The Landers Corporation needs to raise \(1.60 million of debt on a 20-year issue. If it places the bonds privately, the interest rate will be 10 percent. Twenty thousand dollars in out-of-pocket costs will be incurred. For a public issue, the interest rate will be 9 percent, and the underwriting spread will be 2 percent. There will be \)120,000 in out-of-pocket costs. Assume interest on the debt is paid semi-annually, and the debt will be outstanding for the full 20-year period, at which time it will be repaid. For each plan, compare the net amount of funds initially available—inflow— to the present value of future payments of interest and principal to determine net present value. Assume the stated discount rate is 12 percent annually. Use 6 percent semi-annually throughout the analysis. (Disregard taxes.)

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.

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

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.

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

The net present value is $209,111.

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