Problem 1 (8 marks)

Part A (2 marks)

What is the future value of the following investments?

a.   $2000 invested for 5 years at 10% compounded annually

b.   $5000 invested for 7 years at 8% compounded annually

Solution

1 mark each

a.    = $2,000 × (1 + 10%)5  = $3,221.02

b.    = $5,000 × (1 + 8%)7  = $8,569. 12

Part B (2 marks)

After researching various car loan products, you have found that you can borrow from either  Commonwealth Bank or Westpac Bank. Commonwealth Bank is offering a borrowing rate of 10.5% compounded monthly, while Westpac Bank is offering 11% compounded semi-           annually. Which bank offers the better rate?

Solution:

1 mark each for the EAR calculation

 = (1 +     12   )     − 1 = 11.02%

 = (1 +    2   )   − 1 = 11.30%

Commonwealth bank offers the better rate.

Part C (2 marks)

Don has signed a contract that will pay him $60,000 at the end of each year for the next five  years, plus an additional $100,000 at the end of year 6. If the appropriate discount rate is 7%, what is the present value of this contract?

Solution:

1 mark for the annuity

0.5 mark for the last cash flow

0.5 mark for the correct answer

 =  × (1 − ) +  = $312,646.07

Part D (2 marks)

Susan would like to have $1.5 million at the time of her retirement in 30 years by making a  single investment today. If the investment can earn 5% annually, how much will Susan have to invest today? What if Susan has identified an investment that earns 10% annually, how    soon could she retire?

Solution:

1 mark for PV calculation

1 mark for n calculation

1,500,000 =  × (1 + 5%)30

 =  = $347,066.1

1,500,000 = 347,066.1 × (1 + 10%)

(1 + 10%) = 

1500000

 =                              = 15.36

Problem 2 (10 marks)

Part A (6 marks)

Koch Limited is about to replace its existing fleet of diesel trucks with electric ones. The new electric truck will cost $100,000 and has a useful life of 10 years, at which time the truck will be worthless. However, Koch Limited has the practice of replacing its fleet every 5 years, and expects to sell the electric truck for $30,000 then. Due to the efficiency of the new truck, the  company expects to generate additional $20,000 revenue per year over the next five years.     Additionally, the fuel and maintenance costs for the electric truck are $5,000 lower each year than diesel truck. Assume straight-line depreciation and a discount rate of 10% and ignore      tax. Calculate

a.   The accounting rate of return of the new electric truck.

b.   The payback period for the new electric truck.

c.   The net present value of the new electric truck.

Solution:

ARR: 0.5 mark each for depreciation, average profit, average investment and correct answer

PP: 1 mark for correct cash flow, 0.5 for initial investment, 0.5 for correct answer

NPV: 0.5 mark each for initial investment, PV of cash flow, PV of residual and correct answer

 = 100,000 − 30,000 = 14,000

20000 + 5000 − 14000

  =        100000 + 30000        = 16.92%

2

 =  = 4

 = −100000 +  × (1 − ) +  = $13,397.31

Part B (4 marks)

CSL is considering the expansion of its COVID- 19 vaccine production due to high demand.  The new production facility is expected to cost $300 million and will be ready for production immediately. CSL predicts that the pandemic will end after another 3 years, and there will be no more demand for the COVID- 19 vaccine. However, CSL will be able to sell the                production facility to a flu vaccine company for $120 million after 3 years. The following     income statements summarise the forecast for the COVID- 19 vaccine production:

Depreciation has been calculated on a straight-line basis. You should assume that all cash    flows occur at the end of the year in which they arise. The company's cost of capital is 10%. Ignore taxation.

a.   Calculate the NPV for this project. Should the company invest? Why?

b.   Without calculation, is the internal rate of return (IRR) higher or lower than 10%?

Explain briefly

Solution:

1 mark for depreciation

0.5 mark each for initial investment, PV of cash flow, PV of residual and correct answer

 =  = 60                          = −300 +  +  +  +  = $15.55

1 mark

IRR should be higher than 10%, as there is an inverse relation between discount rate and NPV. When discount rate is 10%, NPV is positive, so IRR should be higher.

Problem 3 (12 marks)

Part A (2 marks)

What is a zero coupon bond? And how does investor profit from buying one?

Solution:

Zero coupon bond is bond without coupon payment (1 mark). Zero coupon bond is sold at discount to face value, as a result, investor make a return from the capital gain (1 mark).

Part B (2 marks)

List two factors that affect the yield to maturity of a bond. Explain briefly.

Solution:

1 mark for each. 0.5 mark if explanation is wrong.

Liquidity, call feature, term to maturity and default risk.

Part C (2 marks)

Cardinal Investment is buying a 90-day bank bill today. The bill still has 50 days until         maturity. The face value of the bill is $100,000. If the current market yield on this bill is 3% per annum, what is the price of the bill today?

Solution:

0.5 mark each for face value, interest rate, days left and correct answer

 =  = $99,590.72

Part D (3 marks)

Lion Ltd has just issued a bond with 5-year maturity and a face value of $1,000. The coupon rate is 6%, paid annually. Assume the required yield to maturity is 8%.

a.   What is the bond price?

b.   If the yield to maturity drops to 5%, what is the bond price?

c.   If the bond pays coupon semi-annually instead (assume yield to maturity is 8%), what

would be the price of the bond?

