question archive 1) You are considering an investment in the stock market and have identified three potential stocks, they are Crown (ASX: CWN), Tencent (HKG: 0700) and Commonwealth Bank (ASX: CBA)
1) You are considering an investment in the stock market and have identified three potential stocks, they are Crown (ASX: CWN), Tencent (HKG: 0700) and Commonwealth Bank (ASX: CBA)
Subject:FinancePrice:4.01 Bought8
1) You are considering an investment in the stock market and have identified three potential stocks, they are Crown (ASX: CWN), Tencent (HKG: 0700) and Commonwealth Bank (ASX: CBA). The historical prices for the past 10 years are shown in the table below. Assume no dividend is distributed during this period.
|
Year |
Crown |
Tencent |
Commonwealth (CBA) |
|
2010 |
7.76 |
29.04 |
53.63 |
|
2011 |
8.57 |
40.40 |
52.15 |
|
2012 |
8.09 |
37.94 |
50.39 |
|
2013 |
11.59 |
54.28 |
64.10 |
|
2014 |
16.68 |
108.70 |
73.83 |
|
2015 |
13.61 |
132 |
88.85 |
|
2016 |
12.27 |
144.90 |
78.67 |
|
2017 |
11.4 |
204.40 |
81.66 |
|
2018 |
13.25 |
463.60 |
78.87 |
|
2019 |
11.95 |
346 |
69.91 |
- Calculate the correlation coefficient between (a) Crown and Tencent and (b) Tencent and CBA
- Calculate the expected (annual) return and standard deviation if you owned a portfolio consisting of 50% in Crown and 50% in Tencent.
- Calculate the expected (annual) return and standard deviation if you owned a portfolio consisting of 40% in CBA and 60% in Tencent.
2.
Company ABC has just announced earnings of $2 per share. Based on the last five years, earnings have grown at a rate of 20% per annum and the company expects this to continue for the next five years, after which it expects earnings to remain constant forever. The company has a policy of paying out 30% of its earnings as dividends. ABC stock has a beta of 1.2. The yield to maturity on 10-year government bonds is 2% and market risk premium is 10%.
(a) Calculate the current value per share.
(10 marks)
(b) If the stock is currently trading in the market at $10 per share, comment on whether any profits can be made. What form of market efficiency prevails if this occurs? Examine the other two (2) forms of market efficiency and what the observation on the stock price here implies in terms of market efficiency.
(10 marks)
(c) The company plans to issue a 7-year bond in the near future to finance expansion into neighbouring countries. It expects interest rates to fall in 3 years’ time. State and describe two (2) possible types of bonds the company could issue. Analyse how the company can determine the pricing for its bond issue?
3.
Gerald has taken out a loan of $100,000 today to start a business. He has agreed to repay the loan on the following terms:
• Repayments will be made on a monthly basis. The first repayment will be made exactly one month from today.
• The repayments for the first 5 years will cover interest only to help reduce the financial burden for Gerald’s business at the start.
• After the 5-year interest-only period, Gerald will make level monthly payments that will fully repay the loan after an additional 15 years (i.e. 20 years from today, the loan will be fully repaid).
• The interest charged is 5% p.a. effective.
10 years have passed, and Gerald’s business is doing well. Further, he has made all the repayments on his loan so far as described above, and has just made the repayment due today. However, it has just been announced that the interest rate on Gerald’s loan will go up to 5.5% p.a. compounding semi-annually.
a) Calculate the new equivalent effective monthly rate on the loan. (1 mark)
b) Calculate the current loan outstanding (again, it is 10 years after the loan was initially taken out). Note that the new interest rate only applies from today onwards. (2 marks)
c) Because Gerald’s business is doing well, he decides to repay a lump sum of $10,000 immediately. To further reduce the amount of interest he is paying to the bank, he will increase his monthly repayments to $1,000 per month. How many full repayments of $1,000 does Gerald have to make in order to fully repay this loan? (Note: Gerald may need to make a further, smaller payment in the subsequent month) (2 marks)
d) Calculate the size of the smaller payment.
