 2*(10-2) = 16, solve for RATE.

Semi-annual rate = 2.37% so annual yield = 2.37%*2 = 4.74%

The YTM for Lisa has fallen from 5.2% p.a. to 4.74%

## Question.  The Australian Treasury is issuing 10 years bond that have face value of \$100 paying half yearly coupons at 4 % p.a. . The bond mature at par. Spencer purchase the bond that are priced at a yield to a maturity of 5.2%p.a. Calculate the size of each coupon payment giving your answer correct to the nearest cent

Size of each coupon payment = (Par Value * Coupon rate) /2

Size of each coupon payment = (100*4%)/2

Size of each coupon payment = \$2 every half yearly

## Question  Linsworth investment is offering securities that will promise to pay investors a quarterly distribution of \$0.10 and is expected to grow at 0.5% per quarter. The first distribution is in 3 months time. Calculate the fair value of this security if the market prices it at 10% p.a. Give your answer correct to the nearest cent.

The fair value of the security is \$5.

Explanation:

Compute the quarterly market rate, using the equation as shown below:

Quarterly rate = Annual rate/ 4 = 10%/ 4  = 2.5%

Hence, the quarterly rate is 2.5%.

Compute the fair value of the security, using the equation as shown below:

Fair value = Quarterly distribution/ (Quarterly rate - Growth rate)

= \$0.10/ (2.5% - 0.5%)  = \$0.10/ 2%  = \$5

Hence, the fair value of the security is \$5.

## Question Everlast corporation is expecting to pay \$0.66 in dividend at the end of the year. The Company pay half yearly dividends and they do not expect the dividend to increase. Today the company stock price is \$11. Calculate the effective annual return on equity implied by the price, giving your answer in a % correct to the nearest cent.

The EAR is 6.09%.

Compute the annual return on equity, using the equation as shown below:

Annual rate = Dividend/ Price

= \$0.66/ \$11

= 6%

Hence, the annual return on equity is 6%.

Compute the effective annual rate (EAR), using the equation as shown below:

EAR = {(1 + Rate/ Compounding period)^Compounding period} - 1

= {(1 + 0.06/2)^2} - 1

= {(1 + 0.03)^2} - 1

= 1.0609 - 1

= 6.09%

Hence, the EAR is 6.09%.

## Question  National food limited reported a net profit after tax of \$50M for that year. Explain one factor that may determine how much dividend they will pay their shareholders for this year,

Ans.  The biggest factor in deciding the dividend payout is the CAPEX requirement of the business, CAPEX is Capital Expenditures which is an investment in either maintenance CAPEX that is the money spent on maintaining existing factories, machinery etc or growth CAPEX which is basically investments into new property, plant and equipment by a business to fuel growth. If the business has no growth opportunities and does not need to spend money on maintaining its existing PP&E then it can pay all of its earnings to shareholders as dividends, while if it has CAPEX requirements, it should first fund the CAPEX and then distribute profits to shareholders. This along with certain tax considerations determine how much dividend a company pays their shareholders for the year.

Question   Explain two factor that may impact on the return on equity for a Company.

Ans. Some factors that may effect the Return on Equity of a business are:

1.) The leverage ratios of the business, such as the debt-to-equity ratio because how the assets of a business are funded makes a big difference in the Return on Equity, if two businesses are earning the same Profit-After-Tax, then the business with the lesser equity and more debt will have a higher Return on Equity and vice-versa because (Return on Equity = Profit-After-Tax/ Equity) , so a business with the same profit with lesser equity will have a higher ROE than a business with higher equity.

2.) The net income margin of a business which is Net Income margin = (Profit After Tax*100/ Revenue) because Profit After Tax or net Income is used to calculate the Return on Equity for a business. Now, the Net Income margin is dependent on a lot of factors such as the Operating margins of the business, which show how efficiently the operations of the business are being run, the cost of debt which determines the interest cost for the firm and lastly, the tax rates which are applicable to the firm.

