Question 1
A perpetual net cash flow implies that the stream of cash flows is for an infinite amount of time. This implies that the number of periods used in the valuation of the company is infinite. This is calculated by dividing the cash flows by a specified by a rate of discount.
PV (Present value) of perpetuity = AR (Annual Return) / DR (Discount Rate)
Therefore DR (Discount Rate) = AR (Annual Return) / PV (Present Value)
Present value = RMB 800m
Annual returns (net cash flow) = RMB 100M
DR = AR / PV
= 100, 000,000 / 800,000,000
= 1 / 8
= 0.125 or 12.5%
Question 2
Since Fan Bingbing would only remain at the top for two years, the number of years used in the calculation of the cash flow would only be two years given the company is still valued at Rmb800 million.
| Cash flow | |
| Number of years | 2 |
| Present Value | 800,000,000 |
| Rate | 25% |
| Cash flow | $555,555,555.56 |
| Cash flow for the two years | $1,111,111,111.11 |
Question 3
A discount rate is a rate used in the calculation of present value when conducting a discounted analysis of cash flow. Discounting cash flow is essential in estimating what the valuation of a company is today. The discount rate is determined by uncertainty risk and TVM (time value of money). The higher the discount rate, the greater the uncertainty, which lowers the PV (Present Value) of the cash flows in the future. We cannot explain the high rate of discount as a systematic risk-reward. CAPM, in most cases, provide discount rates that are lower than 25%. Venture capitalists use high discount rates are because of illiquid investments, the value-added that the VC has, forecasts that are optimistic and the market power that VC has. Our discount rate calculated is 12.5%, slightly lower than the discount rate provided in the table which are required by venture capitalist when they want to invest in a company. However, this is a perpetual net cash flow, and it would act as a continuous source of income. This could cause many venture capitalists to never invest in it. By looking at the previous studies and the required rate of return, we can see that the discount rate used by most investors lies between 20% to 80% annually, depending on the cycle of the company. Most of the venture capitalists if they want to invest. They look for an investment that can compensate for the risk they are taking or one that would have a higher return. The discount rate implied by the venture capital should be higher than the risk-free rate. For all investments, uncertainty on their efficient realization results in higher rates of discount. As the company matures, investors tend to lower the rate of discount since as the company grows bigger, the systematic risk tends to become smaller since the growth rates of the company become moderate, and expenses get lower in connection to its turnover. The more the company becomes mature, the more the investment becomes more liquid due to the fact that are more prospective buyers of that particular stock. The low discounted rate is also as a result of the reduced added value brought about by venture capitalists and a decrease in the terminal value of the company.
The implied discount rate calculated in the first part is lower than the return rates that venture capitalists sought, and it would not be reasonable to invest in the project if it were a seed or a start-up. For a seed or a start-up, the required rate of return is supposed to be more than 50%, meaning that 12.5% is very low. This is because such projects tend to be very risky. Based on the rate, if the investors went ahead with the proposed acquisition, the project would not be able to compensate for the risks that they take. The discount rate could have been affected by the company’s stage such that the company may not be a start-up and, therefore, less risky. It could also be due to a liquid investment as a result of more prospective for its stock. The investment may also be less dependent on the venture capitalists because it can manage itself by reducing the value-added that venture capitalist has.
Question 4
CEQ (Certainty equivalent) valuation method
In the CEQ method of valuation, financial claims’ expected cash flows get valued. Risky cash flows get adjusted to their particular equivalent using CAPM. To accept the project, we have to calculate the present value of the cash flows. We will, therefore, require the expected cash flows, cash flow beta, market risk premium, and the risk-free rate to obtain the present values of the cash flows. If the present value obtained is positive, we accept the project, while if it is negative, then we reject the project.
Market information
| Market portfolio return Standard deviation | Correlation coefficient between market portfolio return and cash flow brought to ZTTF by Fan Bingbing | Market Risk premium | Risk-free rate | |
| 1 | 10 | 1.5 | 5% | 2% |
| 2 | 25 | 1.5 | 10% | 5% |
| 3 | 30 | 1.5 | 15% | 6% |
| 4 | 20 | 1.5 | 12% | 5% |
| 5 | 10 | 1.5 | 6% | 3% |
Project Information
| Net cash flow brought to ZTTF by Fan Bingbing (Rmb million) | Probability | Net cash flow brought to ZTTF by Fan Bingbing (Rmb million) | Probability | |
| 0 | -800 | 100% | 0 | 0% |
| 1 | 100 | 80% | 0 | 20% |
| 2 | 100 | 50% | 0 | 50% |
| 3 | 100 | 36% | 0 | 64% |
| 4 | 100 | 20% | 0 | 80% |
| 5 | 100 | 10% | 0 | 90% |
Expected Cash Flow
| Net cash flow brought to ZTTF by Fan Bingbing (Rmb million) (success) | Probability | Net cash flow brought to ZTTF by Fan Bingbing (Rmb million) (failure) | Probability | Expected Cash flow E(CFt) in (Rmb million) | |
| 0 | -800 | 100% | 0 | 0% | -800 |
| 1 | 100 | 80% | 0 | 20% | 80 |
| 2 | 100 | 50% | 0 | 50% | 50 |
| 3 | 100 | 36% | 0 | 64% | 36 |
| 4 | 100 | 20% | 0 | 80% | 20 |
| 5 | 100 | 10% | 0 | 90% | 10 |
Cash flow beta
Estimating the cash flows’ standard deviation
| Net cash flow brought to ZTTF by Fan Bingbing (Rmb million) (success) | Probability | Net cash flow brought to ZTTF by Fan Bingbing (Rmb million) (failure) | Probability | Expected Cash flow E(CFt) in (Rmb million) | Standard deviation of Cash flow | |
| 0 | -800 | 100% | 0 | 0% | -800 | 0 |
| 1 | 100 | 80% | 0 | 20% | 80 | 40 |
| 2 | 100 | 50% | 0 | 50% | 50 | 50 |
| 3 | 100 | 36% | 0 | 64% | 36 | 48 |
| 4 | 100 | 20% | 0 | 80% | 20 | 40 |
| 5 | 100 | 10% | 0 | 90% | 10 | 30 |
Cash beta
| Year | Standard deviation of Cash flow | Market portfolio return Standard deviation | Correlation coefficient between market portfolio return and cash flow brought to ZTTF by Fan Bingbing | Cash flow beta |
| 0 | 0 | 0 | 0 | 0 |
| 1 | 40 | 10 | 1.5 | 6 |
| 2 | 50 | 25 | 1.5 | 3 |
| 3 | 48 | 30 | 1.5 | 2.4 |
| 4 | 40 | 20 | 1.5 | 3 |
| 5 | 30 | 10 | 1.5 | 4.5 |
The CEQ of the cash flows
The present values of the cash flows
| Year | Expected Cash flow E(CFt) in (Rmb million) | Cash flow beta | Market Risk premium | CEQ | Risk-free rate | Present value |
| 0 | -800 | 0 | 0% | -800 | 0% | -800 |
| 1 | 80 | 6 | 5% | 79.7 | 2% | 78.43 |
| 2 | 50 | 3 | 10% | 49.7 | 5% | 45.35 |
| 3 | 36 | 2.4 | 15% | 35.64 | 6% | 30.22 |
| 4 | 20 | 3 | 12% | 19.64 | 5% | 16.45 |
| 5 | 10 | 4.5 | 6% | 9.73 | 3% | 8.264 |
| Total PV | -621.286 |
ZTTF should reject the proposal since the present value of -621.286 is negative.