4.
As a senior analyst for the company, you have been asked to evaluate a new IT software project. The company has just paid a consulting firm $100,000 for a test marketing analysis. After looking at the project plan, you anticipate that the project will need to acquire computer hardware for a cost of $450,000. The Australian Taxation Office rules allow an effective life for the computer hardware of five years. The equipment can be depreciated on a straight-line (prime cost) basis and there is no expected salvage value after the five years.
Your company does not have any available space where the project can be located for five years and you anticipate a new office will cost $65,000 to rent for the first year (same cost for the remaining years). You expect that the project will need to hire 3 new software specialists at $50,000 (each specialist) per year (start in year 1) for the full five years to work on the software (same cost for the remaining years).
The project will use a van currently owned by the company. Although the van is not currently being used by the company, it can be rented out for $15,000 per year for five years. The book value of the van is $20,000. The van is being depreciated straight-line (with five years remaining for depreciation) and is expected to be worthless after the five years.
Expected annual marketing and selling costs will be incurred during the life of the project (5 years), with the first year expecting to be $250,000. The produced software is expected to sell at $85 per unit while the cost to produce each unit is $40. You expect that 10,000 units will be sold in the first year and the number of units sold will increase by 25% a year for the remaining four years. The project will need working capital of $50 000 to commence the business (in year 0) and the investment in working capital is to be completely recovered by the end of the project’s life (in year 5). The company tax rate is 30%, and the discount rate is 10.5%.
Based on the information presented above, answer the following questions (1) – (3).
- (3 marks) In evaluating the new IT software project, are the cost of $100,000 spent on marketing analysis? Explain your answer(s).
- (12 marks) Calculate the incremental free cash flow during the project’s life (starting from year 0 to year
- (10 marks) Calculate the NPV, payback period, and IRR
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1.1). Correlation between Crown & Tencent = 0.6392
Correlation between Tencent & CBA = 0.2975
2). Portfolio consisting of 50% Crown and 50% Tencent:
Average return = 22.95%; Standard deviation = 0.3106
3). Portfolio consisting of 40% Tencent & 60% CBA:
Average return = 24.86%; Standard deviation = 0.2944
The excel calculations are as follows:
Formulas:
Note: Since the question did not mention manual calculations, Excel formulas have been used for the calculations.
please see the attached file.
2.
1.
| As per CAPM | Re=Rf+B*(Rm-Rf) | Re=2%+ 10%*1.2 | Re= 14% | |||
| Rf | 2% | |||||
| Risk premium | 10% | |||||
| Beta | 1.20 | |||||
| Price of the share = present value of dividend for 5 years+ present value of perpetuity | ||||||
| =3.51+(10.6642*0.5194) | ||||||
| 9.05 | $9.05 | |||||
| Year | EPS Growing @ 20% | Dividend pay out @ 30% | PVF@ 14% | PV of dividend per share | ||
| 1 | 2.400 | 0.720 | 0.8772 | 0.63 | ||
| 2 | 2.880 | 0.864 | 0.7695 | 0.66 | ||
| 3 | 3.456 | 1.037 | 0.6750 | 0.70 | ||
| 4 | 4.147 | 1.244 | 0.5921 | 0.74 | ||
| 5 | 4.977 | 1.493 | 0.5194 | 0.78 | ||
| 3.51 | ||||||
| after 5 year earnings constant, hence as per perpetuity p0= D1/ke-g | =1.493/.14-0 | |||||
| 10.66429 |
2
If the current trading price of stock in the market is $ 10 then the stock is overvalued as the current value per share is $9.05 . As an investor, he should go for a short position on such stocks. An overvalued stock is likely to experience a price decline and return to a level which better reflects its financial status. Hence the investor should sell out his holding and make a profit before the price dips. It is a weak form of efficiency as per efficient market hypothesis.
