Question

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

Year	Dry Prepreg			Solvent Prepreg
0	–$	1,810,000		–$	805,000
1		1,111,000			430,000
2		922,000			710,000
3		761,000			412,000

a. What is the payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

	Payback period
Dry Prepreg	1.92 1.92 Incorrect years
Solvent Prepreg	2.20 2.20 Incorrect years

b. What is the NPV for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

	NPV
Dry Prepreg	$ 94643.09 94643.09 Incorrect
Solvent Prepreg	$ 89318.70 89318.70 Incorrect

c. What is the IRR for each project? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

	IRR
Dry Prepreg	19.08 19.08 Incorrect %
Solvent Prepreg	13.69 13.69 Incorrect %

d. Calculate the incremental IRR for the cash flows. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Incremental IRR             Not attempted%

Answer 1

a. The Pay-back Period of the projects are as follows:

• Project Dry Prepreg: 1.76 years (or) 1 year 9 months 3 days) (approx.)
• Project Solvent Prepreg: 1.53 years (or) 1 year 6 months 11 days (approx.)

Computations:

Cumulative Cash flows:

	Dry Prepreg		Solvent Prepreg
Year	Cash flows	Cumulative Cash flows	Cash flows	Cumulative Cash flows
1	$ 1,111,000	$        1,111,000	$   430,000	$ 430,000
2	$ 922,000	$     2,033,000	$    710,000	$1,140,000
3	$ 761,000	$     2,794,000	$    412,000	$1,552,000

From the above table, it can be observed that the cash flows exceeds the initial investment in year 2 in both the projects.

The incremental cash flows required to recover the initial investment and proportionate time taken to recover them are as follows:

	Dry Prepreg	Solvent Prepreg
Initial Investment	$      1,810,000	$   805,000
Less: Cash flows in year 1	$       (1,111,000)	$ (430,000)
Incremental Cash flows required in year 2	$       699,000	$    375,000
Total Cash flows during the year 2	$        922,000	$    710,000
Time taken to recover the incremental cash flows	0.76	0.53
Time taken in months	9.10	6.34
Total Pay-back period	1.76	1.53

b. The NPV of the projects are as follows:

• Project Dry Prepreg: $613,276.43
• Project Solvent Prepreg: $528,971.59

Computation:

Dry Prepreg
Year	Cash flows	PV factor @ 8%	PV of cash flows
1	$ 1,111,000	0.93	$   1,028,703.70
2	$ 922,000	0.86	$    790,466.39
3	$ 761,000	0.79	$     604,106.34
Total PV of cash flows			$   2,423,276.43
Less: Initial Investment			$      (1,810,000)
NPV of the Project			$      613,276.43

Solvent Prepreg
Year	Cash flows	PV factor @ 8%	PV of cash flows
1	$ 430,000	0.93	$      398,148.15
2	$   710,000	0.86	$    608,710.56
3	$   412,000	0.79	$     327,058.88
Total PV of cash flows			$    1,333,917.59
Less: Initial Investment			$      (805,000)
NPV of the Project			$     528,917.59

c. Internal Rate of Return of the projects:

• Project Dry Prepreg: 27.32% (using excel formula) (or) 27.33% (using interpolation technique)
• Project Solvent Prepreg: 41.39% (using excel formula) (or) 41.40% (using interpolation technique)

Computation

Internal Rate of return is that level of discount rate at which the NPV of the project will be 0. It should be calculated using the trial and error method.

