Question

Herr Mining Company plans to open a new coal mine. Developing the mine will cost

​$10 million right​ away, but cash flows of ​$3 million will arrive starting in one year and then continuing for the next four years​ (i.e., years 2 through​ 5). After​ that, no coal will​ remain, and Herr must spend 21 million to restore the land surrounding the mine to its original condition.

a. Construct a timeline showing the cash flows starting at time zero and extending until time 6.

b. What is the total undiscounted cash flow associated with this project over its​ 6-year life? Given this​ answer, do you think there is any way that the project can be financially attractive to Herr​ Mining? Why or why​ not?

A.The total undiscounted cash flow associated with this project over its​ 6-year life is

negative $ 21 million. This project would not be financially attractive to Herr Mining because based on the total undiscounted cash​ flow, they are spending more than they make.

B.The total undiscounted cash flow associated with this project over its​ 6-year life is

$ 15 million. This project would be financially attractive to Herr Mining because based on the total undiscounted cash​ flow, they are making money.

C.The total undiscounted cash flow associated with this project over its​ 6-year life is

negative $ 16 million. This project would not be financially attractive to Herr Mining because based on the total undiscounted cash​ flow, they are spending more than they make.

D.The total undiscounted cash flow associated with this project over its​ 6-year life is

negative $ 10 million. This project would not be financially attractive to Herr Mining because based on the total undiscounted cash​ flow, they are spending more than they make.

c. Calculate the present value of the​ project's cash​ flows, assuming the​ company's opportunity cost is 66​%.

What if the opportunity cost is 12​%?

Comment on what you find.

Answer 1

(a): Time line is shown below:

(b): The answer is option "C" -

The total undiscounted cash flow associated with this project over its​ 6-year life is negative $ 16 million. This project would not be financially attractive to Herr Mining because based on the total undiscounted cash​ flow, they are spending more than they make.

Calculations: Cash flow = -10 +($3 m * 5 years) - 21

= -10m + 15 m - 21m

=- 16 million

(c): Present value when opportunity cost is 66%:

Year	Cash flow (in $ millions)	1+r	PVIF	PV = cash flow*PVIF
0	-10.00	1.66	1.0000	-10.00
1	3.00		0.6024	1.81
2	3.00		0.3629	1.09
3	3.00		0.2186	0.66
4	3.00		0.1317	0.40
5	3.00		0.0793	0.24
6	-21.00		0.0478	-1.00
			NPV	-6.82

Present value when opportunity cost is 12%:

Year	Cash flow (in $ millions)	1+r	PVIF	PV = cash flow*PVIF
0	-10.00	1.12	1.0000	-10.00
1	3.00		0.8929	2.68
2	3.00		0.7972	2.39
3	3.00		0.7118	2.14
4	3.00		0.6355	1.91
5	3.00		0.5674	1.70
6	-21.00		0.5066	-10.64
			NPV	-9.82

Findings: When opportunity cost decreases from 66% to 12% the present value of the project decreases from -$6.82 million to -$9.82 million. Thus with decrease in opportunity cost the present value of the project also decreases.