The other 2 form of market efficiency are
Semi Strong and strong efficiency: The semi-strong form submits that because public information is part of a stock's current price, investors cannot utilize either technical or fundamental analysis, though information not available to the public can help investors.The strong form version states that all information, public and not public, is completely accounted for in current stock prices.
3. if ABC company is planning to issue bonds for 7 years duration and expects the interest rate will fall in future then it can go for a coupon bond or a zero coupon bond. if interest rates decline, bond prices will rise and as lower the interest rate high the yield to maturity.
Zero coupon Bond: ZCBs are issued at discount and at the maturity paid at par value. There is no payment of interest component in ZCB.
Regular coupon bond: these debt instruments pay, interest over the life of the bond and also repay the principal at maturity.
Pricing of Zero coupon Bond = Maturity value after 7 year /(1+ interest yield dividend )
Pricing of a coupon Bond= present value of all future cash flows included the principal repayment that is to be paid by the company after 7 year
3. Loan principal after the 60 the monthly payment(ie. 5*12=60 mths.)= 100000Monthly payment from end of 61st month can be calculated as follows:Loan principal= 100000Pmt.--Monthly pmt. Needs to be found out--r= Rate of interest= 5%/12=0.4167% or 0.004167 p.m.n= 15 yrs. *12=180 mths.so, using the PV of ordinary annuity formula,100000=Pmt.*(1-1.004167^-180)/0.004167so, the monthly pmt. Will be100000/((1-1.004167^-180)/0.004167)=790.81
a) New equivalent effective monthly rate on the loan
As it is compounded semi-annually, we will find the effective semi-annual rate & then divide by 6 , to get the mthly. Rate--(1+r)^2-1=5.5%so, effective s/a r=2.71319% per s/a periodie. 2.71319%/6=0.004522p.m.0.4522%b.Loan balance o/s after another 5 yrs. At original interest rates----ie. Another 60 mths. (10 yrs. From original time 0)Original loan principal= 100000; Mthly. Pmt= 790.81 ,mthly r= 0.4522%, n=60 mths.Loan balance=FV of the original loan amt.-FV of the 60 mthly. annuitiesie. (100000*(1+0.4167%)^60)-(790.81*((1+0.4167%)^60-1)/0.4167%)=74557.98c. So, from b. above, Loan balance pending (at end of 10 yrs. From t=0) is $ 74558 (rounded-off)After the repayment of a lump sum of $10,000 immediately,the loan balance becomes 74558-10000=64558so, equating the above PV of the loan , to the PV of the annuities of $ 1000at the new monthly rate of 0.4522%---- for n no.of mths.64558=1000*(1-(1+0.4522%)^-n)/0.4522%solving for n,no.of months = 76.5135 mths.ie. No.of months of full repayment of $ 1000 =76so, in 76 complete mths. He would have paid1000*(1-(1+0.4522%)^-76)/0.4522%=64195& the smaller payment in the subsequent month will be64558-64195=363
4.
In evaluating any project, Sunk costs are considered irrelevant as they are already spent and have no say in decision making. In the given new IT software project, $1,00,000 has already been spent on marketing analysis and hence is a sunk cost and therefore irrelevant.
