91Ó°ÊÓ

Funds required = $1,600,000

Time = 20 years

Discount rate =12%

Private placement:

Interest rate = 10%

Out-of-pocket costs = $20,000

Public placement:

Interest rate = 9%

Underwriting spread = 2%

Out-of-pocket costs = $120,000

The net amount available is $1,580,000

$$\begin{gathered} \text{Net amount}=\text{Funds raised}-\text{Out - of - pcoket costs} \\ =\$1,600,000-\$20,000 \\ =\$1,580,000 \end{gathered}$$

The present value of future payments is $1,359,259.

$$\begin{gathered} \text{PV}=∑\frac{\text{Interest rate}}{{\left(1+r\right)}^n} \\ =\left(\frac{0.05}{{\left(1+0.06\right)}^1}+\frac{0.05}{{\left(1+0.06\right)}^2}+\frac{0.05}{{\left(1+0.06\right)}^3}+\frac{0.05}{{\left(1+0.06\right)}^4}+\frac{0.05}{{\left(1+0.06\right)}^5} \\ +.................+\frac{0.05}{{\left(1+0.06\right)}^{39}}+\frac{0.05}{{\left(1+0.06\right)}^{40}} \\ \right) \\ =\$1,359,259 \end{gathered}$$

The net present value is $220,741.

$$\begin{gathered} \text{Net present value}=\text{Initial investment}-\text{PV of outflows} \\ =\$1,580,000-\$1,359,259 \\ =\$220,741 \end{gathered}$$

The net amount available is $1,488,000

$$\begin{gathered} \text{Net amount}=\text{Funds raised}-\text{Out - of - pcoket costs}-\text{Underwriting spread} \\ =\$1,600,000-\$120,000-\$32,000 \\ =\$1,488,000 \end{gathered}$$

The present value of future payments is $1,238,888.

$$\begin{gathered} \text{PV}=∑\frac{\text{Interest rate}}{{\left(1+r\right)}^n} \\ =\left(\frac{0.045}{{\left(1+0.06\right)}^1}+\frac{0.045}{{\left(1+0.06\right)}^2}+\frac{0.045}{{\left(1+0.06\right)}^3}+\frac{0.045}{{\left(1+0.06\right)}^4}+\frac{0.045}{{\left(1+0.06\right)}^5} \\ +.................+\frac{0.045}{{\left(1+0.06\right)}^{39}}+\frac{0.045}{{\left(1+0.06\right)}^{40}}\right) \\ =\$1,238,888 \end{gathered}$$

The net present value is $209,111.

$$\begin{gathered} \text{Net present value}=\text{Initial investment}-\text{PV of outflows} \\ =\$1,488,000-\$1,238,888 \\ =\$209,111 \end{gathered}$$