Chapter 3, Problem 20AP

a.

To determine

Calculate net present value (NPV) and identify the opportunity that Firm E should choose.

Explanation of Solution

Opportunity 1:

 Step 1: Calculate present value.

	Year 0	Year 1	Year 2
Before-tax cash flow	$(8,000)	$5,000	$20,000
Less: Tax cost	$(3,200)	$(2,000)	$(8,000)
After-tax cash flow	$4,800	$3,000	$12,000
Multiply: Discount factor at 5%	-	$\times$ 0.952	$\times$ 0 .907
Present value	$(4,800)	$2,856	$10,884

Working note:

Calculate tax cost.

	Year 0	Year 1	Year 2
Taxable income	$8,000	$5,000	$20,000
Multiply: Marginal tax rate	$\times$ 0.40	$\times$ 0 .40	$\times$ 0 .40
Tax cost	$3,200	$2,000	$8,000

Step 2: Calculate NPV.

$\begin{array}{c}\text{NPV }=\left(\begin{array}{l}\text{Present value of Year 0}\\ +\text{ Present value of Year 1}\\ +\text{ Present value of Year 2}\end{array}\right)\\ =\left(\begin{array}{l}-\$4,800+\$2,856\\ +\$10,884\end{array}\right)\\ =\$8,940\end{array}$

Opportunity 2:

Step 1: Calculate present value.

	Year 0	Year 1	Year 2
Before-tax cash flow	$6,000	$5,000	$5,000
Less: Tax cost	$(2,400)	$(2,000)	$(2,000)
After-tax cash flow	$3,600	$3,000	$3,000
Multiply: Discount factor at 5%	-	$\times$ 0.952	$\times$ 0 .907
Present value	$3,600	$2,856	$2,721

Working note:

Calculate tax cost.

	Year 0	Year 1	Year 2
Taxable income	$6,000	$5,000	$5,000
Multiply: Marginal tax rate	$\times$ 0.40	$\times$ 0 .40	$\times$ 0 .40
Tax cost	$2,400	$2,000	$2,000

Step 2: Calculate NPV.

$\begin{array}{c}\text{NPV }=\left(\begin{array}{l}\text{Present value of Year 0}\\ +\text{ Present value of Year 1}\\ +\text{ Present value of Year 2}\end{array}\right)\\ =\left(\begin{array}{l}\$3,600+\$2,856\\ +\$2,721\end{array}\right)\\ =\$9,177\end{array}$

The value of net present value (NPV) of Opportunity 2 is greater than Opportunity 1. Hence, Firm E should choose Opportunity 2.

b.

To determine

Calculate net present value (NPV) and identify the opportunity that Firm E should choose.

Explanation of Solution

Opportunity 1:

 Step 1: Calculate present value.

	Year 0	Year 1	Year 2
Before-tax cash flow	$(8,000)	$5,000	$20,000
Less: Tax cost	$(1,200)	$(750)	$(3,000)
After-tax cash flow	$6,800	$4,250	$17,000
Multiply: Discount factor at 5%	-	$\times$ 0.952	$\times$ 0 .907
Present value	$(6,800)	$4,046	$15,419

Working note:

Calculate tax cost.

	Year 0	Year 1	Year 2
Taxable income	$8,000	$5,000	$20,000
Multiply: Marginal tax rate	$\times$ 0.15	$\times$ 0 .15	$\times$ 0 .15
Tax cost	$1,200	$750	$3,000

Step 2: Calculate NPV.

$\begin{array}{c}\text{NPV }=\left(\begin{array}{l}\text{Present value of Year 0}\\ +\text{ Present value of Year 1}\\ +\text{ Present value of Year 2}\end{array}\right)\\ =\left(\begin{array}{l}-\$6,800+\$4,046\\ +\$15,419\end{array}\right)\\ =\$12,665\end{array}$

Opportunity 2:

Step 1: Calculate present value.

	Year 0	Year 1	Year 2
Before-tax cash flow	$6,000	$5,000	$5,000
Less: Tax cost	$(900)	$(750)	$(750)
After-tax cash flow	$5,100	$4,250	$4,250
Multiply: Discount factor at 5%	-	$\times$ 0.952	$\times$ 0 .907
Present value	$5,100	$4,046	$3,855

Working note:

Calculate tax cost.

	Year 0	Year 1	Year 2
Taxable income	$6,000	$5,000	$5,000
Multiply: Marginal tax rate	$\times$ 0.15	$\times$ 0 .15	$\times$ 0 .15
Tax cost	$900	$750	$750

Step 2: Calculate NPV.

$\begin{array}{c}\text{NPV }=\left(\begin{array}{l}\text{Present value of Year 0}\\ +\text{ Present value of Year 1}\\ +\text{ Present value of Year 2}\end{array}\right)\\ =\left(\begin{array}{l}\$5,100+\$4,046\\ +\$3,855\end{array}\right)\\ =\$13,001\end{array}$

The value of net present value (NPV) of Opportunity 2 is greater than Opportunity 1. Hence, Firm E should choose Opportunity 2.

c.

To determine

Calculate net present value (NPV) and identify the opportunity that Firm E should choose.

Explanation of Solution

Opportunity 1:

 Step 1: Calculate present value.

	Year 0	Year 1	Year 2
Before-tax cash flow	$(8,000)	$5,000	$20,000
Less: Tax cost	$(3,200)	$(750)	$(3,000)
After-tax cash flow	$4,800	$4,250	$17,000
Multiply: Discount factor at 5%	-	$\times$ 0.952	$\times$ 0 .907
Present value	$(4,800)	$4,046	$15,419

Working note:

Calculate tax cost.

	Year 0	Year 1	Year 2
Taxable income	$8,000	$5,000	$20,000
Multiply: Marginal tax rate	$\times$ 0.40	$\times$ 0 .15	$\times$ 0 .15
Tax cost	$3,200	$750	$3,000

Step 2: Calculate NPV.

$\begin{array}{c}\text{NPV }=\left(\begin{array}{l}\text{Present value of Year 0}\\ +\text{ Present value of Year 1}\\ +\text{ Present value of Year 2}\end{array}\right)\\ =\left(\begin{array}{l}-\$4,800+\$4,046\\ +\$15,419\end{array}\right)\\ =\$14,665\end{array}$

Opportunity 2:

Step 1: Calculate present value.

	Year 0	Year 1	Year 2
Before-tax cash flow	$6,000	$5,000	$5,000
Less: Tax cost	$(2,400)	$(750)	$(750)
After-tax cash flow	$3,600	$4,250	$4,250
Multiply: Discount factor at 5%	-	$\times$ 0.952	$\times$ 0 .907
Present value	$3,600	$4,046	$3,855

Working note:

Calculate tax cost.

	Year 0	Year 1	Year 2
Taxable income	$6,000	$5,000	$5,000
Multiply: Marginal tax rate	$\times$ 0.40	$\times$ 0 .15	$\times$ 0 .15
Tax cost	$2,400	$750	$750

Step 2: Calculate NPV.

$\begin{array}{c}\text{NPV }=\left(\begin{array}{l}\text{Present value of Year 0}\\ +\text{ Present value of Year 1}\\ +\text{ Present value of Year 2}\end{array}\right)\\ =\left(\begin{array}{l}\$3,600+\$4,046\\ +\$3,855\end{array}\right)\\ =\$11,501\end{array}$

The value of net present value (NPV) of Opportunity 1 is greater than Opportunity 2. Hence, Firm E should choose Opportunity 1.