Solution:

1 mark each for a, b and c

Deduct 0.25 mark each for coupon, YTM, n, FV and correct answer, until 0

 = 1000 × 6% = 60

 =  × (1 − ) +  = $920.15

 =  × (1 − ) +  = $1,043.29

 =  × (1 − ) +  = $918.89

Part E (3 marks)

Electronicca is an electric car start-up and growing rapidly. The company has just paid a      dividend of $2 per share. Dividends are expected to grow at a rate of 30% over the next five years, with the growth rate falling off to a constant 5% thereafter. If the required return is    12%, what is the current share price?

Solution:

1 mark for TV

1 mark for PV of first 5 dividends

1 mark for correct answer

2 × (1 + 30%)5  × (1 + 5%)

  =                                                                 = $111.39

 =                          × (1 − (                 )  ) +                         = $79.19

Problem 4 (10 marks)

Part A (2 marks)

You have bought one Microsoft share a year ago at $185. Over the year, Microsoft has paid dividend of $2.24 per share. If the current share price is $255, what is your return over the  year?

Solution:

Deduct 0.5 mark each for each component

 =

Part B (2 marks)

255 + 2.24 185

− 1 = 39.05%

If the volatility (standard deviation) of company A is higher than company B, then the beta for company A must be higher than the beta for company B. Is this statement correct?

Explain your answer.

Solution:

0.5 mark for No, and 1.5 marks for explanation.

No, volatility measures the total risk while beta measures the systematic risk.

Part C (4 marks)

Consider the following information:

a.   Your portfolio is invested 25% in A and B, and 50% in C. What is the expected return of the portfolio?

b.   What is the standard deviation of the portfolio?

Solution:

a.   0.25 mark for return in each economic state, 1 mark for portfolio expected return

Alternatively, student can calculate the expected return of each stock and then portfolio weighted average

  = 0.25 × 30% + 0.25 × 45% + 0.5 × 30% = 33.75%

  = 13.75%

  = −1.5%

  = −13.75%

 ( ) = 0. 10 × 33.75% + 0.50 × 13.75% + 0.30 × −1.5% + 0. 1 × −13.75% = 8.425%

Or

( ) = 0. 1 × 30% + 0.50 × 11% + 0.30 × 2% + 0. 1 × −12% =7.9% ( ) = 7.6%

( ) = 9. 1%

 ( ) = 0.25 × 7.9% + 0.25 × 7.6% + 0.5 × 9. 1% = 8.425%

b.   1 mark for correct formula with number input, 1 mark for correct answer

 2  = 0. 1 × (33.75% − 8.425%)2  + 0.5 × (13.75% − 8.425%)2  + 0.3

× (−1.5% − 8.425%)2  + 0. 1 × (−13.75% − 8.425%)2  = 0.015704  = 12.53%

Part D (2 marks)

Newstead Brewery Ltd has an expected return of 11.2%, the risk-free rate is 3.5%, and the market risk premium is 6.5%. What is the beta for the company?

Solution:

1 mark for CAPM formula, 1 mark for correct beta

11.2% = 3.5% +  × 6.5%

 = 1.1846

Problem 5 (10 marks)

Part A (2 marks)

Why do we use an after-tax figure for cost of debt but not for cost of equity in calculating WACC?

Solution:

Interest expense is tax deductible (1 mark) while dividend payment is not (1 mark).

Part B (4 marks)

Brookfield Railway Ltd has 4 million shares outstanding with a current share price of $15,    and the book value per share is $10. Brookfield also has two bond issues outstanding. The    first bond issue has a face value of $20 million, a coupon rate of 5.0%, a yield to maturity of 5.4% and sells for 97% of par. The second issue has a face value of $30 million, a coupon    rate of 5.5%, a yield to maturity of 5.0% and sells for 102% of par. The first issue matures in 10 years, while the second in 5 years. Assume the cost of equity is 12% and a tax rate of       30%.

a.   What is the company’s capital structure?

b.   What is the company’s WACC? The overall cost of debt is the weighted average of

the two outstanding bonds.

Solution:

a.    = 4 × $15 = $60     (0.5 mark)

  = 20 × 97% + 30 × 102% = $50    (0.5 mark)

 = 60 + 50 = $110   (0.5 mark)

 =  = 45.45%  (0.5 mark)

b.    =  × 5.4% +  × 5.0% = 5. 1552%  (0.5 mark) 0.5 mark for cost of equity, tax and correct answer

 =  × 12% +  × 5. 1552% × (1 − 30%) = 8. 19%

Part C (2 marks)

Modigliani and Miller capital structure theorem states that firm value is not affected by the capital structure. Does this mean cost of equity and cost of debt remain the same with        different level of leverage? Explain your answer.

Solution:

No, cost of equity increases with leverage as the financial risk has increased (1 mark). Cost of debt remain unchanged in perfect capital market (1 mark). WACC remain unchanged.

Part D (2 marks)

HP Electronic Ltd can borrow at 6.0%, but currently has no debt. The cost of equity is 12.5%. The current value of the firm is $500,000. What will be the value of equity if HP Electronic    borrows $300,000 and uses the proceeds to pay dividends? Assume perfect capital market.

Solution: