Question

Use the following for Questions 1 - 4:

You are considering two mutually exclusive projects, A and B.

Project A costs $70,000 and generates cash flows of $12,000 for 10 years.

Project B costs $60,000 and generates cash flows of $2,000 for six years and then cash flows of $29,000 for four years.

Report rates in percentage form to two decimal places i.e. 10.03% not 10%

Question 1

At what discount rate would make you indifferent between choosing one project or another?

Question 2

Which project would you ACCEPT if your discount rate was 10%?

A) Project A

B) Project B

C) Both Project A and B

D) Neither Project A or B

Question 3

Which project would you ACCEPT if your discount rate was 5%?

A) Project A

B) Project B

C) Both Project A and B

D) Neither Project A or B

Question 4

What is the highest discount rate in which you can still produce a non-negative NPV?

Answer 1

Answer 1
Calculation of discount rate that would make you indifferent between choosing one project or another
To find out this rate , we have to take difference of cash flows between two projects and then apply IRR formula to this difference.
Year	Cash flows
	Project A	Project B	Difference
0	-70000	-60000	-10000
1	12000	2000	10000
2	12000	2000	10000
3	12000	2000	10000
4	12000	2000	10000
5	12000	2000	10000
6	12000	2000	10000
7	12000	29000	-17000
8	12000	29000	-17000
9	12000	29000	-17000
10	12000	29000	-17000
IRR of cash flow difference =			7.47%
Discount rate that would make you indifferent between choosing one project or another = 7.47%
Answer 2
We decide about the projects based on NPV.The project with higher NPV will be selected.
Year	Discount factor @ 10%	Project A		Project B
		Cash flow	Present Value	Cash flow	Present Value
0	1	-$70,000.00	-$70,000.00	-$60,000.00	-$60,000.00
1	0.909091	$12,000.00	$10,909.09	$2,000.00	$1,818.18
2	0.826446	$12,000.00	$9,917.36	$2,000.00	$1,652.89
3	0.751315	$12,000.00	$9,015.78	$2,000.00	$1,502.63
4	0.683013	$12,000.00	$8,196.16	$2,000.00	$1,366.03
5	0.620921	$12,000.00	$7,451.06	$2,000.00	$1,241.84
6	0.564474	$12,000.00	$6,773.69	$2,000.00	$1,128.95
7	0.513158	$12,000.00	$6,157.90	$29,000.00	$14,881.59
8	0.466507	$12,000.00	$5,598.09	$29,000.00	$13,528.71
9	0.424098	$12,000.00	$5,089.17	$29,000.00	$12,298.83
10	0.385543	$12,000.00	$4,626.52	$29,000.00	$11,180.76
NPV			$3,734.81		$600.41
NPV of Project A		$3,734.81
NPV of Project B		$600.41
As NPV of project A is higher , it will be selected.
The answer is Option A.
Answer 3
We decide about the projects based on NPV.The project with higher NPV will be selected.
Year	Discount factor @ 5%	Project A		Project B
		Cash flow	Present Value	Cash flow	Present Value
0	1	-$70,000.00	-$70,000.00	-$60,000.00	-$60,000.00
1	0.952381	$12,000.00	$11,428.57	$2,000.00	$1,904.76
2	0.907029	$12,000.00	$10,884.35	$2,000.00	$1,814.06
3	0.863838	$12,000.00	$10,366.05	$2,000.00	$1,727.68
4	0.822702	$12,000.00	$9,872.43	$2,000.00	$1,645.40
5	0.783526	$12,000.00	$9,402.31	$2,000.00	$1,567.05
6	0.746215	$12,000.00	$8,954.58	$2,000.00	$1,492.43
7	0.710681	$12,000.00	$8,528.18	$29,000.00	$20,609.76
8	0.676839	$12,000.00	$8,122.07	$29,000.00	$19,628.34
9	0.644609	$12,000.00	$7,735.31	$29,000.00	$18,693.66
10	0.613913	$12,000.00	$7,366.96	$29,000.00	$17,803.48
NPV			$22,660.82		$26,886.63
NPV of Project A		$22,660.82
NPV of Project B		$26,886.63
As NPV of project B is higher , it will be selected.
The answer is Option B.
Answer 4
Calculation of highest discount rate in which you can still produce a non-negative NPV
To find out this rate , we have to find out IRR for both projects.
Year	Cash flows
	Project A	Project B
0	-70000	-60000
1	12000	2000
2	12000	2000
3	12000	2000
4	12000	2000
5	12000	2000
6	12000	2000
7	12000	29000
8	12000	29000
9	12000	29000
10	12000	29000
IRR =	11.23%	10.14%
Highest discount rate for project A				11.23%
Highest discount rate for project B				10.14%