## Question State two featured regarding debt and equity instruments that results in equity instruments having a higher cost of capital

Ans. Equity instruments of a company will have a high cost of capital if :

1.) The total debt instruments -to- total equity instruments ratio of the company is high because higher debt means a higher risk of bankruptcy for the firm, hence, the increased cost of the equity instruments such as preferred shares, common shares the company issues in the market.

2.) The cost of debt also has an effect on the cost of equity of the business, if the cost of debt instruments such as bonds, debentures issued by the company rises, it means the markets view the company to be more risky, hence, even the cost of equity of such a company rises.

Answers to risk-adjusted, free cashflows, net present value, discounted payback period, internal rate of return question

a). The risk adjusted discount rate represents the return on investment. It is the total of the return on the risk-free asset i.e. risk free rate add market premium. It is based on the risk aversion of investor

A higher risky investment will involve higher risk adjusted rate and vice versa.

b). The free cash flow for year 1 to 8 in millions of dollars

Free Cash flow from year 1 to 4

FCF = \$30 million + \$9 million + 0 = \$39 million

Free Cash flow from year 5 to 7

FCF = \$40 million + \$9 million + 0 = \$49 million

Free Cash flow for year 8

FCF = \$40 million + \$9 million + \$3million = \$52 million

c). Net Present Value is \$104.607 million.

d).  Discounted Payback period is 2.54 years.

e). The Internal Rate of Return (IRR) is the discount rate at which net present value of the project is is zero. The decrease in risk adjusted rate from 17% to 15% will not impact IRR as it doesn't change with change in risk adjusted discount rate.

Explanation:

Depreciation per year under Straight line method = (Cost of the asset - Salvage value) / Useful life of the asset

= (\$75 million - \$3 million) / 8 years

= \$9 million

b).Calculation of free cash flow for year 1 to 8 in million of dollars

Free Cash flow = Net revenue + Depreciation + Salvage Value

Free Cash flow from year 1 to 4

FCF = \$30 million + \$9 million + 0 = \$39 million

Free Cash flow from year 5 to 7

FCF =  \$40 million + \$9 million + 0 = \$49 million

Free Cash flow for year 8

FCF = \$40 million + \$9 million + \$3million  = \$52 million

Since depreciation is a non cash expense it is added back and information regarding tax and working capital is not given in the question it has been ignored.

c). NPV = Present Value of Cash Inflow - Present Value of Cash Outflow

(in millions)

Year    Cash flow       PV Factor @ 17%      PV of Cash flow

0          (75)                  1                                              (75)

1          39                    0.855                                       33.345

2          39                    0.731                                       28.509

3          39                    0.624                                       24.336

4          39                    0.534                                       20.826

5          49                    0.456                                       22.344

6          49                    0.390                                       19.110

7          49                    0.333                                       16.317

8          52                    0.285                                       14.820

NPV \$104.607

d). Calculation of the discounted Payback Period

Year Cash flow          PV Factor @ 17%      PV of Cash flow Cumulative PV of Cash Flow

0          (75)                  1                                  (75)                                          (75)

1          39                    0.855                           33.345                                     (41.655)

2          39                    0.731                           28.509                                     (13.146)

3          39                    0.624                           24.336                                     11.190

4          39                    0.534                           20.826                                     32.016

5          49                    0.456                           22.344                                     54.360

6          49                    0.390 1                        9.110                                       73.470

7          49                    0.333                           16.317                                     89.787

8          52                    0.285                           14.820                                     104.607

Discounted Payback Period = A + (B/C)

where,

A = Last year with negative cumulative discounted Cash flow = 2

B = Value of discounted cumulative cash flow at end of year A = (13.146)

C = Discounted Cash flow during the year following year A = 24.336

Solving,

= 2years + [13.146 / 24.336]

= 2 years + 0.54 year

= 2.54 years

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