Question

Your company is trying to decide which one of two projects it should accept. Both projects have the same start-up costs. Project 1 will produce annual cash flows of $52 000 at the end of each year for six years. Project 2 will produce cash flows of $39 000 at the beginning of each year for eight years. The company requires a 15% return. Required:

a. Whichprojectshouldthecompanyselectandwhy?

b. Whichprojectshouldthecompanyselectiftheinterestrateis12%atthe

cash flows in Project 2 is also at the end of each year?

Answer 1

Question:

Your company is trying to decide which one of two projects it should accept. Both projects have the same start-up costs. Project 1 will produce annual cash flows of $52 000 at the end of each year for six years. Project 2 will produce cash flows of $39 000 at the beginning of each year for eight years. The company requires a 15% return. Required:

a. Which project should the company select and why?

Solution:

NPV of Project 1:

Here:

Cash Flows = $ 52,000 per year at the end of each year.

Discount Rate = 15 %

Number of Years = 6 Years

Tabulation of Calculation of Net Present Value of Project 1:

Years	Cash Flows	Present Value of Net Cash Flow = Net Cash Flow / (1 + Discount Rate / 100) ^Number of Year
0	$ 52,000	(52,000) / (1+0.15) ^0    =                             $ 52,000.00
1	$ 52,000	(52,000) / (1+0.15) ^1    =                             $ 45,217.39
2	$ 52,000	(52,000) / (1+0.15) ^2    =                             $ 39,319.47
3	$ 52,000	(52,000) / (1+0.15) ^3    =                             $ 34,190.84
4	$ 52,000	(52,000) / (1+0.15) ^4    =                             $ 29,731.17
5	$ 52,000	(52,000) / (1+0.15) ^5    =                            $ 25,853.19
Total		Net Present Value of Project 1=                 $ 226,313.00

Net Present Value of Project 2:

Here:

Cash Flows = $ 39,000 per year at the beginning of each year.

Discount Rate = 15 %

Number of Years = 8 Years

Tabulation of Calculation of Net Present Value of Project 2:

Years	Cash Flows	Present Value of Cash Flow = Cash Flow / (1 + Discount Rate / 100) ^Number of Years
1	$ 39,000	(39,000) / (1+0.15) ^1    =                          $ 33913.04
2	$ 39,000	(39,000) / (1+0.15) ^2    =                          $ 29489.60
3	$ 39,000	(39,000) / (1+0.15) ^3    =                          $ 25643.13
4	$ 39,000	(39,000) / (1+0.15) ^4    =                          $ 22298.38
5	$ 39,000	(39,000) / (1+0.15) ^5    =                          $ 19389.89
6	$ 39,000	(39,000) / (1+0.15) ^6   =                          $ 16860.78
7	$ 39,000	(39,000) / (1+0.15) ^7    =                          $ 14661.54
8	$ 39,000	(39,000) / (1+0.15) ^8    =                          $ 12749.17
Total		Net Present Value of Project 2=                    $ 175,006.00

Ans: Company should select Project 1 because the NPV of Project 1 is higher than that of Project 2

NPV of Project 1 = $ 226,313.00 > NPV of Project 2 = $ 175,006.00

b. Which project should the company select if the interest rate is 12% at the

cash flows in Project 2 is also at the end of each year?

Solution:

NPV of Project 2 with New Data:

Here:

Cash Flows = $ 39,000 per year at the end of each year.

Discount Rate = 12 %

Number of Years = 8 Years

Tabulation of Calculation of Net Present Value of Project 2:

Years	Cash Flows	Present Value of Cash Flow = Cash Flow / (1 + Discount Rate / 100) ^Number of Years
0	$ 39,000	(39,000) / (1+0.12) ^0   = $ 39,000.00
1	$ 39,000	(39,000) / (1+0.12) ^1    =                                  $ 34,821.43
2	$ 39,000	(39,000) / (1+0.12) ^2    =                                  $ 31,090.56
3	$ 39,000	(39,000) / (1+0.12) ^3    = $ 27,759.43
4	$ 39,000	(39,000) / (1+0.12) ^4    = $ 24,785.21
5	$ 39,000	(39,000) / (1+0.12) ^5    =                                  $ 22,129.65
6	$ 39,000	(39,000) / (1+0.12) ^6   =                                   $ 19,758.61
7	$ 39,000	(39,000) / (1+0.12) ^7    =                                  $ 17,641.62
Total		Net Present Value of Project 2=                    $ 216,987.00

Ans: In this case also, Company should select Project 1 because the NPV of Project 1 is higher than that of Project 2

NPV of Project 1 = $ 226,313.00 > NPV of Project 2 = $ 216,987.00