Question

Sandhill Incorporated management is considering investing in two alternative production systems. The systems are mutually exclusive, and the cost of the new equipment and the resulting cash flows are shown in the accompanying table. The firm uses a 10 percent discount rate for production systems. Year System 1 System 2 0 -$12,590 -$48,783 1 12,731 33,490 2 12,731 33,490 3 12,731 33,490 Compute the IRR for both production system 1 and production system 2. (Do not round intermediate calculations. Round answers to 2 decimal places, e.g. 15.25%.) IRR of system 1 is % and IRR of system 2 is %. Which has the higher IRR? has higher IRR. Compute the NPV for both production system 1 and production system 2. (Do not round intermediate calculations. Round answers to 2 decimal places, e.g. 15.25.) NPV of system 1 is $ and NPV of system 2 $ . Which production system has the higher NPV? has higher NPV.

Answer 1

Computation of IRR using trial and error method:

System 1:

Computation of NPV using discount rate of 85 %:

Year	Cash Flow S1	Computation of PV Factor	PV Factor @ 85 % (F)	PV (S1 x F)
0	-$12,590	1/(1+0.85)^0	1	-$12,590
1	12731	1/(1+0.85)^1	0.54054054054054	6881.62162
2	12731	1/(1+0.85)^2	0.29218407596786	3719.79547
3	12731	1/(1+0.85)^3	0.15793733836101	2010.70025
			NPV1	$22.11734

As NPV is positive, let’s compute NPV at discount rate of 86 %.

Year	Cash Flow S1	Computation of PV Factor	PV Factor @ 86 % (F)	PV (S1 x F)
0	-$12,590	1/(1+0.86)^0	1	-$12,590
1	12731	1/(1+0.86)^1	0.53763440860215	6844.62366
2	12731	1/(1+0.86)^2	0.28905075731298	3679.90519
3	12731	1/(1+0.86)^3	0.15540363296397	1978.44365
			NPV2	-$ 87.02750

IRR = R1 + [NPV1 x (R2 – R1)/ (NPV1 – NPV2)]

= 85 % + [$ 22.11734 x (86% - 85%)/ ($ 22.11734 – (-$ 87.02750))]

= 85 % + [($ 22.11734 x 1 %)/ ($ 22.11734 +$ 87.02750)]

= 85 % + ($ 22.11734/ $ 109.14485)

= 85 % + 0.002026422

= 85 % + 0.20 % = 85.20 %

System 2:

Computation of NPV using discount rate of 47 %:

Year	Cash Flow S2	Computation of PV Factor	PV Factor @ 47 % (F)	PV (S2 x F)
0	-$48,783	1/(1+0.47)^0	1	-$48,783
1	33490	1/(1+0.47)^1	0.68027210884354	22782.31293
2	33490	1/(1+0.47)^2	0.46277014207043	15498.17206
3	33490	1/(1+0.47)^3	0.31480962045608	10542.97419
			NPV1	$40.45918

As NPV is positive, let’s compute NPV at discount rate of 48 %.

Year	Cash Flow S2	Computation of PV Factor	PV Factor @ 48 % (F)	PV (S2 x F)
0	-$48,783	1/(1+0.48)^0	1	-$48,783
1	33490	1/(1+0.48)^1	0.67567567567568	22628.37838
2	33490	1/(1+0.48)^2	0.45653761869978	15289.44485
3	33490	1/(1+0.48)^3	0.30847136398634	10330.70598
			NPV 2	-$ 534.47079

IRR = R1 + [NPV1 x (R2 – R1)/ (NPV1 – NPV2)]

= 47 % + [$ 40.45918 x (48% - 47%)/ ($ 40.45918 – (-$ 534.47079))]

= 47 % + [($ 40.45918 x 1 %)/ ($ 40.45918 +$ 534.47079)]

= 47 % + ($ 0.4045918/ $ 574.92996)

= 47 % + 0.000703723

= 47 % + 0.07 % = 47.07 %

IRR of System 1 is 85.20 %

IRR of System 2 is 47.07 %

System 1 has higher IRR.

Computation of NPV:

System 1:

Year	Cash Flow S1	Computation of PV Factor	PV Factor @ 10 % (F)	PV (S1 x F)
0	-$12,590	1/(1+0.1)^0	1	-$12,590
1	12731	1/(1+0.1)^1	0.90909090909091	11573.63636
2	12731	1/(1+0.1)^2	0.82644628099174	10521.48760
3	12731	1/(1+0.1)^3	0.75131480090158	9564.98873
			NPV S1	$19,070.11269

System 2:

Year	Cash Flow S2	Computation of PV Factor	PV Factor @ 10 % (F)	PV (S2 x F)
0	-$48,783	1/(1+0.1)^0	1	-$48,783
1	33490	1/(1+0.1)^1	0.90909090909091	30445.45455
2	33490	1/(1+0.1)^2	0.82644628099174	27677.68595
3	33490	1/(1+0.1)^3	0.75131480090158	25161.53268
			NPV S2	$34,501.67318

NPV of System 1 is $ 19,070.11

NPV of System 2 is $ 34,501.67

System 2 has higher NPV.