Question

1. What is the present value of the following set of cash flows when the discount rate is 11% p.a. compounded monthly?  (Rounded to the nearest dollar).

Year 1 $260

Year 2 $330

Year 3 $800

Year 4 $760

1. $1,605
2. $1,660
3. $1,565
4. $1,560
5. None of the above

2. What is the future value of $6,000 invested for 8 years at an annually compounded interest rate of 11.5% p.a.? (Rounded to the nearest dollar).

1. $14,980
2. $14,220
3. $14,333
4. $14,560
5. None of the above

3. Melbourne Ltd is expected to generate an EPS next year of $0.90 and its shares are currently priced in the marketplace at $12.00.  Launceston Ltd is expected to generate an EPS next year of $0.66 and its shares are currently priced in the marketplace at $10.24. Brisbane Ltd is expected to generate an EPS next year of $0.45 and its shares are currently priced in the marketplace at $7.30. Sydney Ltd is expected to generate an EPS next year of $0.78 and its shares are currently priced in the marketplace at $8.85. These companies all operate in the same industry, are expected to all have the same growth prospects and all have the same risk. The industry PE prospective ratio is known to be 14 multiplied by the expected eranings. Based upon the PE ratios which of the following would be the best investment strategy?

1. Sell Launceston and Brisbane shares and buy Sydney and Melbourne shares.
2. Sell Melbourne and Launceston shares and buy Sydney and Brisbane shares.
3. Buy Melbourne and Launceston shares and sell Sydney and Brisbane shares.
4. Buy Launceston and Brisbane shares and sell Sydney and Melbourne shares.
5. None of the above

4. Which of the following statements is most true?

1. Regardless of the value of the interest rate, increasing the compounding frequency will decrease the future value.
2. There is a relationship between the future value of investment and the effect of compounding frequency. At high interest rates, increases in compounding frequency will decrease the future value.
3. There is a relationship between the future value of investment and the effect of compounding frequency. At low interest rates, increases in compounding frequency will decrease the future value.
4. Regardless of the value of the interest rate, increasing the compounding frequency will increase the future value
5. None of the above

5. Edwards Enterprises is expected to pay a dividend of $3.66 at the end of the current year and analysts predict that dividends are expected to grow at a constant rate of 5% p.a. after that. If Edwards Enterprises' shareholders require a return of 12% p.a. on equity capital provided to the firm what will be its current share price?

1. $64.50
2. $52.29
3. $58.90
4. $52.90
5. None of the above

6. What is the market price (to the nearest dollar) of a 15% p.a. quarterly coupon bond with a face value of $100, three years to go until maturity when the current market yield is 13% p.a.?

1. $92.50
2. $98.00
3. $104.90
4. $150.00
5. None of the above

7. What is the Future Value of an asset that pays five cash flows of $1.2 million per year starting today?  The required rate of return is 10% p.a.  

1. $6.33 Million
2. $6.23 Million
3. $7.33 Million
4. $7.23 Million
5. None of the above

8. What are ‘free cash flows’ of a company?   

1. The future value of its total cash flows from real assets, after reinvestment costs
2. The present value of its total cash flows from real assets, after reinvestment costs
3. The future value of its net cash flows from real assets, after reinvestment costs
4. The present value of its net cash flows from real assets, after reinvestment costs
5. None of the above

(The following information relates to Question 19 and Question 20 below).

Today is Harry's 40^thbirthday.  Given the recent changes in the tax law relating to retirement, the earliest he can retire is his 70^thbirthday.  His employer contributions to his superannuation are $6,000 p.a. on each birthday, starting immediately.  Harry estimates that he will need $75,000 per annum to live on from his 71^stbirthday to his 95^thbirthday (inclusive).  Harry estimates that he can earn 9% p.a. between now and his 95th birthday.

9. How much money will Harry have saved by his 70^thbirthday if his assumptions are correct?

1. $890,450
2. $890,076
3. $896,321
4. $897,451
5. None of the above

10. What is the total amount of money Harry would need to have saved so he can afford to withdraw $75,000 per annum from his 71^stbirthday to his 95^thbirthday (inclusive)?

1. $890,450
2. $790,076
3. $956,321
4. $736,693
5. None of the above

** Please show the all mathematical steps and the Financial Calculator step if possible, Thanks.

Answer 1

1) Present value (P. V.) of cash flows @ 11% compounded monthly :

i = 11% / 12 months = 0.92% or 0.0092

i) Year 1 : n = 1 year * 12 months = 12

P. V. (year 1) = Cash flow / (1 + i) ^n

P. V (year 1)= $260 / (1+0.0092)^12

P. V. (year 1) = $260 / 1.1162 = $233

ii) Year 2 : n = 2 year * 12 months = 24

P. V. (year 2) = $330 / (1+0.0092)^24

P. V. (year 2) = $330 / 1.2458 = $265

iii) Year 3 : n = 3 years * 12 months = 36

P. V (year 3) = $800 / (1+0.0092)^36

P. V. (year 3) = $800 / 1.3905 = $575

iv) Year 4 : n = 4 years * 12 months = 48

P. V (year 4) = $760 / (1+0.0092)^48

P. V. (year 4) = $760 / 1.5521 = $490

Total Present Value (year 1 - 4) = $233 + $265 + $575 + $490

Total present value = $1563

Ans - C) 1565

Note : Figures are rounded off due to which it is showing nominal amount of difference.

2) Future value(F.V) of investment compounded annually for 8 years

n = 8 years , i = 11.50% or 0.1150

F. V. = Amount * (1 + i)^n

F. V. = $6000 * (1 + 0.1150)^8

F. V. = $6000 * 2.3889 = $14333.40

Ans : C) $14333

3) Industry PE ratio = 14

PE ratio = Market price / Earnings per share

If PE ratio of company is lower than industry PE then price is undervalued and share should be bought and vice versa.

Following PE ratio is calculated using the above mentioned formula:

i) Melbourne Ltd - PE = $12 / 0.90 = 13.33

Here, PE of Melbourne Ltd is lower than 14 industry PE & hence share should be bought.

ii) Launceston Ltd - PE = $10.24 / $0.66 = 15.52

It's PE ratio is higher than industry PE 14 & hence share should be sold.

iii) Brisbane Ltd - PE = $7.30 / $0.45 = 16.22

It's PE ratio is higher than industry PE 14 & hence share should be sold.

iv) Sydney Ltd - PE = $8.85 / $0.75 = 11.80

It's PE ratio is lower than industry PE 14 & hence share should be bought.

Ans: a) Sell Launceston & Brisbane shares & buy Sydney & Melbourne shares.

4) Ans : d) Regardless of the value of interest rate increasing the compounding frequency will increase the future value.

5) Price of share = Expected dividend / (Cost of equity - Growth rate)

Here

Expected dividend = $3.66

Cost of equity = 12% or 0.12

Growth rate = 5% or 0.05

Now,

Price of equity = $3.66 / (0.12 - 0.05)

Price of equity = $52.29

Ans - b) $52.29