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# 金融代写|企业融资代写Corporate Finance代考|BBOA3010 Present Value and Discounting

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## 金融代写|企业融资代写Corporate Finance代考|Present Value and Discounting

We now know that an annual interest rate of 9 percent enables the investor to transform $\$ 1$today into$\$1.1881$ two years from now. In addition, we would like to know:
How much would an investor need to lend today so that she could receive $\$ 1$two years from today? Algebraically, we can write this as $$\mathrm{PV} \times(1.09)^2=\ 1$$ In the preceding equation, PV stands for present value, the amount of money we must lend today in order to receive$\$1$ in two years’ time.

Solving for PV in this equation, we have
$$\mathrm{PV}=\frac{\ 1}{1.1881}=\ 0.84$$
This process of calculating the present value of a future cash flow is called discounting. It is the opposite of compounding. The difference between compounding and discounting is illustrated in Figure 4.8.

To be certain that $\$ 0.84$is in fact the present value of$\$1$ to be received in two years, we must check whether or not, if we loaned out $\$ 0.84$and rolled over the loan for two years, we would get exactly$\$1$ back. If this were the case, the capital markets would be saying that $\$ 1$received in two years’ time is equivalent to having$\$0.84$ today. Checking the exact numbers, we get
$$\ 0.84168 \times 1.09 \times 1.09=\ 1$$

## 金融代写|企业融资代写Corporate Finance代考|The Algebraic Formula

To derive an algebraic formula for net present value of a cash flow, recall that the PV of receiving a cash flow one year from now is
$$\mathrm{PV}=C_1 /(1+r)$$
and the $\mathrm{PV}$ of receiving a cash flow two years from now is
$$\mathrm{PV}=C_2 /(1+r)^2$$
We can write the NPV of a $T$-period project as
$$\mathrm{NPV}=-C_0+\frac{C_1}{1+r}+\frac{C_2}{(1+r)^2}+\ldots+\frac{C_T}{(1+r)^T}=-C_0+\sum_{i=1}^T \frac{C_i}{(1+r)^i}$$
The initial flow, $-C_0$, is assumed to be negative because it represents an investment. The $\Sigma$ is shorthand for the sum of the series.

## 金融代写|企业融资代写Corporate Finance代考|Present Value and Discounting

$$\mathrm{PV}=\frac{\ 1}{1.1881}=\ 0.84$$

$$\ 0.84168 \times 1.09 \times 1.09=\ 1$$

## 金融代写|企业融资代写Corporate Finance代考|The Algebraic Formula

$$\mathrm{PV}=C_1 /(1+r)$$

$$\mathrm{PV}=C_2 /(1+r)^2$$

$$\mathrm{NPV}=-C_0+\frac{C_1}{1+r}+\frac{C_2}{(1+r)^2}+\ldots+\frac{C_T}{(1+r)^T}=-C_0+\sum_{i=1}^T \frac{C_i}{(1+r)^i}$$

## MATLAB代写

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