CALCULATION OF INCREMENTAL FREE CASH FLOW
| Particulars | Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
| Hardware | (4,50,000) | 0 | 0 | 0 | 0 | 0 |
| Office Rent | 0 | (65,000) | (65,000) | (65,000) | (65,000) | (65,000) |
| Software Specialist | 0 | (1,50,000) | (1,50,000) | (1,50,000) | (1,50,000) | (1,50,000) |
| Working Capital | (50,000) | 0 | 0 | 0 | 0 | 50,000 |
| Marketing and Selling costs | 0 | (2,50,000) | (2,50,000) | (2,50,000) | (2,50,000) | (2,50,000) |
| Sales Less Cost (WN-1) | 0 | 4,50,000 | 5,62,500 | 7,03,125 | 8,78,895 | 10,98,630 |
| Tax (WN-2) | 0 | 31,500 | (2,250) | (44,438) | (97,168) | (1,63,089) |
| Van Rent foregone | 0 | (15,000) | (15,000) | (15,000) | (15,000) | (15,000) |
| Incremental Free Cash Flow | (5,00,000) | 1,500 | 80,250 | 1,78,687 | 3,01,727 | 5,05,541 |
Working Notes:
1) Calculation of Sales less Cost:
Sales p.u = $85, Cost p.u = $40 Hence Sales Less Cost p.u = $45
| Pariculars | Year1 | Year 2 | Year 3 | Year 4 | Year 5 |
| No. of Units | 10,000 | 12,500 | 15,625 | 19,531 | 24,414 |
| Sales Less Cost | 4,50,000 | 5,62,500 | 7,03,125 | 8,78,895 | 10,98,630 |
2) Calculation of Tax:
| Particulars | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
| Sales Less Cost (WN-1) | 4,50,000 | 5,62,500 | 7,03,125 | 8,78,895 | 10,98,630 |
| Office Rent | (65,000) | (65,000) | (65,000) | (65,000) | (65,000) |
| Software Specialist | (1,50,000) | (1,50,000) | (1,50,000) | (1,50,000) | (1,50,000) |
| Marketing and Selling Costs | (2,50,000) | (2,50,000) | (2,50,000) | (2,50,000) | (2,50,000) |
| Depreciation on Hardware | (90,000) | (90,000) | (90,000) | (90,000) | (90,000) |
| Profit | (1,05,000) | 7,500 | 1,48,125 | 3,23,895 | 5,43,630 |
| Tax | 31,500 | (2,250) | (44,438) | (97,168) | (1,63,089) |
Depreciation on Van will be deducted from Profit irrespective of this Project.
CALCULATION OF NPV
| Particulars | Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
| Incremental Free Cash Flow | (5,00,000) | 1,500 | 80,250 | 1,78,687 | 3,01,727 | 5,05,541 |
| Discount Rate @ 10.5% | 1 | 0.905 | 0.819 | 0.741 | 0.671 | 0.607 |
| Discounted Cash Flow | (5,00,000) | 1,358 | 65,725 | 1,32,407 | 2,02,459 | 3,06,863 |
NPV of New IT Software Project = $2,08,812
CALCULATION OF PAYBACK PERIOD
| Year | Discounted Cash Flow | Cummulative Cash Flow |
| 0 | (5,00,000) | (5,00,000) |
| 1 | 1,358 | (4,98,642) |
| 2 | 65,725 | (4,32,917) |
| 3 | 1,32,407 | (3,00,510) |
| 4 | 2,02,459 | (98,051) |
| 5 | 3,06,863 | 2,08,812 |
Payback Period = 4+(98051/306863) = 4.32 years
CALCULATION OF IRR
| Particulars | Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Total |
| Incremental Free Cash Flow | (5,00,000) | 1,500 | 80,250 | 1,78,687 | 3,01,727 | 5,05,541 | |
| Discount Rate @ 20% | 1 | 0.833 | 0.694 | 0.579 | 0.482 | 0.402 | |
| Discounted Cash Flow @ 20% | (5,00,000) | 1,250 | 55,694 | 1,03,460 | 1,45,432 | 2,03,227 | 9,063 |
| Discount Rate @ 21% | 1 | 0.826 | 0.683 | 0.564 | 0.467 | 0.386 | |
| Discounted Cash Flow @ 21% | (5,00,000) | 1,239 | 54,811 | 1,00,779 | 1,40,907 | 1,95,139 | (7,125) |
By Interpolation Method,
IRR = 20 + 9063/(9063+7125) = 20.56%
PFA
