# Question 1

You recently received a bonus of $8,000 and are thinking of investing this sum of money for your retirement 20 years later. Sandy Chen, your financial planner, approached you recently an offered two investment products.

Product Aee will earn an annual return of 5% per year for the first 5 years. If there is no recession in Singapore during the first 5 years, all amounts invested will earn an annual return of 7% for the next 10 years, otherwise, returns will be 3% per year.

Alternatively, Product Bee allows you to invest $800 per year (at the beginning of each year) for the next 10 years. It will earn a return of 5% per year. This product will mature 20 years later.

Over the next two decades, the deposit rate offered by local banks is expected to be 2% per year, which is compounded daily. Whereas, lending rates are expected to be 6% per year (compounded monthly).

Based on a recent article you read from Business Times, economists have predicted that there will be a 70% chance of a recession happening over the next several years.

- Calculate the amount you expect to receive at the end of 15 years for Product Aee if there is no recession during the first 5 years.

- Calculate the amount you expect to receive at the end of 15 years for Product Aee if there is a recession during the first 5 years.

- Calculate the value of Product Bee on maturity.

- Calculate the effective interest rate of both deposit and lending rates.

# Question 2

Ravi, a fund manager working for a private equity firm headquartered in Singapore, is considering including the following stocks in the firm’s portfolio:

Probability | State of Economy | Rate of Return | ||

Stock RST | Stock VVR | Stock BAB | ||

25% | Boom | 0% | 20.00% | 40.00% |

40% | Normal | 6% | 12.00% | 15.00% |

35% | Recession | 15% | -4.00% | -26.00% |

He plans to invest 40% of the portfolio funds in stock RST and the balance equally between VVR and BAB. Beta of stock VVR is 0.15 higher than RST.

The firm’s in-house economist anticipates the probability of boom, normal and recession to be 25%, 40% and 35% respectively. The yield on long term government securities is 3% per year.

- Calculate the expected return and standard deviation for each stock.

- Calculate the expected return, expected risk premium and standard deviation for the portfolio.

- Interpret your answer for part (a) and (b) and advise Ravi on his asset allocation plan for the portfolio.

- Explain whether stock RST or stock VVR is riskier.

# Question 3

Decacorn Capital LLP (“Decacorn”) is evaluating two greenfield solar energy projects with the following forecasted free cash flows:

Year | Project Sumo | Project Steel |

1 | 80000 | 160000 |

2 | 95000 | 160000 |

3 | 80000 | 160000 |

4 | 73000 | 160000 |

5 | -60000 | -520000 |

The initial investment for Project Sumo and Project Steel is $200,000 and $170,000 respectively. Decacorn would like to invest in only one project and uses a discount rate of 12% for solar energy projects.

Besides the solar energy projects, there is another investment opportunity to acquire a ride hailing business, Easy Ride Pte Ltd (“Easy Ride”). Currently, this firm does not have any debt and its cost of equity is estimated to be 18%. Post-acquisition, Decacorn intends to change Ride Easy’s debt-to-equity ratio to 0.25. The firm is envisaged to have a borrowing cost is 7% and corporate tax rate is 17%.

- Calculate the net present value (NPV) and internal rate of return (IRR).
- Calculate the modified IRR for Project Steel.
- Interpret your answer for part (a) and (b) and advise Decacorn which project it should undertake.
- Calculate Easy Ride’s weighted average cost of capital (WACC) post-acquisition. Assume Modigliani and Miller (M&M) theory with tax holds true.

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