HI5002 Finance for Business Online Tutoring
Week 3
- a) What is the effective annual interest rate (EAR) you would get for your investment in the first 10 years? (2marks)
EAR can be calculated using the following formula:
| EAR = | (1 + i/n)^n -1 |
| EAR = | 8.160% |
- b) How much money do you have in your account today? (4 marks)
| period | investment | rate | compounded | future value | earnings |
| 1-10 | 12,500 | 8% | semi-annually | 27,389 | 14,889 |
| 11-15 | 32,500 | 6.50% | annually | 44,528 | 12,028 |
| 45,000 | 71,917 | 26,917 |
From the above calculations it is clear that I would have $71,971 in my account on present day.
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- c) If you wish to have $85,000 now, how much should you have invested 15 years ago? (4 marks)
The answer assumes that investments and earnings made 5 years ago remain constant, and only investment made 15 years ago has to be changed.
Thus, to have $85,000 in account today, I would need an additional $13,038 compared to my bank value calculated above. This would need an additional present value injection of $5,971 ten years ago, which means I should have invested $18,471 ten years ago and additional $20,000 5 years ago to have an aggregate of $85,000 in my account on present day.
Week 4
Giant Equipment Ltd. is considering two projects to invest next year. Both projects have the same start-up costs. Project A will produce annual cash flows of $42,000 at the beginning of each year for eight years. Project B will produce cash flows of $48,000 at the end of each year for seven years. The company requires a 12% return.
Required:
- a) Which project should the company select and why? (5 marks)
| PROJECT A | |||
| cash flow | $42,000 | ||
| occurrence | beginning of year | ||
| period | 8 years | ||
| return | 12% | ||
| PV calculated using the annuity due formula: | $578,578 | ||
| PROJECT B | |||
| cash flow | $48,000 | ||
| occurrence | end of year | ||
| period | 7 years | ||
| return | 12% | ||
| PV calculated using the ordinary annuity formula: | $484,273 | ||
Conclusion: The company should opt for Project A as it results in higher present value and accordingly higher NPV as compare with Project B.
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- b) Which project should the company select if the interest rate is 14% at the cash flows in Project B is also at the beginning of each year? (5 marks)
| PROJECT A | |||
| cash flow | $42,000 | ||
| occurrence | beginning of year | ||
| period | 8 years | ||
| return | 14% | ||
| PV calculated using the annuity due formula: | $633,584 | ||
| PROJECT B | |||
| cash flow | $48,000 | ||
| occurrence | beginning of year | ||
| period | 7 years | ||
| return | 14% | ||
| PV calculated using the ordinary annuity formula: | $587,172 | ||
Conclusion: The company should still opt for Project A as it still results in higher present value and accordingly higher NPV as compare with Project B.
Week 5
Rachel is a financial investor who actively buys and sells in the securities market. Now she has a portfolio of all blue chips, including: $13,500 of Share A, $7,600 of Share B, $14,700 of Share C, and $5,500 of Share D.
Required:
- a) Compute the weights of the assets in Rachel’s portfolio? (2 marks)
| Share type | no. of shares | Weightage |
| A | 13,500 | 33% |
| B | 7,600 | 18% |
| C | 14,700 | 36% |
| D | 5,500 | 13% |
| 41,300 | 100% |
- b) If Rachel’s portfolio has provided her with returns of 9.7%, 12.4%, -5.5% and 17.2% over the past four years, respectively, calculate the geometric average return of the portfolio for this period. (2 marks)
| Year | Return | |
| 1 | 9.7% | |
| 2 | 12.4% | |
| 3 | -5.5% | |
| 4 | 17.2% | |
| Geometric return = | (((1+D46)*(1+D47)*(1+D48)*(1+D49))^(1/4))-1 | |
| Geometric return = | 8.10% |
- c) Assume that expected return of the stock A in Rachel’s portfolio is 13.6% this year. The risk premium on the stocks of the same industry are 4.8%, betas of these stocks is 1.5 and the inflation rate was 2.7%. Calculate the risk-free rate of return using Capital Market Asset Pricing Model (CAPM). (2marks)
| CAPM equation: | Ri = Rf + β x (Rm – Rf) |
| Calcualtion of Rf, where: | |
| Ri = | 13.60% |
| β = | 1.5 |
| (Rm – Rf) = | 4.80% |
| Rf = | 13.6%-(1.5*4.8%) |
| 6.40% | |
Note: CAPM model assumes there is no inflation in the market.
- d) Following is forecast for economic situation and Rachel’s portfolio returns next year, calculate the expected return, variance and standard deviation of the portfolio. (4 marks)
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