Question

Consider the following cash flows on two mutually exclusive projects for the Bahamas Recreation Corporation (BRC). Both projects require an annual return of 15%. Year Deepwater Fishing New Submarine Ride 0 -600,000 -1,800,000 1 270,000 1,000,000 2 350,000 700,000 3 300,000 900,000 as a financial analyst for BRC, you are asked the following questions: a. Based on the discounted payback period rule, which project should be chosen? b. If your decision rule is to accept the project with the greater IRR, which project should you use? c. Since you are fully aware of the IRR rule’s scale problem, you calculate the modified IRR (MIRR) for the two projects. Based on your computation, which project should you choose? d. To be prudent, you compute the NPV for both projects. Which project should you choose? Is it consistent with the MIRR rule?

please give steps in detail, do not use excel  

Answer 1

	Project A	Project B
Year0	-6,00,000	-18,00,000
Year1	2,70,000	10,00,000
Year2	3,50,000	7,00,000
Year3	3,00,000	9,00,000

a) Discouted payback period

	Project A	Discounted cash flow@15%
Year0	-6,00,000	1	-600000	-600000
Year1	2,70,000	0.869	234630	-365370
Year2	3,50,000	0.756	264600	-100770
Year3	3,00,000	0.657	197100	96330

Discounted payback period =Year before the discounted payback period occurs+(cummulative cash flow in the year before recovery/Discounted cash flow in the year after recovery)

=2+100770/197100= 2.511 years

	Project B	Discounted cash flow@15%
Year0	-18,00,000	1	-1800000	-1800000
Year1	10,00,000	0.869	869000	-931000
Year2	7,00,000	0.756	529200	-401800
Year3	9,00,000	0.657	591300	189500

Discounted payback period = 2+401800/591300 = 2.680 years

Project A is better because it will sooner generate cash flows to cover initial cost in 2.511 years as compare to Project B in 2.680 years.

b. IRR Method

IRR= r_a+(NPV_a/NPV_a-NPV_b)[r_b-r_a)

r_a= Lower discount rate

NPV_a= NPV at ra

NPV_b= NPV at rb

r_b= Higher discount rate

Let's assume r_a= 10% _and r_b= 20%

	Project A	Discounted Rate@10%	Present Value	Discounted rate@20%	Present Value
Year0	-6,00,000	1	-600000	1	-600000
Year1	2,70,000	0.909	245430	0.833	224910
Year2	3,50,000	0.826	289100	0.694	242900
Year3	3,00,000	0.751	225300	0.578	173400
		NPV	159830		41210

IRR= 10+ (159830/159830-41210)*5

=16.735%

	Project B	Discounted Rate@10%	Present Value	Discounted rate@20%	Present Value
Year0	-18,00,000	1	-1800000	1	-1800000
Year1	10,00,000	0.909	909000	0.833	833000
Year2	7,00,000	0.826	578200	0.694	485800
Year3	9,00,000	0.751	675900	0.578	520200
		NPV	363100		39000

IRR= 10+ (363100/363100-39000)*5

=15.60%

Project A is better as higher the IRR , higher would be the rate of return

MIRR Project A

PV of outflows at 15%	-600000
FV of inflows at 15%
Year1	2,70,000	1.15	310500
Year2	3,50,000	1.15*1.15	462875
Year3	3,00,000	1.15*1.15*1.15	456262.5
		Total future inflows	1229637.5

600000=1229637.5/(1+K)³

=600000(1+K)³ =1229637.5

(1+K)³=2.049

1+K=1.270

K= 27 %

MIRR Project B

PV of outflows at 15%	-18,00,000
FV of inflows at 15%
Year1	10,00,000	1.15	1150000
Year2	7,00,000	1.322	925400
Year3	9,00,000	1.521	1368900
		Total future inflows	3444300

18,00,000=3444300/(1+K)³

(1+K)³= 0.523

K= -19.4%

By MIRR it is clear that project A is better because MIRR of Project A is also greater than cost of capital. Also as per IRR project A is better. Due to assumptions in IRR, we calculated MIRR which provides more clarity for the similar aspects.

NPV Project A.

	Project A	Discounted Rate@15%	Present Value
Year0	-6,00,000	1	-600000
Year1	2,70,000	0.869	234630
Year2	3,50,000	0.756	264600
Year3	3,00,000	0.657	197100
		NPV	96330

	Project B	Discounted Rate@15%	Present Value
Year0	-18,00,000	1	-1800000
Year1	10,00,000	0.869	869000
Year2	7,00,000	0.756	529200
Year3	9,00,000	0.657	591300
		NPV	189500

As per NPV rule, Project B should be accepted. It is conflicting with MIRR rule due to difference in projects parameters.As per MIRR, cash inflows from a project must be reinvested at the rate of cost of capital.