End of Chapter: Capital Budgeting and Cost Analysis

Problem for Self-Study

Part A

Returning to the Vector hybrid bus project, assume that Vector is a nonprofit organization and that the expected additional operating cash inflows are $240,000 in years 1 through 4 and $210,000 in year 5. Using data from section Relevant Cash Flows in Discounted Cash Flow Analysis, the net initial investment is $661,500 (new bus, $660,000, plus additional working capital, $30,000, minus current disposal value of old bus, $28,500). All other facts are unchanged: a 5-year useful life, no terminal disposal value, and an 8% RRR. Year 5 cash inflows are $240,000, which includes a $30,000 recovery of working capital.

Required

Calculate the following:

Net present value
Internal rate of return
Payback period
Accrual accounting rate of return on net initial investment

Solution

$\begin{array}{lll} NPV & = & ($ 240,000 \times 3.993) - $ 661,500 \\ = & $ 958,320 - $ 661,500 = $ 296,820 \end{array}$

2. There are several approaches to computing IRR. One is to use a calculator with an IRR function. This approach gives an IRR of 23.8%. Another approach is to use Table 4 in Appendix A at the end of the text:

$\begin{array}{rcl} $ 661,500 & = & $ 240,000 F \\ F & = & \frac{$ 661,500}{$ 240,000} = 2.756 \end{array}$

On the five-period line of Table 4, the column closest to 2.756 is 24%. To obtain a more-accurate number, use straight-line interpolation:

The table depicts a calculation with straight-line interpolation. The details of the table are as follows:

1. 22 percent

Present value factors, left column: 2.864
Present value factors, right column: 2.864

2. IRR

Present value factors, left column: Blank
Present value factors, right column: 2.756

3. 24 percent

Present value factors, left column: 2.745
Present value factors, right column: Blank

4. Difference

Present value factors, left column: 0.119
Present value factors, right column: 0.108

$IRR = 22 % + \frac{0.108}{0.119} (2 %) = 23.8 % per year$

$\begin{array}{l} Payback period & = & \frac{Net initial investment}{Uniform increase in annual future cash flows} \\ = & $ 661,500 \div $ 240,000 = 2.76 years \end{array}$

$\begin{array}{rcl} AARR & = & \frac{annual operating income}{Net initial investment} \\ Increase in expected average \\ annual operating cash inflows & = & [($ 240,000 \times 4) + $ 210,000] \div 5 years \\ = & $ 1,170,000 \div 5 = $ 234,000 \\ Increase in annual depreciation & = & $ 120,000 ($ 132,000 - $ 12,000, see p. 863) \\ Increase in expected average & = & $ 234,000 - $ 120,000 = $ 114,000 \\ annual operating income \\ A A R R & = & \frac{$ 114,000}{$ 661,500} = 17.2 % per year \end{array}$

Part B

Assume that Vector is subject to income tax at a 40% rate. All other information from Part A is unchanged. Compute the NPV of the new hybrid bus project.

Solution

To save space, Exhibit 22-7 shows the calculations using a format slightly different from the format used in this chapter. Item 2a is where the new cash flow assumptions affect the NPV analysis (compared with Exhibit 22-6). All other amounts in Exhibit 22-7 are identical to the corresponding amounts in Exhibit 22-6. For years 1 through 4, after-tax cash flow (excluding the depreciation effect) is as follows:

Exhibit 22-7

Net Present Value Method Incorporating Income Taxes: Vector’s Hybrid Bus With Revised Annual Cash Flow From Operations

Details are as follows:

1a. l hybrid bus investment

Present Value of Cash Flows: $(660,000) in parentheses

Present Value of $1 Discounted at 8%: 1.000

Relevant Cash Flows at End of Year 0: $(660,000) in parentheses

1b. Initial working-capital investment:

Present Value of Cash Flows: (30,000) in parentheses

Present Value of $1 Discounted at 8%: 1.000

Relevant Cash Flows at End of Year 0: $ (30,000) in parentheses

1c. After-tax cash inﬂow from current disposal of old bus

Present Value of Cash Flows: 41,100

Present Value of $1 Discounted at 8%: 1.000

Relevant Cash Flows at End of Year 0: $ 41,100

Net initial investment: (648,900) in parentheses (sum of all "Present Value of Cash Flows")

2a. Annual after-tax cash ﬂow from operations (excluding the depreciation effect)

Year 1

Present Value of Cash Flows: 133,344

Present Value of $1 Discounted at 8%: 0.926

Relevant Cash Flows at End of Year 1: $144,000

Year 2

Present Value of Cash Flows: 123,408

Present Value of $1 Discounted at 8%: 0.857

Relevant Cash Flows at End of Year 2: $144,000

Year 3

Present Value of Cash Flows: 114,336

Present Value of $1 Discounted at 8%: 0.794

Relevant Cash Flows at End of Year 3: $144,000

Year 4

Present Value of Cash Flows: 105,840

Present Value of $1 Discounted at 8%: 0.735

Relevant Cash Flows at End of Year 4: $144,000

Year 5

Present Value of Cash Flows: 85,806

Present Value of $1 Discounted at 8%: 0.681

Relevant Cash Flows at End of Year 5: $126,000

2b. Income tax cash savings from annual depreciation deductions

Year 1

Present Value of Cash Flows: 44,448

Present Value of $1 Discounted at 8%: 0.926

Relevant Cash Flows at End of Year 1: $48,000

Year 2

Present Value of Cash Flows: 41,136

Present Value of $1 Discounted at 8%: 0.857

Relevant Cash Flows at End of Year 2: $48,000

Year 3

Present Value of Cash Flows: 38,112

Present Value of $1 Discounted at 8%: 0.794

Relevant Cash Flows at End of Year 3: $48,000

Year 4

Present Value of Cash Flows: 35,280

Present Value of $1 Discounted at 8%: 0.735

Relevant Cash Flows at End of Year 4: $48,000

Year 5

Present Value of Cash Flows: 32,688

Present Value of $1 Discounted at 8%: 0.681

Relevant Cash Flows at End of Year 5: $48,000

3. After-tax cash ﬂow from recovery of

a. Terminal disposal of bus

Present Value of Cash Flows: 0

Present Value of $1 Discounted at 8%: 0.681

Relevant Cash Flows at End of Year 4: $0

b. Recovery of working capital:

Present Value of Cash Flows: 20,430

Present Value of $1 Discounted at 8%: 0.681

Relevant Cash Flows at End of Year 4: $30,000

NPV if new hybrid bus purchased: $125,928 (sum of all "Present Value of Cash Flows")

The table depicts after-tax cash flow from operations with the new bus for years 1 through 4. The details of the table are as follows:

1. Annual cash flow from operations with new bus: 240,000 dollars

2. Deduct income tax payments, 0.40 times 240,000 dollars: 96,000 dollars

3. Annual after-tax cash flow from operations: 144,000 dollars

For year 5, after-tax cash flow (excluding the depreciation effect) is as follows:

The table depicts after-tax cash flow from operations with the new bus for year 5. The details of the table are as follows:

1. Annual cash flow from operations with new bus: 210,000 dollars

2. Deduct income tax payments, 0.40 times 210,000 dollars: 84,000 dollars

3. Annual after-tax cash flow from operations: 126,000 dollars

The NPV in Exhibit 22-7 is $125,928. As computed in Part A, the NPV when there are no income taxes is $296,820. The difference in these two NPVs illustrates the impact of income taxes in capital budgeting analysis.