Question

NPV​, with rankings Botany​ Bay, Inc., a maker of casual​ clothing, is considering four projects shown in the following​ table,

Initial investment   $50,100   $100,000   $80,100   $180,200
Year   Cash inflows          
1   $20,600   $35,400   $20,800   $100,400
2   $20,600   $51,500   $39,800   $79,300
3   $20,600   $51,100   $60,700   $60,400

Because of past financial​ difficulties, the company has a high cost of capital at 14.7 %.

a. Calculate the NPV of each​ project, using a cost of capital of 14.7 %.

b. Rank acceptable projects by NPV.

c. Calculate the IRR of each project and use it to determine the highest cost of capital at which all of the projects would be acceptable.

Answer 1

Present Value = Future value/ ((1+r)^t)
where r is the interest rate that is 14.7% and t is the time period in years.
Net present value (NPV) = initial investment + sum of present values of future cash flows.
The internal rate of return is the rate of return for which the NPV is zero.
Use the financial formulas function in excel to calculate the IRR of each project.
PROJECT 1
Year	0	1	2	3
cash flow	-50100	20600	20600	20600
present value		17959.9	15658.15	13651.39
NPV	-2830.564
IRR	11.28%
PROJECT 2
Year	0	1	2	3
cash flow	-100000	35400	51500	51100
present value		30863.12	39145.37	33863.41
NPV	3871.89706
IRR	16.87%
PROJECT 3
Year	0	1	2	3
cash flow	-80100	20800	39800	60700
present value		18134.26	30252.15	40225.22
NPV	8511.63355
IRR	20.00%
PROJECT 4
Year	0	1	2	3
cash flow	-180200	100400	79300	60400
present value		87532.69	60276.27	40026.41
NPV	7635.37565
IRR	17.47%
a) Using a cost of capital of 14.7% the following are the NPV's
PROJECT 1	-2830.56
PROJECT 2	3871.90
PROJECT 3	8511.63
PROJECT 4	7635.38
b) Acceptable projects by NPV
RANK	PROJECT
1	PROJECT 3.
2	PROJECT 4.
3	PROJECT 2.
4	PROJECT 1.
c) The following are the IRR's
PROJECT 1	11.28%
PROJECT 2	16.87%
PROJECT 3	20.00%
PROJECT 4	17.47%
The highest cost of capital for which all projects would be acceptable
is 11.28%.
If the cost of capital is more than 11.28% then project 1 will not be acceptable.