Chapter 7, Problem 7.29P

1

To determine

Introduction: The variability between present value of all cash outflow and present value of all cash inflow is known as net present value (NPV). The discount rate at which the net present value is equal to zero is knows as Internal rate of return (IRR). The ratio of income and capital gain is known as simple rate of return.

To compute: The net present value for all three investments.

Answer to Problem 7.29P

Net present value for Common stock is $7505.227, for preferred stock is (8790.85) and bond is ($3199.35)

Explanation of Solution

Net present value for Common Stock:

  $\begin{array}{l}\mathrm{Pr}esentvalueofcashflow=FV\left(\frac{1}{{(1+r)}^n}\right)\\ =160000\left(\frac{1}{{(1+1.16)}^3}\right)\\ =102505.227\end{array}$

  $\begin{array}{l}\begin{array}{l}Netpresentvalue\text{ =Present}\text{value}\text{of cash}\text{}\text{lfow-}\text{Cost}\text{of }\text{common}\text{stock}\\ \text{= }102,505.227-95,000\end{array}\hfill \\ =\$7505.227\hfill \end{array}$

Net present value of preferred Stock:

Cash inflow is 5400 for three year each:

Future value	PV factor	Present value
1800	0.847	1524.6
1800	0.718	1292.4
1800	0.608	1094.4
Total		3911.4

Sale of preferred stock is $27000

  $\begin{array}{l}\mathrm{Pr}esentvalueofpreferedstocksellingprice=FV\left(\frac{1}{{(1+r)}^n}\right)\\ =27000\left(\frac{1}{{(1+0.16)}^3}\right)\\ =17297.75\end{array}$

Total present value of all cash inflow

  $\begin{array}{l}Totalpresentvalueofcashinflow=17297.75+3911.4\\ =21209.15\end{array}$

  $\begin{array}{l}Netpresentvalueofpreferredstock=21209.15-30000\\ =(\$8790.85)\end{array}$

Net present value for bond

Cash inflow is 5400 for three year each:

Future value	PV factor	Present value
6000	0.847	5082
6000	0.718	4308
6000	0.608	3648
Total		13038

Selling price of bond is $52,700

  $\begin{array}{l}\mathrm{Pr}esentvalueofpreferedstocksellingprice=FV\left(\frac{1}{{(1+r)}^n}\right)\\ =52700\left(\frac{1}{{(1+0.16)}^3}\right)\\ =33762.65\end{array}$

Total present value of all cash inflow

  $\begin{array}{l}Totalpresentvalueofcashinflow=33762.65+13038\\ =\$46800.65\end{array}$

  $\begin{array}{l}Netpresentvalueofbond=46800.65-50,000\\ =(\$3199.35)\end{array}$

Total Net present values of all three investments are:

  $\begin{array}{l}TotalNetpresentvaluesofallthreeinvestmentsare=7505.227-8790.85-3199.35\\ =(4484.973)\end{array}$

2

To determine

Introduction: The variability between present value of all cash outflow and present value of all cash inflow is known as net present value (NPV). The discount rate at which the net present value is equal to zero is knows as Internal rate of return (IRR). The ratio of income and capital gain is known as simple rate of return.

If L earn a 16% rate of return on all investment or not.

Answer to Problem 7.29P

No L does not earn 16% rate of interest.

Explanation of Solution

The net present value of all three projects is negative therefore L did not earn 16% rate of return from her investment.

3

To determine

Introduction: The variability between present value of all cash outflow and present value of all cash inflow is known as net present value (NPV). The discount rate at which the net present value is equal to zero is knows as Internal rate of return (IRR). The ratio of income and capital gain is known as simple rate of return.

The minimum annual net cash inflow

Answer to Problem 7.29P

The minimum annual net cash inflow should be $42350

Explanation of Solution

Net proceed for investment is $239,700

Required rate of return 20%

  $\begin{array}{l}Presentvalueannuityfactor=\frac{{(1+R)}^n-1}{R{(1+R)}^n}\\ =\frac{{(1+14\%)}^{12}-1}{14\%{(1+14\%)}^{15}}\\ =5.66\end{array}$

Annual cash inflow:

  $\begin{array}{l}Annualcashinflow=\frac{investment}{factorfor12year}\\ =\frac{\$239,700}{5.66}\\ =\$42349.8\end{array}$

Annual cash inflow should be $42350