Question

The Sorensen Supplies Company recently purchased a new delivery truck. The initial cash outflow for the new truck is $20,000, and it is expected to generate after-tax cash flows of $6,975 per year. The truck has a 5-year expected life. The expected year-end abandonment values (after-tax salvage values) for the truck are given below. The company's WACC is 8%.

Year	Annual After-Tax Cash Flow		Abandonment Value
0	($20,000)			-
1	6,975			$14,000
2	6,975			10,500
3	6,975			8,500
4	6,975			3,500
5	6,975			0

1. What is the truck's optimal economic life? Round your answer to the nearest whole number.

      year(s)

2. Would the introduction of abandonment values, in addition to operating cash flows, ever reduce the expected NPV and/or IRR of a project?

   -Select-YesNo

Answer 1

(a.) Determination of Truck's Optimal Life :

We need to calculate Net Present Value assuming abondonment at the end of various years

Assuming Abondonment is at the end of year 1

Annual Cash Flow for year of Abondonment = Annual After tax Cash Flow + Abondonment value

Below is the table showing calculation :

Year	Cash Inflow	Present Value Factor @8%	Present value of cash inflow
1	20975 (6975 + 14000)	0.925925926	19421.2963
		Total Present value of cash inflow	19421.2963
		Less : Cash outflow	20000
		Net Present Value	-578.7037

Assuming Abondonment is at the end of year 2

Annual Cash Flow for year of Abondonment = Annual After tax Cash Flow + Abondonment value

Below is the table showing calculation :

Year	Cash Inflow	Present Value Factor @8%	Present value of cash inflow
1	6975	0.925925926	6458.333333
2	17475 (6975+ 10500)	0.85733882	14981.99588
		Total Present value of cash inflow	21440.32922
		Less : Cash outflow	20000
		Net Present Value	1440.3292

Assuming Abondonment is at the end of year 3

Annual Cash Flow for year of Abondonment = Annual After tax Cash Flow + Abondonment value

Below is the table showing calculation :

Year	Cash Inflow	Present Value Factor @8%	Present value of cash inflow
1	6975	0.925925926	6458.333333
2	6975	0.85733882	5979.938272
3	15475(6975+8500)	0.793832241	12284.55393
		Total Present value of cash inflow	24722.82553
		Less : Cash outflow	20000
		Net Present Value	4722.8255

Assuming Abondonment is at the end of year 4

Annual Cash Flow for year of Abondonment = Annual After tax Cash Flow + Abondonment value

Below is the table showing calculation :

Year	Cash Inflow	Present Value Factor @8%	Present value of cash inflow
1	6975	0.925925926	6458.333333
2	6975	0.85733882	5979.938272
3	6975	0.793832241	5536.979881
4	10475(6975+3500)	0.735029853	7699.437708
		Total Present value of cash inflow	25674.68919
		Less : Cash outflow	20000
		Net Present Value	5674.6892

Assuming Abondonment is at the end of year 5

Annual Cash Flow for year of Abondonment = Annual After tax Cash Flow + Abondonment value

Below is the table showing calculation :

Year	Cash Inflow	Present Value Factor @8%	Present value of cash inflow
1	6975	0.925925926	6458.333333
2	6975	0.85733882	5979.938272
3	6975	0.793832241	5536.979881
3	6975	0.735029853	5126.833223
4	6975	0.680583197	4747.067799
		Total Present value of cash inflow	27849.15251
		Less : Cash outflow	20000
		Net Present Value	7849.1525

Since Net Present value (7849.15 NPV) is maximum at year 5 , therefore Truck's Optimal Life is 5 years

(b.) No the introduction of abandonment values, in addition to operating cash flows, never reduce the expected NPV and/or IRR of a project