Question

Consider the following cash flows of two mutually exclusive projects for A–Z Motorcars. Assume the discount rate for both projects is 11 percent.

Year	Mini	Full
0	-495000	-845000
1	329000	359000
2	198000	438000
3	159000	299000

a. What is the payback period for each project?

b. What is the NPV for each project?

c. What is the IRR for each project?

Answer 1

Project Mini

Year	0	1	2	3
Cashflow(in $)	(495,000)	329,000	198,000	159,000
Cumulative Cashflow(in $)	(495,000)	(166,000)	32,000	191,000

Payback Period = A+(B/C)

where

A - last period containing negative cumulative cash flow = 1

B - absolute value of cumulative cash flow in A = 166000

C - cash flow during the period after A = 198000

Payback Period = 1+(166000/198000)

= 1.84 years

Year	0	1	2	3
Cashflow(in $)	(495,000)	329,000	198,000	159,000
PVF @11%	1	0.901	0.812	0.731
Discounted Cashflow (Cash flow * PVF)	(495,000)	296,396	160,701	116,259

NPV = PV of Inflows - PV of Outflows

= (296396+160701+116259)-495000

= 573357-495000

= 78357

IRR is the rate at which NPV=0. ie: PV of inflows = PV of outflows. It is calculated by trial and error method.

Lets find NPV at say 21%.

Year	0	1	2	3
Cashflow(in $)	(495,000)	329,000	198,000	159,000
PVF @21%	1	0.826	0.683	0.564
Discounted Cashflow (Cash flow * PVF)	(495,000)	271,901	135,237	89,751

NPV = PV of Inflows - PV of Outflows

= (271901+135237+89751)-495000

= 496889-495000

= 1889

Since NPV is positive, Take a higher rate say 22%

Year	0	1	2	3
Cashflow(in $)	(495,000)	329,000	198,000	159,000
PVF @22%	1	0.820	0.672	0.551
Discounted Cashflow (Cash flow * PVF)	(495,000)	269,672	133,029	87,562

NPV = PV of Inflows - PV of Outflows

= (269672+133029+87562)-495000

= 490263-495000

= -4737

Now we got two rates R1 and R2 such that NPV at R1(NPV1) is higher and NPV at R2(NPV2) is lower.

IRR = R1 + ((NPV1 x (R2 - R1)) / (NPV1 - NPV2))

= 21+((1889*(22-21))/(1889+4737)

= 21.2850890432

= 21.29%

Project Full

Year	0	1	2	3
Cashflow(in $)	-845000	359000	438000	299000
Cumulative Cashflow(in $)	(845,000)	(486,000)	(48,000)	251,000

Payback Period = A+(B/C)

where

A - last period containing negative cumulative cash flow = 2

B - absolute value of cumulative cash flow in A = 48000

C - cash flow during the period after A = 299000

Payback Period = 2+(48000/299000)

= 2.16 years

Year	0	1	2	3
Cashflow(in $)	-845000	359000	438000	299000
PVF @11%	1	0.901	0.812	0.731
Discounted Cashflow (Cash flow * PVF)	(845,000)	323,423	355,491	218,626

NPV = PV of Inflows - PV of Outflows

= (323423+355491+218626)-845000

= 897540-845000

= 52540

IRR is the rate at which NPV=0. ie: PV of inflows = PV of outflows. It is calculated by trial and error method.

Lets find NPV at say 14%.

Year	0	1	2	3
Cashflow(in $)	-845000	359000	438000	299000
PVF @14%	1	0.877	0.769	0.675
Discounted Cashflow (Cash flow * PVF)	(845,000)	314,912	337,027	201,816

NPV = PV of Inflows - PV of Outflows

= (314912+337027+201816)-845000

= 853756-845000

= 8756

Since NPV is positive, Take a higher rate say 15%

Year	0	1	2	3
Cashflow(in $)	-845000	359000	438000	299000
PVF @15%	1	0.870	0.756	0.658
Discounted Cashflow (Cash flow * PVF)	(845,000)	312,174	331,191	196,597

NPV = PV of Inflows - PV of Outflows

= (312174+331191+196597)-845000

= 839962-845000

= -5038

Now we got two rates R1 and R2 such that NPV at R1(NPV1) is higher and NPV at R2(NPV2) is lower.

IRR = R1 + ((NPV1 x (R2 - R1)) / (NPV1 - NPV2))

= 14+((8756*(15-14))/(8756+5038)

= 14.63476874

= 14.63%