Question

Year	dry processing	solvent preparing
0	-1810000	-805000
1	1111000	430000
2	922000	710000
3	761000	412000

Consider the following cash flows of two mutually exclusive projects for Spartan Rubber Company. Assume the discount rate for both projects is 8 percent.

a.

What is the payback period for both projects? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.) b. What is the NPV for both projects? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.) c. What is the IRR for both projects? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) d. Calculate the incremental IRR for the cash flows. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a)

Project A
Year	dry processing	Cumulative cash flows
0	-1810000
1	1111000	1111000
2	922000	2033000
3	761000	2794000

Payback period A= 1 + [ 1,810,000 - 1,111,000 ] 922,000

Payback period A = 1.76 years

Project B
Year	solvent preparing	Cumulative cash flows
0	-805,000
1	430,000	430000
2	710,000	1140000
3	412,000	1552000

Payback period = 1 + [ 805,000 - 430,000 ]   710,000

Payback period = 1.53 years

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b)

The NPV of project A = - $ 1,810,000 + $ 1,111,000 (1+0.08)¹ + $ 922,000 (1+0.08)² + $ 761,000 (1+0.08)³

The NPV of project A = $613,276.43

The NPV of project B = - $ 805,000+ $ 430,000 (1+0.08)¹ + $ 710,000 (1+0.08)² + $ 412,000 (1+0.08)³

The NPV of project B = $528,917.59

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c)

The IRR is the discount rate which makes the net present value of the project equal to zero.

IRR project A

0 =  - $ 1,810,000 + $ 1,111,000 (1+discount rate)¹ + $ 922,000 (1+discount rate)² + $ 761,000 (1+discount rate)³  

Solving for the discount rate

IRR of project A = 27.32 %

IRR of project B

0 =  - $ 805,000+ $ 430,000 (1+discount rate)¹ + $ 710,000 (1+discount rate)² + $ 412,000 (1+discount rate)³

IRR of project B = 41.39%

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d)

Year	dry processing	solvent preparing	Incremental cash flows project A - project B
0	-1810000	-805000	-1005000
1	1111000	430000	681000
2	922000	710000	212000
3	761000	412000	349000

Incremental IRR for the cash flows is the discount rate that makes the net present value of the incremental cash flows equal to zero.

0 =  - $ 1,005,000+ $ 681,000 (1+discount rate)¹ + $ 212,000 (1+discount rate)² + $ 349,000 (1+discount rate)³

Incremental IRR = 13.38%