IRR of project Dry prepreg:

Let the discount rate be 27%. The NPV of the project will be:

Dry Prepreg
Year	Cash flows	PV factor @ 27%	PV of cash flows
1	$        1,111,000	0.79	$     874,803.15
2	$       922,000	0.62	$       571,641.14
3	$        761,000	0.49	$       371,512.55
Total PV of cash flows			$    1,817,956.85
Less: Initial Investment			$     (1,810,000)
NPV of the Project			$        7,956.85

If the discount rate is 28%, the resulting NPV would be:

Dry Prepreg
Year	Cash flows	PV factor @ 28%	PV of cash flows
1	$   1,111,000	0.78	$    867,968.75
2	$ 922,000	0.61	$     562,744.14
3	$   761,000	0.48	$    362,873.08
Total PV of cash flows			$   1,793,585.97
Less: Initial Investment			$     (1,810,000)
NPV of the Project			$      (16,414.03)

From the above 2 tables, it can be observed that the IRR lies somewhere in between 27% and 28%

To find out IRR, we should follow interpolation technique.

Incremental NPV at 27% (a)	$        7,956.85
NPV lost when discount rate changed from 27% to 28% (b)	$      24,370.88
Incremental IRR to recover the incremental NPV = (a) / (b)	0.33

Total IRR = 27% + 0.33% = 27.33% (approx)

IRR of project Solvent prepreg:

Let discount rate of the project be 41%, then NPV is:

Solvent Prepreg
Year	Cash flows	PV factor @ 41%	PV of cash flows
1	$      430,000	0.71	$    304,964.54
2	$       710,000	0.50	$      357,124.89
3	$       412,000	0.36	$     146,973.78
Total PV of cash flows			$    809,063.22
Less: Initial Investment			$      (805,000)
NPV of the Project			$        4,063.22

Let us assume the discount rate to be 42%, the resulting NPV is:

Solvent Prepreg
Year	Cash flows	PV factor @ 42%	PV of cash flows
1	$ 430,000	0.70	$    302,816.90
2	$   710,000	0.50	$      352,112.68
3	$   412,000	0.35	$     143,890.52
Total PV of cash flows			$     798,820.10
Less: Initial Investment			$      (805,000)
NPV of the Project			$       (6,179.90)

From the above 2 tables, it can be observed that the IRR lies somewhere in between 41% and 42%

To find out IRR, we should follow interpolation technique.

Incremental NPV at 41% (a)	$        4,063.22
NPV lost when discount rate changed from 41% to 42% (b)	$      10,242.128
Incremental IRR to recover the incremental NPV = (a) / (b)	0.40

Total IRR = 41% + 0.40% = 41.40% (approx)

d. Incremental IRR of the projects is 13.38%

Incremental cash flows:

Year	Dry Prepreg	Solvent Prepreg	Incremental Cash flows
1	$     1,111,000	$ 430,000	$ 681,000
2	$        922,000	$ 710,000	$    212,000
3	$        761,000	$ 412,000	$    349,000
Incremental Initial Investment	$    (1,810,000)	$(805,000)	$ (1,005,000)

Incremental IRR using trial and error method:

Let the discount rate be 13%. The resulting NPV is:

Year	Cash flows	PV factor @ 13%	PV of cash flows
1	$      681,000	0.88	$    602,654.87
2	$       212,000	0.78	$     166,027.10
3	$     349,000	0.69	$      241,874.51
Total PV of cash flows			$   1,010,556.47
Less: Initial Investment			$    (1,005,000)
NPV of the Project			$        5,556.47

Let the discount rate be 14%. The resulting NPV is:

Year	Cash flows	PV factor @ 14%	PV of cash flows
1	$     681,000	0.88	$    597,368.42
2	$      212,000	0.77	$       163,127.12
3	$    349,000	0.67	$    235,565.06
Total PV of cash flows			$ 996,060.60
Less: Initial Investment			$    (1,005,000)
NPV of the Project			$      (8,939.40)

From the above 2 tables, it can be observed that the IRR lies somewhere in between 13% and 14%

To find out IRR, we should follow interpolation technique.

Incremental NPV at 13% (a)	$        5,556.47
NPV lost when discount rate changed from 13% to 14% (b)	$      14,495.87
Incremental IRR to recover the incremental NPV = (a) / (b)	0.38

Total IRR = 13% + 0.38% = 13.38% (approx)